Статті в журналах: "INLA (Integrated Nested Laplace Approximation)"

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Gómez-Rubio, Virgilio, Roger S. Bivand, and Håvard Rue. "Bayesian Model Averaging with the Integrated Nested Laplace Approximation." Econometrics 8, no. 2 (June 1, 2020): 23. http://dx.doi.org/10.3390/econometrics8020023.

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The integrated nested Laplace approximation (INLA) for Bayesian inference is an efficient approach to estimate the posterior marginal distributions of the parameters and latent effects of Bayesian hierarchical models that can be expressed as latent Gaussian Markov random fields (GMRF). The representation as a GMRF allows the associated software R-INLA to estimate the posterior marginals in a fraction of the time as typical Markov chain Monte Carlo algorithms. INLA can be extended by means of Bayesian model averaging (BMA) to increase the number of models that it can fit to conditional latent GMRF. In this paper, we review the use of BMA with INLA and propose a new example on spatial econometrics models.

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Maulina, Retsi Firda, Anik Djuraidah, and Anang Kurnia. "PEMODELAN KEMISKINAN DI JAWA MENGGUNAKAN BAYESIAN SPASIAL PROBIT PENDEKATAN INTEGRATED NESTED LAPLACE APPROXIMATION (INLA)." MEDIA STATISTIKA 12, no. 2 (December 30, 2019): 140. http://dx.doi.org/10.14710/medstat.12.2.140-151.

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Poverty is a complex and multidimensional problem so that it becomes a development priority. Applications of poverty modeling in discrete data are still few and applications of the Bayesian paradigm are also still few. The Bayes Method is a parameter estimation method that utilizes initial information (prior) and sample information so that it can provide predictions that have a higher accuracy than the classical methods. Bayes inference using INLA approach provides faster computation than MCMC and possible uses large data sets. This study aims to model Javanese poverty using the Bayesian Spatial Probit with the INLA approach with three weighting matrices, namely K-Nearest Neighbor (KNN), Inverse Distance, and Exponential Distance. Furthermore, the result showed poverty analysis in Java based on the best model is using Bayesian SAR Probit INLA with KNN weighting matrix produced the highest level of classification accuracy, with specificity is 85.45%, sensitivity is 93.75%, and accuracy is 89.92%.

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Bilancia, Massimo, and Giacomo Demarinis. "Bayesian scanning of spatial disease rates with integrated nested Laplace approximation (INLA)." Statistical Methods & Applications 23, no. 1 (October 2, 2013): 71–94. http://dx.doi.org/10.1007/s10260-013-0241-8.

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Ruiz-Cárdenas, Ramiro, Elias T. Krainski, and Håvard Rue. "Direct fitting of dynamic models using integrated nested Laplace approximations — INLA." Computational Statistics & Data Analysis 56, no. 6 (June 2012): 1808–28. http://dx.doi.org/10.1016/j.csda.2011.10.024.

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Illian, Janine B., Sigrunn H. Sørbye, and Håvard Rue. "A toolbox for fitting complex spatial point process models using integrated nested Laplace approximation (INLA)." Annals of Applied Statistics 6, no. 4 (December 2012): 1499–530. http://dx.doi.org/10.1214/11-aoas530.

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Morales-Otero, Mabel, and Vicente Núñez-Antón. "Comparing Bayesian Spatial Conditional Overdispersion and the Besag–York–Mollié Models: Application to Infant Mortality Rates." Mathematics 9, no. 3 (January 31, 2021): 282. http://dx.doi.org/10.3390/math9030282.

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In this paper, we review overdispersed Bayesian generalized spatial conditional count data models. Their usefulness is illustrated with their application to infant mortality rates from Colombian regions and by comparing them with the widely used Besag–York–Mollié (BYM) models. These overdispersed models assume that excess of dispersion in the data may be partially caused from the possible spatial dependence existing among the different spatial units. Thus, specific regression structures are then proposed both for the conditional mean and for the dispersion parameter in the models, including covariates, as well as an assumed spatial neighborhood structure. We focus on the case of response variables following a Poisson distribution, specifically concentrating on the spatial generalized conditional normal overdispersion Poisson model. Models were fitted by making use of the Markov Chain Monte Carlo (MCMC) and Integrated Nested Laplace Approximation (INLA) algorithms in the specific context of Bayesian estimation methods.

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Abd Naeeim, Nurul Syafiah, and Nuzlinda Abdul Rahman. "Estimating relative risk for dengue disease in Peninsular Malaysia using INLA." Malaysian Journal of Fundamental and Applied Sciences 13, no. 4 (December 26, 2017): 721–27. http://dx.doi.org/10.11113/mjfas.v0n0.575.

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Study in spatio-temporal disease mapping models give a great worth in epidemiology, in describing the pattern of disease incidence across geographical space and time. This paper studies generalized linear mixed models (GLMM) for the analysis of spatial and temporal variability of dengue disease rates. For spatio-temporal study, the models accommodate spatially correlated random effects as well as temporal effects together with the space time interaction. The space time interaction is used to capture any additional effects that are not explained by the main factors of space and time. However, as study including time dimension is quite complex for disease mapping, the temporal effects that only relate to structured and unstructured time pattern are considered in these models as initial screening in studying disease pattern and time trend. The models are fitted within a hierarchical Bayesian framework using Integrated Nested Laplace Approximation (INLA) methodology. For this study, there are three main objectives. First, to choose the best model that represent the disease phenomenon. Second, to estimate the relative risk of disease based on the model selected and lastly, to visualize the risk spatial pattern and temporal trend using graphical representation. The models are applied to monthly dengue fever data in Peninsular Malaysia reported to Ministry of Health Malaysia for year 2015 by district level.

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Asmarian, Naeimehossadat, Seyyed Mohammad Taghi Ayatollahi, Zahra Sharafi, and Najaf Zare. "Bayesian Spatial Joint Model for Disease Mapping of Zero-Inflated Data with R-INLA: A Simulation Study and an Application to Male Breast Cancer in Iran." International Journal of Environmental Research and Public Health 16, no. 22 (November 13, 2019): 4460. http://dx.doi.org/10.3390/ijerph16224460.

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Hierarchical Bayesian log-linear models for Poisson-distributed response data, especially Besag, York and Mollié (BYM) model, are widely used for disease mapping. In some cases, due to the high proportion of zero, Bayesian zero-inflated Poisson models are applied for disease mapping. This study proposes a Bayesian spatial joint model of Bernoulli distribution and Poisson distribution to map disease count data with excessive zeros. Here, the spatial random effect is simultaneously considered into both logistic and log-linear models in a Bayesian hierarchical framework. In addition, we focus on the BYM2 model, a re-parameterization of the common BYM model, with penalized complexity priors for the latent level modeling in the joint model and zero-inflated Poisson models with different type of zeros. To avoid model fitting and convergence issues, Bayesian inferences are implemented using the integrated nested Laplace approximation (INLA) method. The models are compared according to the deviance information criterion and the logarithmic scoring. A simulation study with different proportions of zero exhibits INLA ability in running the models and also shows slight differences between the popular BYM and BYM2 models in terms of model choice criteria. In an application, we apply the fitting models on male breast cancer data in Iran at county level in 2014.

