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Relevant bibliographies by topics / Hierarchical Bayesian Priors

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Academic literature on the topic 'Hierarchical Bayesian Priors'

Author: Grafiati

Published: 6 September 2023

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Journal articles on the topic "Hierarchical Bayesian Priors"

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Song, Chengyuan, Dongchu Sun, Kun Fan, and Rongji Mu. "Posterior Propriety of an Objective Prior in a 4-Level Normal Hierarchical Model." Mathematical Problems in Engineering 2020 (February 14, 2020): 1–10. http://dx.doi.org/10.1155/2020/8236934.

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The use of hierarchical Bayesian models in statistical practice is extensive, yet it is dangerous to implement the Gibbs sampler without checking that the posterior is proper. Formal approaches to objective Bayesian analysis, such as the Jeffreys-rule approach or reference prior approach, are only implementable in simple hierarchical settings. In this paper, we consider a 4-level multivariate normal hierarchical model. We demonstrate the posterior using our recommended prior which is proper in the 4-level normal hierarchical models. A primary advantage of the recommended prior over other proposed objective priors is that it can be used at any level of a hierarchical model.

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Jiao, Yan, Christopher Hayes, and Enric Cortés. "Hierarchical Bayesian approach for population dynamics modelling of fish complexes without species-specific data." ICES Journal of Marine Science 66, no. 2 (September 26, 2008): 367–77. http://dx.doi.org/10.1093/icesjms/fsn162.

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Abstract Jiao, Y., Hayes, C., and Cortés, E. 2009. Hierarchical Bayesian approach for population dynamics modelling of fish complexes without species-specific data. – ICES Journal of Marine Science, 66: 367–377. Modelling the population dynamics of fish complexes is challenging, and many species have been assessed and managed as a complex that was treated as a single species. Two Bayesian state-space surplus production models with multilevel priors (hierarchical models) were developed to simulate variability in population growth rates of species in a complex, using the hammerhead shark complex (Sphyrna spp.) of the Atlantic and Gulf of Mexico coasts of the US as an example. The complex consists of three species: scalloped (Sphyrna lewini), great (Sphyrna mokarran), and smooth hammerhead (Sphyrna zygaena). Bayesian state-space surplus production models with multilevel priors fitted the hammerhead data better than a model based on single-level priors. The hierarchical Bayesian approach represents an intermediate strategy between traditional models that do not include variability among species, and highly parameterized models that assign an estimate of parameters to each species. By ignoring the variability among species, confidence intervals of the estimates of stock status indicators can be unrealistically narrow, possibly leading to high-risk management strategies being adopted. Use of multilevel priors in a hierarchical Bayesian approach is suggested for future hammerhead shark stock assessments and for modelling fish complexes lacking species-specific data.

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Zhang, Hai, Puyu Wang, Qing Dong, and Pu Wang. "Sparse Bayesian linear regression using generalized normal priors." International Journal of Wavelets, Multiresolution and Information Processing 15, no. 03 (February 16, 2017): 1750021. http://dx.doi.org/10.1142/s0219691317500217.

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A sparse Bayesian linear regression model is proposed that generalizes the Bayesian Lasso to a class of Bayesian models with scale mixtures of normal distributions as priors for the regression coefficients. We assume a hierarchical Bayesian model with a binary indicator for whether a predictor variable is included in the model, a generalized normal prior distribution for the coefficients of the included variables, and a Student-t error model for robustness to heavy tailed noise. Our model out-performs other popular sparse regression estimators on synthetic and real data.

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Chan, Joshua C. C. "Minnesota-type adaptive hierarchical priors for large Bayesian VARs." International Journal of Forecasting 37, no. 3 (July 2021): 1212–26. http://dx.doi.org/10.1016/j.ijforecast.2021.01.002.

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Scarpa, Bruno, and David B. Dunson. "Bayesian Hierarchical Functional Data Analysis Via Contaminated Informative Priors." Biometrics 65, no. 3 (January 23, 2009): 772–80. http://dx.doi.org/10.1111/j.1541-0420.2008.01163.x.

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Gu, Xiaojing, Henry Leung, and Xingsheng Gu. "Bayesian Sparse Estimation Using Double Lomax Priors." Mathematical Problems in Engineering 2013 (2013): 1–17. http://dx.doi.org/10.1155/2013/176249.

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Sparsity-promoting prior along with Bayesian inference is an effective approach in solving sparse linear models (SLMs). In this paper, we first introduce a new sparsity-promoting prior coined as Double Lomax prior, which corresponds to a three-level hierarchical model, and then we derive a full variational Bayesian (VB) inference procedure. When noninformative hyperprior is assumed, we further show that the proposed method has one more latent variable than the canonical automatic relevance determination (ARD). This variable has a smoothing effect on the solution trajectories, thus providing improved convergence performance. The effectiveness of the proposed method is demonstrated by numerical simulations including autoregressive (AR) model identification and compressive sensing (CS) problems.