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SANTOS, Naiara Caroline Aparecido dos, and Jorge Luiz BAZÁN. "RESIDUAL ANALYSIS IN RASCH POISSON COUNTS MODELS." REVISTA BRASILEIRA DE BIOMETRIA 39, no. 1 (March 31, 2021): 206–20. http://dx.doi.org/10.28951/rbb.v39i1.531.

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A Rasch Poisson counts (RPC) model is described to identify individual latent traits and facilities of the items of tests that model the error (or success) count in several tasks over time, instead of modeling the correct responses to items in a test as in the dichotomous item response theory (IRT) model. These types of tests can be more informative than traditional tests. To estimate the model parameters, we consider a Bayesian approach using the integrated nested Laplace approximation (INLA). We develop residual analysis to assess model t by introducing randomized quantile residuals for items. The data used to illustrate the method comes from 228 people who took a selective attention test. The test has 20 blocks (items), with a time limit of 15 seconds for each block. The results of the residual analysis of the RPC were promising and indicated that the studied attention data are not well tted by the RPC model.

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Maniatis, G., N. Demiris, A. Kranis, G. Banos, and A. Kominakis. "Comparison of inference methods of genetic parameters with an application to body weight in broilers." Archives Animal Breeding 58, no. 2 (July 27, 2015): 277–86. http://dx.doi.org/10.5194/aab-58-277-2015.

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Abstract. REML (restricted maximum likelihood) has become the standard method of variance component estimation in animal breeding. Inference in Bayesian animal models is typically based upon Markov chain Monte Carlo (MCMC) methods, which are generally flexible but time-consuming. Recently, a new Bayesian computational method, integrated nested Laplace approximation (INLA), has been introduced for making fast non-sampling-based Bayesian inference for hierarchical latent Gaussian models. This paper is concerned with the comparison of estimates provided by three representative programs (ASReml, WinBUGS and the R package AnimalINLA) of the corresponding methods (REML, MCMC and INLA), with a view to their applicability for the typical animal breeder. Gaussian and binary as well as simulated data were used to assess the relative efficiency of the methods. Analysis of 2319 records of body weight at 35 days of age from a broiler line suggested a purely additive animal model, in which the heritability estimates ranged from 0.31 to 0.34 for the Gaussian trait and from 0.19 to 0.36 for the binary trait, depending on the estimation method. Although in need of further development, AnimalINLA seems a fast program for Bayesian modeling, particularly suitable for the inference of Gaussian traits, while WinBUGS appeared to successfully accommodate a complicated structure between the random effects. However, ASReml remains the best practical choice for the serious animal breeder.

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Teng, Jiaqi, Shuzhen Ding, Xiaoping Shi, Huiguo Zhang, and Xijian Hu. "MCMCINLA Estimation of Missing Data and Its Application to Public Health Development in China in the Post-Epidemic Era." Entropy 24, no. 7 (June 30, 2022): 916. http://dx.doi.org/10.3390/e24070916.

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Medical data are often missing during epidemiological surveys and clinical trials. In this paper, we propose the MCMCINLA estimation method to account for missing data. We introduce a new latent class into the spatial lag model (SLM) and use a conditional autoregressive specification (CAR) spatial model-based approach to impute missing values, making the model fit into the integrated nested Laplace approximation (INLA) framework. Combining the advantages of both the Markov chain Monte Carlo (MCMC) and INLA frameworks, the MCMCINLA algorithm is used to implement imputation of the missing data and fit the model to derive estimates of the parameters from the posterior margins. Finally, the economic data and the hemorrhagic fever with renal syndrome (HFRS) disease data of mainland China from 2016–2018 are used as examples to explore the development of public health in China in the post-epidemic era. The results show that compared with expectation maximization (EM) and full information maximum likelihood estimation (FIML), the predicted values of the missing data obtained using our method are closer to the true values, and the spatial distribution of HFRS in China can be inferred from the imputation results with a southern-heavy and northern-light distribution. It can provide some references for the development of public health in China in the post-epidemic era.

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LEE, Changro, and Keyho PARK. "ANALYZING THE RENT-TO-PRICE RATIO FOR THE HOUSING MARKET AT THE MICRO-SPATIAL SCALE." International Journal of Strategic Property Management 22, no. 3 (May 17, 2018): 223–33. http://dx.doi.org/10.3846/ijspm.2018.1416.

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The rent-to-price ratio is one of the popular indicators for monitoring the property market. This study explores micro-scale spatial dynamics of the ratio for houses at the individual property level in Seoul, South Korea. We match the apartment unit sold and the one leased based on the carefully chosen criteria and apply a Bayesian multi-level modeling approach to this matched dataset. We employ the Integrated Nested Laplace Approximations (INLA) algorithm in order to estimate relevant parameters in the multi-level model. The ratio determinants found in the study include property age, apartment unit area, interest rate, and floor. This study also presents the importance of taking into account the hierarchical structure of apartment units, as well as seasonal and spatial variations when estimating the ratio and predicting future trends in the property market based on the ratio.

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Selle, Maria Lie, Ingelin Steinsland, John M. Hickey, and Gregor Gorjanc. "Flexible modelling of spatial variation in agricultural field trials with the R package INLA." Theoretical and Applied Genetics 132, no. 12 (September 18, 2019): 3277–93. http://dx.doi.org/10.1007/s00122-019-03424-y.

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Abstract Key message Established spatial models improve the analysis of agricultural field trials with or without genomic data and can be fitted with the open-source R package INLA. Abstract The objective of this paper was to fit different established spatial models for analysing agricultural field trials using the open-source R package INLA. Spatial variation is common in field trials, and accounting for it increases the accuracy of estimated genetic effects. However, this is still hindered by the lack of available software implementations. We compare some established spatial models and show possibilities for flexible modelling with respect to field trial design and joint modelling over multiple years and locations. We use a Bayesian framework and for statistical inference the integrated nested Laplace approximations (INLA) implemented in the R package INLA. The spatial models we use are the well-known independent row and column effects, separable first-order autoregressive ($$\mathrm{AR1} \otimes \mathrm{AR1}$$ AR 1 ⊗ AR 1 ) models and a Gaussian random field (Matérn) model that is approximated via the stochastic partial differential equation approach. The Matérn model can accommodate flexible field trial designs and yields interpretable parameters. We test the models in a simulation study imitating a wheat breeding programme with different levels of spatial variation, with and without genome-wide markers and with combining data over two locations, modelling spatial and genetic effects jointly. The results show comparable predictive performance for both the $$\mathrm{AR1} \otimes \mathrm{AR1}$$ AR 1 ⊗ AR 1 and the Matérn models. We also present an example of fitting the models to a real wheat breeding data and simulated tree breeding data with the Nelder wheel design to show the flexibility of the Matérn model and the R package INLA.

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Díaz-Avalos, Carlos, Pablo Juan, Somnath Chaudhuri, Marc Sáez, and Laura Serra. "Association between the New COVID-19 Cases and Air Pollution with Meteorological Elements in Nine Counties of New York State." International Journal of Environmental Research and Public Health 17, no. 23 (December 4, 2020): 9055. http://dx.doi.org/10.3390/ijerph17239055.

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The principal objective of this article is to assess the possible association between the number of COVID-19 infected cases and the concentrations of fine particulate matter (PM2.5) and ozone (O3), atmospheric pollutants related to people’s mobility in urban areas, taking also into account the effect of meteorological conditions. We fit a generalized linear mixed model which includes spatial and temporal terms in order to detect the effect of the meteorological elements and COVID-19 infected cases on the pollutant concentrations. We consider nine counties of the state of New York which registered the highest number of COVID-19 infected cases. We implemented a Bayesian method using integrated nested Laplace approximation (INLA) with a stochastic partial differential equation (SPDE). The results emphasize that all the components used in designing the model contribute to improving the predicted values and can be included in designing similar real-world data (RWD) models. We found only a weak association between PM2.5 and ozone concentrations with COVID-19 infected cases. Records of COVID-19 infected cases and other covariates data from March to May 2020 were collected from electronic health records (EHRs) and standard RWD sources.

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Baghfalaki, T., and M. Ganjali. "Approximate Bayesian inference for joint linear and partially linear modeling of longitudinal zero-inflated count and time to event data." Statistical Methods in Medical Research 30, no. 6 (April 19, 2021): 1484–501. http://dx.doi.org/10.1177/09622802211002868.

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Joint modeling of zero-inflated count and time-to-event data is usually performed by applying the shared random effect model. This kind of joint modeling can be considered as a latent Gaussian model. In this paper, the approach of integrated nested Laplace approximation (INLA) is used to perform approximate Bayesian approach for the joint modeling. We propose a zero-inflated hurdle model under Poisson or negative binomial distributional assumption as sub-model for count data. Also, a Weibull model is used as survival time sub-model. In addition to the usual joint linear model, a joint partially linear model is also considered to take into account the non-linear effect of time on the longitudinal count response. The performance of the method is investigated using some simulation studies and its achievement is compared with the usual approach via the Bayesian paradigm of Monte Carlo Markov Chain (MCMC). Also, we apply the proposed method to analyze two real data sets. The first one is the data about a longitudinal study of pregnancy and the second one is a data set obtained of a HIV study.

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Yu, Zhuoran, Yimeng Duan, Shen Zhang, Xin Liu, and Kui Li. "A Spatiotemporal Prediction Model for Regional Scheduling of Shared Bicycles Based on the INLA Method." Journal of Advanced Transportation 2021 (July 31, 2021): 1–10. http://dx.doi.org/10.1155/2021/4959504.

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Dock-less bicycle-sharing programs have been widely accepted as an efficient mode to benefit health and reduce congestions. And modeling and prediction has always been a core proposition in the field of transportation. Most of the existing demand prediction models for shared bikes take regions as research objects; therefore, a POI-based method can be a beneficial complement to existing research, including zone-level, OD-level, and station-level techniques. Point of interest (POI) is the location description of spatial entities, which can reflect the cycling route characteristics for both commuting and noncommuting trips to a certain extent, and is also the main generating point and attraction point of shared-bike travel flow. In this study, we make an effort to model a POI-level cycling demand with a Bayesian hierarchical method. The proposed model combines the integrated nested Laplace approximation (INLA) and random partial differential equation (SPDE) to cope with the huge computation in the modeling process. In particular, we have adopted the dock-less bicycle-sharing rental records of Mobike as a case study to validate our method; the study area was one of the fastest growing urban districts in Shanghai in August 2016. The operation results show that the method can help better understand, measure, and characterize spatiotemporal patterns of bike-share ridership at the POI level and quantify the impact of the spatiotemporal effect on bicycle-sharing use.

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MORAES, Talita Evelin Nabarrete Tristão de, Isolde PREVIDELLI, and Giovani Loiola da SILVA. "A BAYESIAN WEIBULL ANALYSIS OF BREAST CANCER DATA WITH LONG-TERM SURVIVORS IN PARANA STATE, BRAZIL." REVISTA BRASILEIRA DE BIOMETRIA 39, no. 2 (June 17, 2021): 293–310. http://dx.doi.org/10.28951/rbb.v39i2.469.

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Breast cancer is one of the most common diseases among women worldwide with about 25% of new cases each year. In Brazil, 59,700 new cases of breast cancer were expected in 2019, according to the Brazilian National Cancer Institute (INCA). Survival analysis has been an useful tool for the identifying the risk and prognostic factors for cancer patients. This work aims to characterize the prognostic value of demographic, clinical and pathological variables in relation to the survival time of 2,092 patients diagnosed with breast cancer in Parana State, Brazil, from 2004 to 2016. In this sense, we propose a Bayesian analysis of survival data with long-term survivors by using Weibull regression models through integrated nested Laplace approximations (INLA). The results point to a proportion of long-term survivors around 57:6% in the population under study. In regard to potential risk factors, we namely concluded that 40-50 year age group has superior survival than younger and older age groups, white women have higher breast cancer risk than other races, and marital status decreases that risk. Caution on the general use of these results is nevertheless advised, since we have analyzed population-based breast cancer data without proper monitoring by a healthprofessional.

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Nothdurft, Arne. "Climate sensitive single tree growth modeling using a hierarchical Bayes approach and integrated nested Laplace approximations (INLA) for a distributed lag model." Forest Ecology and Management 478 (December 2020): 118497. http://dx.doi.org/10.1016/j.foreco.2020.118497.

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Olopha, Paul Omoh, Akin Olusoga Fasoranbaku, and Ezra Gayawan. "Spatial pattern and determinants of sufficient knowledge of mother to child transmission of HIV and its prevention among Nigerian women." PLOS ONE 16, no. 6 (June 25, 2021): e0253705. http://dx.doi.org/10.1371/journal.pone.0253705.

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The lack of sufficient knowledge of mother to child transmission (MTCT) of human immunodeficiency virus (HIV) among pregnant women is considered a major contributor to new pediatric HIV infections globally, and increasing HIV related infant mortality especially in developing countries. Nigeria has the highest number of new HIV infections among children in the world. This study was designed to examine the spatial pattern and determinants of acquisition of sufficient knowledge of MTCT and prevention of mother to child transmission (PMTCT) in Nigeria. The data used in the study were extracted from the 2018 Nigeria Democratic Health Survey. The spatial modeling was through a Bayesian approach with appropriate prior distributions assigned to the different parameters of the model and inference was through the integrated nested Laplace approximation technique (INLA). Results show considerable spatial variability in the acquisition of sufficient knowledge of MTCT and its prevention with women in the southwestern and southeastern part of the country having higher likelihood. The nonlinear effects findings show that acquisition of sufficient knowledge of MTCT and PMTCT increased with age of women and peaked at around age 35yearswhere it thereafter dropped drastically among the older women. Furthermore, sufficient knowledge of MTCT and PMTCT was found to be driven by ethnicity, respondents’ education and wealth status.

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Liu, Daqian, Wei Song, Chunliang Xiu, and Jun Xu. "Understanding the Spatiotemporal Pattern of Crimes in Changchun, China: A Bayesian Modeling Approach." Sustainability 13, no. 19 (September 22, 2021): 10500. http://dx.doi.org/10.3390/su131910500.

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Chinese cities have been undergoing extraordinary changes in many respects during the process of urbanization, which has caused crime patterns to evolve accordingly. This research applies a Bayesian spatiotemporal model to explore and understand the spatiotemporal patterns of crime risk from 2008 to 2017 in Changchun, China. The overall temporal trend of crime risk, the effects of land use covariates, spatial random effects, and area-specific differential trends are estimated through a Bayesian spatiotemporal model fitted using the Integrated Nested Laplace Approximation (INLA). The analytical results show that the regression coefficient for the overall temporal trend of crime risk changed from significantly positive to negative after the land use variables are incorporated into the Bayesian spatiotemporal model. The covariates of road density, commercial and recreational land per capita, residential land per capita, and industrial land per capita are found to be significantly associated with crime risk, which relates to classic theories in environmental criminology. In addition, some areas still exhibit significantly increasing crime risks compared with the general trend even after controlling for the land use covariates and the spatial random effects, which may provide insights for law enforcement and researchers regarding where more attention is required since there may be some unmeasured factors causing higher crime trend in these areas.

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Vicente, G., T. Goicoa, and M. D. Ugarte. "Bayesian inference in multivariate spatio-temporal areal models using INLA: analysis of gender-based violence in small areas." Stochastic Environmental Research and Risk Assessment 34, no. 10 (May 22, 2020): 1421–40. http://dx.doi.org/10.1007/s00477-020-01808-x.

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Abstract Multivariate models for spatial count data are currently receiving attention in disease mapping to model two or more diseases jointly. They have been thoroughly studied from a theoretical point of view, but their use in practice is still limited because they are computationally expensive and, in general, they are not implemented in standard software to be used routinely. Here, a new multivariate proposal, based on the recently derived M models for spatial data, is developed for spatio-temporal areal data. The model takes account of the correlation between the spatial and temporal patterns of the phenomena being studied, and it also includes spatio-temporal interactions. Though multivariate models have been traditionally fitted using Markov chain Monte Carlo techniques, here we propose to adopt integrated nested Laplace approximations to speed up computations as results obtained using both fitting techniques were nearly identical. The techniques are used to analyse two forms of crimes against women in India. In particular, we focus on the joint analysis of rapes and dowry deaths in Uttar Pradesh, the most populated Indian state, during the years 2001–2014.

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Zondi, Mthobisi Mxolisi, Henry G. Mwambi, and Sileshi Fanta Melesse. "Spatial Modelling of Under-five Mortality in Lesotho with Reference to 2014 Demographic and Health Surveillance Dataset." Open Public Health Journal 13, no. 1 (June 18, 2020): 289–97. http://dx.doi.org/10.2174/1874944502013010289.

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Background: Lesotho is the country located in the Sub-Saharan region of Africa countries where under-five mortality (U5M) is still a big issue due to some significant social and demographic risk factors. Hence, the investigation of some social and demographic factors that are associated with the U5M, is a critical problem that needs due consideration. Methods: This study used the 2014 Lesotho Demographic and Health Survey (LDHS) that had a sample of over 9000 representative households. Individually, data consisting of a nationally representative sample of 9,543 households in the 2014 Lesotho Demographic and Health Survey were analysed. The Random Walk second-order (RW2) model was adopted for analysis. Maps construction and modelling were done through the spatially structured and unstructured random effects using the Gaussian Markov Random Field and a zero-mean Gaussian process, respectively. The full Bayesian inference was adopted to produce the results using the Integrated Nested Laplace Approximation (INLA) function in R-software. Results: In this study, age at death of an under-five child was found to have a linear association with the U5M in Lesotho. The non-stationary models outperform the stationary models. The low-risk pattern was found in the north of Lesotho, and the highest risk occurs in the centre through the south, east, west, southeast, and northwest. Breastfeeding has contributed significantly to under-five mortality to most of Lesotho districts. Conclusion: This study adopted the newly developed statistical models to model and mapped the U5M in Lesotho. The full Bayesian inference was used to produce the results using R-INLA package. The findings from this study can help introduce new policies that will help reduce disparity in Lesotho.

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Cosandey-Godin, Aurelie, Elias Teixeira Krainski, Boris Worm, and Joanna Mills Flemming. "Applying Bayesian spatiotemporal models to fisheries bycatch in the Canadian Arctic." Canadian Journal of Fisheries and Aquatic Sciences 72, no. 2 (February 2015): 186–97. http://dx.doi.org/10.1139/cjfas-2014-0159.

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Understanding and reducing the incidence of accidental bycatch, particularly for vulnerable species such as sharks, is a major challenge for contemporary fisheries management. Here we establish integrated nested Laplace approximations (INLA) and stochastic partial differential equations (SPDE) as two powerful tools for modelling patterns of bycatch through time and space. These novel, computationally fast approaches are applied to fit zero-inflated hierarchical spatiotemporal models to Greenland shark (Somniosus microcephalus) bycatch data from the Baffin Bay Greenland halibut (Reinhardtius hippoglossoides) gillnet fishery. Results indicate that Greenland shark bycatch is clustered in space and time, varies significantly from year to year, and there are both tractable factors (number of gillnet panels, total Greenland halibut catch) and physical features (bathymetry) leading to the high incidence of Greenland shark bycatch. Bycatch risk could be reduced by limiting access to spatiotemporal hotspots or by establishing a maximum number of panels per haul. Our method explicitly models the spatiotemporal correlation structure inherent in bycatch data at a very reasonable computational cost, such that the forecasting of bycatch patterns and simulating conservation strategies becomes more accessible.

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Seck, Ismaila, Modou Moustapha Lo, Assane Gueye Fall, Mariane Diop, Mamadou Ciss, Catherine Béatrice Cêtre-Sossah, Coumba Faye, et al. "Identification of drivers of Rift Valley fever after the 2013–14 outbreak in Senegal using serological data in small ruminants." PLOS Neglected Tropical Diseases 16, no. 2 (February 2, 2022): e0010024. http://dx.doi.org/10.1371/journal.pntd.0010024.

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Rift Valley fever (RVF) is a mosquito-borne disease mostly affecting wild and domestic ruminants. It is widespread in Africa, with spillovers in the Arab Peninsula and the southwestern Indian Ocean. Although RVF has been circulating in West Africa for more than 30 years, its epidemiology is still not clearly understood. In 2013, an RVF outbreak hit Senegal in new areas that weren’t ever affected before. To assess the extent of the spread of RVF virus, a national serological survey was implemented in young small ruminants (6–18 months old), between November 2014 and January 2015 (after the rainy season) in 139 villages. Additionally, the drivers of this spread were identified. For this purpose, we used a beta-binomial (BB) logistic regression model. An Integrated Nested Laplace Approximation (INLA) approach was used to fit the spatial model. Lower cumulative rainfall, and higher accessibility were both associated with a higher RVFV seroprevalence. The spatial patterns of fitted RVFV seroprevalence pointed densely populated areas of western Senegal as being at higher risk of RVFV infection in small ruminants than rural or southeastern areas. Thus, because slaughtering infected animals and processing their fresh meat is an important RVFV transmission route for humans, more human populations might have been exposed to RVFV during the 2013–2014 outbreak than in previous outbreaks in Senegal.

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Canelas, Tiago, Edward Thomsen, Daniel McDermott, Eleanore Sternberg, Matthew B. Thomas, and Eve Worrall. "Spatial targeting of Screening + Eave tubes (SET), a house-based malaria control intervention, in Côte d’Ivoire: A geostatistical modelling study." PLOS Global Public Health 1, no. 11 (November 15, 2021): e0000030. http://dx.doi.org/10.1371/journal.pgph.0000030.

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New malaria control tools and tailoring interventions to local contexts are needed to reduce the malaria burden and meet global goals. The housing modification, screening plus a targeted house-based insecticide delivery system called the In2Care® Eave Tubes, has been shown to reduce clinical malaria in a large cluster randomised controlled trial. However, the widescale suitability of this approach is unknown. We aimed to predict household suitability and define the most appropriate locations for ground-truthing where Screening + Eave Tubes (SET) could be implemented across Côte d’Ivoire. We classified DHS sampled households into suitable for SET based on the walls and roof materials. We fitted a Bayesian beta-binomial logistic model using the integrated nested Laplace approximation (INLA) to predict suitability of SET and to define priority locations for ground-truthing and to calculate the potential population coverage and costs. Based on currently available data on house type and malaria infection rate, 31% of the total population and 17.5% of the population in areas of high malaria transmission live in areas suitable for SET. The estimated cost of implementing SET in suitable high malaria transmission areas would be $46m ($13m –$108m). Ground-truthing and more studies should be conducted to evaluate the efficacy and feasibility of SET in these settings. The study provides an example of implementing strategies to reflect local socio-economic and epidemiological factors, and move beyond blanket, one-size-fits-all strategies.

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Osei, Frank, Alfred Stein, and Anthony Ofosu. "Poisson-Gamma Mixture Spatially Varying Coefficient Modeling of Small-Area Intestinal Parasites Infection." International Journal of Environmental Research and Public Health 16, no. 3 (January 26, 2019): 339. http://dx.doi.org/10.3390/ijerph16030339.

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Understanding the spatially varying effects of demographic factors on the spatio-temporal variation of intestinal parasites infections is important for public health intervention and monitoring. This paper presents a hierarchical Bayesian spatially varying coefficient model to evaluate the effects demographic factors on intestinal parasites morbidities in Ghana. The modeling relied on morbidity data collected by the District Health Information Management Systems. We developed Poisson and Poisson-gamma spatially varying coefficient models. We used the demographic factors, unsafe drinking water, unsafe toilet, and unsafe liquid waste disposal as model covariates. The models were fitted using the integrated nested Laplace approximations (INLA). The overall risk of intestinal parasites infection was estimated to be 10.9 per 100 people with a wide spatial variation in the district-specific posterior risk estimates. Substantial spatial variation of increasing multiplicative effects of unsafe drinking water, unsafe toilet, and unsafe liquid waste disposal occurs on the variation of intestinal parasites risk. The structured residual spatial variation widely dominates the unstructured component, suggesting that the unaccounted-for risk factors are spatially continuous in nature. The study concludes that both the spatial distribution of the posterior risk and the associated exceedance probability maps are essential for monitoring and control of intestinal parasites.

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González-Carrasco, Mònica, Marc Sáez, and Ferran Casas. "Subjective Well-Being in Early Adolescence: Observations from a Five-Year Longitudinal Study." International Journal of Environmental Research and Public Health 17, no. 21 (November 8, 2020): 8249. http://dx.doi.org/10.3390/ijerph17218249.

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This article aims to redress the lack of longitudinal studies on adolescents’ subjective well-being (SWB) and highlight the relevance of knowledge deriving from such research in designing public policies for improving their health and wellbeing in accordance with the stage of development they are in. To achieve this, the evolution of SWB during early adolescence (in adolescents aged between 10 and 14 in the first data collection) was explored over a five year period, considering boys and girls together and separately. This involved comparing different SWB scales and contrasting results when considering the year of data collection versus the cohort (year of birth) participants belonged to. The methodology comprised a generalized linear mixed model using the INLA (Integrated Nested Laplace Approximation) estimation within a Bayesian framework. Results support the existence of a decreasing-with-age trend, which has been previously intuited in cross-sectional studies and observed in only a few longitudinal studies and contrasts with the increasing-with-age tendency observed in late adolescence. This decrease is also found to be more pronounced for girls, with relevant differences found between instruments. The decreasing-with-age trend observed when the year of data collection is taken into account is also observed when considering the cohort, but the latter provides additional information. The results obtained suggest that there is a need to continue studying the evolution of SWB in early adolescence with samples from other cultures; this, in turn, will make it possible to establish the extent to which the observed decreasing-with-age trend among early adolescents is influenced by cultural factors.

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Wang, Kai, Shanshan Zhao, and Eric Jackson. "Multivariate Poisson Lognormal Modeling of Weather-Related Crashes on Freeways." Transportation Research Record: Journal of the Transportation Research Board 2672, no. 38 (June 11, 2018): 184–98. http://dx.doi.org/10.1177/0361198118776523.

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Adverse weather conditions are one of the primary causes of motor vehicle crashes. To identify the factors contributing to crashes during adverse weather conditions and recommend cost-effective countermeasures, it is necessary to develop reliable crash prediction models to estimate weather-related crash frequencies. To account for the variations in crash count among different adverse weather conditions, crash types, and crash severities for both rain- and snow-related crashes, crash data on freeways was collected from the State of Connecticut, and crash prediction models were developed to estimate crash counts by crash type and severity for each weather condition. To account for the potential correlations among crash type and severity counts due to the common unobserved factors, integrated nested Laplace approximation (INLA) multivariate Poisson lognormal (MVPLN) models were developed to estimate weather-related crashes counts by crash type and severity simultaneously (four MVPLN models were estimated in total). To verify the model prediction ability, univariate Poisson lognormal (UPLN) models were estimated and compared with the MVPLN models. The results show that the effects of factors contributing to crashes, including median width, horizontal curve, lane width, and shoulder width, vary not only among different adverse weather conditions, but also among different crash types and severities. The crash types and severities are shown to be highly correlated and the model comparison verifies that the MVPLN models significantly improve the model prediction accuracy compared with the UPLN models. Therefore, the MVPLN model is recommended to provide more unbiased parameter estimates when estimating weather-related crashes by crash type and severity.

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Carbó, Ester, Pablo Juan, Carlos Añó, Somnath Chaudhuri, Carlos Diaz-Avalos, and Ernesto López-Baeza. "Modeling Influence of Soil Properties in Different Gradients of Soil Moisture: The Case of the Valencia Anchor Station Validation Site, Spain." Remote Sensing 13, no. 24 (December 19, 2021): 5155. http://dx.doi.org/10.3390/rs13245155.

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The prediction of spatial and temporal variation of soil water content brings numerous benefits in the studies of soil. However, it requires a considerable number of covariates to be included in the study, complicating the analysis. Integrated nested Laplace approximations (INLA) with stochastic partial differential equation (SPDE) methodology is a possible approach that allows the inclusion of covariates in an easy way. The current study has been conducted using INLA-SPDE to study soil moisture in the area of the Valencia Anchor Station (VAS), soil moisture validation site for the European Space Agency SMOS (Soil Moisture and Ocean Salinity). The data used were collected in a typical ecosystem of the semiarid Mediterranean conditions, subdivided into physio-hydrological units (SMOS units) which presents a certain degree of internal uniformity with respect to hydrological parameters and capture the spatial and temporal variation of soil moisture at the local fine scale. The paper advances the knowledge of the influence of hydrodynamic properties on VAS soil moisture (texture, porosity/bulk density and soil organic matter and land use). With the goal of understanding the factors that affect the variability of soil moisture in the SMOS pixel (50 km × 50 km), five states of soil moisture are proposed. We observed that the model with all covariates and spatial effect has the lowest DIC value. In addition, the correlation coefficient was close to 1 for the relationship between observed and predicted values. The methodology applied presents the possibility to analyze the significance of different covariates having spatial and temporal effects. This process is substantially faster and more effective than traditional kriging. The findings of this study demonstrate an advancement in that framework, demonstrating that it is faster than previous methodologies, provides significance of individual covariates, is reproducible, and is easy to compare with models.

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Ivanoff, Rayd, Maria Grazia Pennino, Marie-Christine Rufener, Carolus Maria Vooren, and Paul Gerhard Kinas. "Modelagem espacial bayesiana para riqueza de elasmobrânquios do extremo sul do Brasil." Revista CEPSUL - Biodiversidade e Conservação Marinha 8 (January 30, 2019): e2019002. http://dx.doi.org/10.37002/revistacepsul.vol8.790e2019002.

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Compreender a distribuição espacial de espécies vulneráveis a exploração pesqueira pode subsidiar ações de manejo e conservação. O objetivo deste estudo foi mapear possíveis habitats essenciais para riqueza de elasmobrânquios no sul do Brasil. Os dados são oriundos de cruzeiro científico realizado em fevereiro de 2005 entre o arroio Chuí (33°45'S) e o Cabo de Santa Marta Grande (28°36'S). As informações disponíveis são posições georeferenciadas de 64 estações oceanográficas, a quantificação das capturas de elasmobrânquios e teleósteos com pesca de arrasto de fundo e o registro dos parâmetros ambientais de profundidade, temperatura e salinidade. Os dados foram ajustados a um Modelo Linear Generalizado (GLM) Bayesiano via INLA (Integrated Nested Laplace Approximations) e módulo SPDE (Stochastic Partial Differential Equations), implementados no software R. A qualidade de ajuste e o poder preditivo do modelo foram avaliados mediante DIC (Deviance Information Criterion), WAIC (Watanabe-Akaike Information Criterion) e LCPO (Logarithm Conditional Predictive Ordinate). Foram registradas 16 espécies de elasmobrânquios, cujo número variou de 1 à 9 por lance. No modelo proposto, o efeito espacial e as variáveis ambientais foram relevantes para explicar a variação da riqueza de elasmobrânquios na costa do Rio Grande do Sul. Esta abordagem estatística permite estimar a probabilidade de ocorrência das espécies em áreas não amostradas, levando em conta a autocorrelação espacial dos dados e o conhecimento dos valores das co-variávies ambientais.

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Gilbert, L., E. Rouby, E. Tew-Kaï, J. Spitz, H. Peltier, V. Quilfen, and M. Authier. "Spatiotemporal models highlight influence of oceanographic conditions on common dolphin bycatch risk in the Bay of Biscay." Marine Ecology Progress Series 679 (November 25, 2021): 195–212. http://dx.doi.org/10.3354/meps13894.

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The population of short-beaked common dolphins Delphinus delphis of the Bay of Biscay (northeast Atlantic) has been subjected to potentially dangerous levels of bycatch since the 1990s. As the phenomenon intensifies, it represents a potent threat to the population. Here, we investigated the relationship between bycatch mortality and oceanographic processes. We assumed that oceanographic processes spatiotemporally structure the availability and aggregation of prey, creating areas prone to attract both common dolphins and fish targeted by fisheries. We used 2 datasets from 2012 to 2019: oceanographic data resulting from a circulation model and mortality data inferred from strandings. The latter allows location of mortality areas and quantification of the intensity of mortality events at sea. We fitted a series of spatiotemporal hierarchical Bayesian models using integrated nested Laplace approximations (INLA). Results provided first insights on how bycatch of common dolphins in the Bay of Biscay might be related to key seasonal and dynamic oceanographic features. We showed that from a statistical predictive point of view, the monthly trend of 2019 bycatch mortality could be predicted with few oceanographic covariates. This study highlights how gaining knowledge about environmental influences on interactions between short-beaked common dolphins and fisheries could have great conservation and management value. Identified relationships with oceanographic covariates were complex, as expected given the dynamic aspects of oceanographic processes, dolphins and fisheries distributions. Further research focusing on smaller time scales is needed to elucidate proximal drivers of common dolphin bycatch in the Bay of Biscay.

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Nigussie, Teshager Zerihun, Temesgen T. Zewotir, and Essey Kebede Muluneh. "Spatiotemporal Trends and Distributions of Malaria Incidence in the Northwest Ethiopia." Journal of Tropical Medicine 2022 (March 31, 2022): 1–10. http://dx.doi.org/10.1155/2022/6355481.

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Understanding and extracting noticeable patterns of malaria surveillance data at the district level are crucial for malaria prevention, control, and elimination progress. This study aimed to analyze spatiotemporal trends and nonparametric dynamics of malaria incidences in northwest Ethiopia, considering spatial and temporal correlations. The data were analyzed using count regression spatiotemporal models under the Bayesian setups, and parameters were estimated using integrated nested Laplace approximations (INLA). The region had a declining linear trend, and the average annual malaria incidence rate was 24.8 per 1,000 persons between 2012 and 2020. The malaria incidence rate was decreased by 0.984 (95% CI: 0.983, 0.986) per unit increase in months between July 2012 and June 2020. Districts found in the western and northwestern parts of the region had a steeper trend, while districts in the eastern and southern parts had a less steep trend than the average trend of the region. Compared to the regional level trend, the decreasing rate of malaria incidence trends was lower in most town administrations. The nonparametric dynamics showed that the monthly malaria incidence had a sinusoidal wave shape that varied throughout study periods. Malaria incidence had a decreasing linear trend changed across districts of the study region, and the steepness of trends of districts might not depend on incidences. Thus, an intervention and controlling mechanism that considers malaria incidences and district-specific differential trends would be indispensable to mitigate malaria transmission in the region.

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Lee, Naae, Sungchan Kang, Woojoo Lee, and Seung-sik Hwang. "The Association between Community Water Fluoridation and Bone Diseases: A Natural Experiment in Cheongju, Korea." International Journal of Environmental Research and Public Health 17, no. 24 (December 9, 2020): 9170. http://dx.doi.org/10.3390/ijerph17249170.

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The present study aimed to investigate the association between bone diseases and community water fluoridation (CWF). An ecological study with a natural experiment design was conducted in Cheongju, South Korea, from 1 January 2004 to 31 December 2013. The community water fluoridation program was implemented in Cheongju and divided into CWF and non-CWF areas. To observe adverse health effects related to bone diseases, we conducted a spatio-temporal analysis of the prevalence of hip fracture, osteoporosis, and bone cancer in residents who have lived in CWF and non-CWF areas using National Health Insurance Service data. First, we used standardized incidence ratios to estimate the disease risk. Second, the hierarchical Bayesian Poisson spatio-temporal regression model was used to investigate the association between the selected bone diseases and CWF considering space and time interaction. The method for Bayesian estimation was based on the R-integrated nested Laplace approximation (INLA). Comparing the CWF area with the non-CWF area, there was no clear evidence that exposure to CWF increased health risks at the town level in Cheongju since CWF was terminated after 2004. The posterior relative risks (RR) of hip fracture was 0.95 (95% confidence intervals 0.87, 1.05) and osteoporosis was 0.94 (0.87, 1.02). The RR in bone cancer was a little high because the sample size very small compared to the other bone diseases (RR = 1.20 (0.89, 1.61)). The relative risk of selected bone diseases (hip fractures, osteoporosis, and bone cancer) increased over time but did not increase in the CWF area compared to non-CWF areas. CWF has been used to reduce dental caries in all population groups and is known for its cost-effectiveness. These findings suggest that CWF is not associated with adverse health risks related to bone diseases. This study provides scientific evidence based on a natural experiment design. It is necessary to continue research on the well-designed epidemiological studies and develop public health prevention programs to help in make suitable polices.

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Pescott, Oliver L., and Mark Jitlal. "Reassessing the observational evidence for nitrogen deposition impacts in acid grassland: spatial Bayesian linear models indicate small and ambiguous effects on species richness." PeerJ 8 (April 29, 2020): e9070. http://dx.doi.org/10.7717/peerj.9070.

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Nitrogen deposition (Ndep) is considered a significant threat to plant diversity in grassland ecosystems around the world. The evidence supporting this conclusion comes from both observational and experimental research, with “space-for-time” substitution surveys of pollutant gradients a significant portion of the former. However, estimates of regression coefficients for Ndep impacts on species richness, derived with a focus on causal inference, are hard to locate in the observational literature. Some influential observational studies have presented estimates from univariate models, overlooking the effects of omitted variable bias, and/or have used P-value-based stepwise variable selection (PSVS) to infer impacts, a strategy known to be poorly suited to the accurate estimation of regression coefficients. Broad-scale spatial autocorrelation has also generally been unaccounted for. We re-examine two UK observational datasets that have previously been used to investigate the relationship between Ndep and plant species richness in acid grasslands, a much-researched habitat in this context. One of these studies (Stevens et al., 2004, Science, 303: 1876–1879) estimated a large negative impact of Ndep on richness through the use of PSVS; the other reported smaller impacts (Maskell et al., 2010, Global Change Biology, 16: 671–679), but did not explicitly report regression coefficients or partial effects, making the actual size of the estimated Ndep impact difficult to assess. We reanalyse both datasets using a spatial Bayesian linear model estimated using integrated nested Laplace approximation (INLA). Contrary to previous results, we found similar-sized estimates of the Ndep impact on plant richness between studies, both with and without bryophytes, albeit with some disagreement over the most likely direction of this effect. Our analyses suggest that some previous estimates of Ndep impacts on richness from space-for-time substitution studies are likely to have been over-estimated, and that the evidence from observational studies could be fragile when confronted with alternative model specifications, although further work is required to investigate potentially nonlinear responses. Given the growing literature on the use of observational data to estimate the impacts of pollutants on biodiversity, we suggest that a greater focus on clearly reporting important outcomes with associated uncertainty, the use of techniques to account for spatial autocorrelation, and a clearer focus on the aims of a study, whether explanatory or predictive, are all required.

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Yoon, Ji Won. "Model selection for mixture model via integrated nested Laplace approximation." Electronics Letters 51, no. 6 (March 2015): 484–86. http://dx.doi.org/10.1049/el.2014.4338.

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Gómez-Rubio, Virgilio, and Håvard Rue. "Markov chain Monte Carlo with the Integrated Nested Laplace Approximation." Statistics and Computing 28, no. 5 (October 6, 2017): 1033–51. http://dx.doi.org/10.1007/s11222-017-9778-y.

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Illian, Janine B., Sara Martino, Sigrunn H. Sørbye, Juan B. Gallego-Fernández, María Zunzunegui, M. Paz Esquivias, and Justin M. J. Travis. "Fitting complex ecological point process models with integrated nested Laplace approximation." Methods in Ecology and Evolution 4, no. 4 (February 19, 2013): 305–15. http://dx.doi.org/10.1111/2041-210x.12017.

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Gómez‐Rubio, Virgilio, and Francisco Palmí‐Perales. "Multivariate posterior inference for spatial models with the integrated nested Laplace approximation." Journal of the Royal Statistical Society: Series C (Applied Statistics) 68, no. 1 (June 19, 2018): 199–215. http://dx.doi.org/10.1111/rssc.12292.

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Grilli, L., S. Metelli, and C. Rampichini. "Bayesian estimation with integrated nested Laplace approximation for binary logit mixed models." Journal of Statistical Computation and Simulation 85, no. 13 (July 11, 2014): 2718–26. http://dx.doi.org/10.1080/00949655.2014.935377.

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Beguin, Julien, Sara Martino, Håvard Rue, and Steven G. Cumming. "Hierarchical analysis of spatially autocorrelated ecological data using integrated nested Laplace approximation." Methods in Ecology and Evolution 3, no. 5 (May 10, 2012): 921–29. http://dx.doi.org/10.1111/j.2041-210x.2012.00211.x.

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Martins, Thiago G., and Håvard Rue. "Extending Integrated Nested Laplace Approximation to a Class of Near-Gaussian Latent Models." Scandinavian Journal of Statistics 41, no. 4 (February 18, 2014): 893–912. http://dx.doi.org/10.1111/sjos.12073.

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Seppä, Karri, Håvard Rue, Timo Hakulinen, Esa Läärä, Mikko J. Sillanpää, and Janne Pitkäniemi. "Estimating multilevel regional variation in excess mortality of cancer patients using integrated nested Laplace approximation." Statistics in Medicine 38, no. 5 (October 17, 2018): 778–91. http://dx.doi.org/10.1002/sim.8010.

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Elsner, James B., and Holly M. Widen. "Predicting Spring Tornado Activity in the Central Great Plains by 1 March." Monthly Weather Review 142, no. 1 (January 1, 2014): 259–67. http://dx.doi.org/10.1175/mwr-d-13-00014.1.

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Abstract The authors illustrate a statistical model for predicting tornado activity in the central Great Plains by 1 March. The model predicts the number of tornado reports during April–June using February sea surface temperature (SST) data from the Gulf of Alaska (GAK) and the western Caribbean Sea (WCA). The model uses a Bayesian formulation where the likelihood on the counts is a negative binomial distribution and where the nonstationarity in tornado reporting is included as a trend term plus first-order autocorrelation. Posterior densities for the model parameters are generated using the method of integrated nested Laplacian approximation (INLA). The model yields a 51% increase in the number of tornado reports per degree Celsius increase in SST over the WCA and a 15% decrease in the number of reports per degree Celsius increase in SST over the GAK. These significant relationships are broadly consistent with a physical understanding of large-scale atmospheric patterns conducive to severe convective storms across the Great Plains. The SST covariates explain 11% of the out-of-sample variability in observed F1–F5 tornado reports. The paper demonstrates the utility of INLA for fitting Bayesian models to tornado climate data.

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Western, Luke M., Zhe Sha, Matthew Rigby, Anita L. Ganesan, Alistair J. Manning, Kieran M. Stanley, Simon J. O'Doherty, Dickon Young, and Jonathan Rougier. "Bayesian spatio-temporal inference of trace gas emissions using an integrated nested Laplacian approximation and Gaussian Markov random fields." Geoscientific Model Development 13, no. 4 (April 28, 2020): 2095–107. http://dx.doi.org/10.5194/gmd-13-2095-2020.

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Abstract. We present a method to infer spatially and spatio-temporally correlated emissions of greenhouse gases from atmospheric measurements and a chemical transport model. The method allows fast computation of spatial emissions using a hierarchical Bayesian framework as an alternative to Markov chain Monte Carlo algorithms. The spatial emissions follow a Gaussian process with a Matérn correlation structure which can be represented by a Gaussian Markov random field through a stochastic partial differential equation approach. The inference is based on an integrated nested Laplacian approximation (INLA) for hierarchical models with Gaussian latent fields. Combining an autoregressive temporal correlation and the Matérn field provides a full spatio-temporal correlation structure. We first demonstrate the method on a synthetic data example and follow this using a well-studied test case of inferring UK methane emissions from tall tower measurements of atmospheric mole fraction. Results from these two test cases show that this method can accurately estimate regional greenhouse gas emissions, accounting for spatio-temporal uncertainties that have traditionally been neglected in atmospheric inverse modelling.

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Luan, Hui, Matthew Quick, and Jane Law. "Analyzing Local Spatio-Temporal Patterns of Police Calls-for-Service Using Bayesian Integrated Nested Laplace Approximation." ISPRS International Journal of Geo-Information 5, no. 9 (September 9, 2016): 162. http://dx.doi.org/10.3390/ijgi5090162.

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Mathew, Boby, Anna Marie Holand, Petri Koistinen, Jens Léon, and Mikko J. Sillanpää. "Reparametrization-based estimation of genetic parameters in multi-trait animal model using Integrated Nested Laplace Approximation." Theoretical and Applied Genetics 129, no. 2 (November 18, 2015): 215–25. http://dx.doi.org/10.1007/s00122-015-2622-x.

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Myrvoll-Nilsen, Eirik, Sigrunn Holbek Sørbye, Hege-Beate Fredriksen, Håvard Rue, and Martin Rypdal. "Statistical estimation of global surface temperature response to forcing under the assumption of temporal scaling." Earth System Dynamics 11, no. 2 (April 8, 2020): 329–45. http://dx.doi.org/10.5194/esd-11-329-2020.

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Abstract. Reliable quantification of the global mean surface temperature (GMST) response to radiative forcing is essential for assessing the risk of dangerous anthropogenic climate change. We present the statistical foundations for an observation-based approach using a stochastic linear response model that is consistent with the long-range temporal dependence observed in global temperature variability. We have incorporated the model in a latent Gaussian modeling framework, which allows for the use of integrated nested Laplace approximations (INLAs) to perform full Bayesian analysis. As examples of applications, we estimate the GMST response to forcing from historical data and compute temperature trajectories under the Representative Concentration Pathways (RCPs) for future greenhouse gas forcing. For historic runs in the Model Intercomparison Project Phase 5 (CMIP5) ensemble, we estimate response functions and demonstrate that one can infer the transient climate response (TCR) from the instrumental temperature record. We illustrate the effect of long-range dependence by comparing the results with those obtained from one-box and two-box energy balance models. The software developed to perform the given analyses is publicly available as the R package INLA.climate.

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Barboza, Gia Elise. "The Geography of Child Maltreatment: A Spatiotemporal Analysis Using Bayesian Hierarchical Analysis With Integrated Nested Laplace Approximation." Journal of Interpersonal Violence 34, no. 1 (April 1, 2016): 50–80. http://dx.doi.org/10.1177/0886260516639583.

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This study quantifies the spatiotemporal risk of child abuse and neglect in Los Angeles at the census tract level over a recent 4-year period, identifies areas of increased risk, and evaluates the role of structural disadvantage in substantiated child maltreatment referrals. Child maltreatment data on 83,379 child maltreatment cases in 1,678 census tracts spanning 2006-2009 were obtained from the Los Angeles County Department of Children and Family Services. Substantiated referral counts were analyzed across census tracts with Bayesian hierarchical spatial models using integrated nested Laplace approximations. Results showed that the unadjusted yearly rate of child abuse and neglect held fairly steady over the study period decreasing by only 2.57%. However, the temporal term in the spatiotemporal model reflected a downward trend beginning in 2007. High rates of abuse and neglect were predicted by several neighborhood-level measures of structural burden. Every 1-unit decrease in the social vulnerability index reduced the risk of child abuse and neglect by 98.3% (95% CrI = 1.869-2.1042) while every 1-unit increase in the Black–White dissimilarity index decreased child abuse and neglect risk by 70.6%. The interaction of these variables demonstrated the protective effect of racial heterogeneity in socially vulnerable neighborhoods. No such effect was found in neighborhoods characterized by low levels of vulnerability. Population-based child abuse and neglect prevention and intervention efforts should be aided by the characteristics of neighborhoods that demonstrate strong spatial patterns even after accounting for the role of race and place.

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Neyens, Thomas, Christel Faes, and Geert Molenberghs. "Integrated nested Laplace approximation for the analysis of count data via the combined model: A simulation study." Communications in Statistics - Simulation and Computation 48, no. 3 (January 17, 2018): 819–36. http://dx.doi.org/10.1080/03610918.2017.1400053.

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Heath, Anna, Ioanna Manolopoulou, and Gianluca Baio. "Estimating the expected value of partial perfect information in health economic evaluations using integrated nested Laplace approximation." Statistics in Medicine 35, no. 23 (May 18, 2016): 4264–80. http://dx.doi.org/10.1002/sim.6983.

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