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Liang, Xinya, Akihito Kamata, and Ji Li. "Hierarchical Bayes Approach to Estimate the Treatment Effect for Randomized Controlled Trials." Educational and Psychological Measurement 80, no. 6 (March 16, 2020): 1090–114. http://dx.doi.org/10.1177/0013164420909885.

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One important issue in Bayesian estimation is the determination of an effective informative prior. In hierarchical Bayes models, the uncertainty of hyperparameters in a prior can be further modeled via their own priors, namely, hyper priors. This study introduces a framework to construct hyper priors for both the mean and the variance hyperparameters for estimating the treatment effect in a two-group randomized controlled trial. Assuming a random sample of treatment effect sizes is obtained from past studies, the hyper priors can be constructed based on the sampling distributions of the effect size mean and precision. The performance of the hierarchical Bayes approach was compared with the empirical Bayes approach (hyperparameters are fixed values or point estimates) and the ordinary least squares (OLS) method via simulation. The design factors for data generation included the sample treatment effect size, treatment/control group size ratio, and sample size. Each generated data set was analyzed using the hierarchical Bayes approach with three hyper priors, the empirical Bayes approach with twelve priors (including correct and inaccurate priors), and the OLS method. Results indicated that the proposed hierarchical Bayes approach generally outperformed the empirical Bayes approach and the OLS method, especially with small samples. When more sample effect sizes were available, the treatment effect was estimated more accurately regardless of the sample sizes. Practical implications and future research directions are discussed.

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Nam, Hyun Woo. "Modeling hyper-priors for Bayesian IRT equating: Fixed hyper-parameters or Hierarchical hyper-priors." Korean Society for Educational Evaluation 32, no. 4 (December 30, 2019): 777–95. http://dx.doi.org/10.31158/jeev.2019.32.4.777.

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Wang, Mengxi, Qingwang Liu, Liyong Fu, Guangxing Wang, and Xiongqing Zhang. "Airborne LIDAR-Derived Aboveground Biomass Estimates Using a Hierarchical Bayesian Approach." Remote Sensing 11, no. 9 (May 3, 2019): 1050. http://dx.doi.org/10.3390/rs11091050.

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Conventional ground survey data are very accurate, but expensive. Airborne lidar data can reduce the costs and effort required to conduct large-scale forest surveys. It is critical to improve biomass estimation and evaluate carbon stock when we use lidar data. Bayesian methods integrate prior information about unknown parameters, reduce the parameter estimation uncertainty, and improve model performance. This study focused on predicting the independent tree aboveground biomass (AGB) with a hierarchical Bayesian model using airborne LIDAR data and comparing the hierarchical Bayesian model with classical methods (nonlinear mixed effect model, NLME). Firstly, we chose the best diameter at breast height (DBH) model from several widely used models through a hierarchical Bayesian method. Secondly, we used the DBH predictions together with the tree height (LH) and canopy projection area (CPA) derived by airborne lidar as independent variables to develop the AGB model through a hierarchical Bayesian method with parameter priors from the NLME method. We then compared the hierarchical Bayesian method with the NLME method. The results showed that the two methods performed similarly when pooling the data, while for small sample sizes, the Bayesian method was much better than the classical method. The results of this study imply that the Bayesian method has the potential to improve the estimations of both DBH and AGB using LIDAR data, which reduces costs compared with conventional measurements.

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Krishnan, Ranganath, Mahesh Subedar, and Omesh Tickoo. "Specifying Weight Priors in Bayesian Deep Neural Networks with Empirical Bayes." Proceedings of the AAAI Conference on Artificial Intelligence 34, no. 04 (April 3, 2020): 4477–84. http://dx.doi.org/10.1609/aaai.v34i04.5875.

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Stochastic variational inference for Bayesian deep neural network (DNN) requires specifying priors and approximate posterior distributions over neural network weights. Specifying meaningful weight priors is a challenging problem, particularly for scaling variational inference to deeper architectures involving high dimensional weight space. We propose MOdel Priors with Empirical Bayes using DNN (MOPED) method to choose informed weight priors in Bayesian neural networks. We formulate a two-stage hierarchical modeling, first find the maximum likelihood estimates of weights with DNN, and then set the weight priors using empirical Bayes approach to infer the posterior with variational inference. We empirically evaluate the proposed approach on real-world tasks including image classification, video activity recognition and audio classification with varying complex neural network architectures. We also evaluate our proposed approach on diabetic retinopathy diagnosis task and benchmark with the state-of-the-art Bayesian deep learning techniques. We demonstrate MOPED method enables scalable variational inference and provides reliable uncertainty quantification.

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Dissertations / Theses on the topic "Hierarchical Bayesian Priors"

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Israeli, Yeshayahu D. "Whitney Element Based Priors for Hierarchical Bayesian Models." Case Western Reserve University School of Graduate Studies / OhioLINK, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=case1621866603265673.

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George, Robert Emerson. "The role of hierarchical priors in robust Bayesian inference /." The Ohio State University, 1993. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487847761308082.

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Sonksen, Michael David. "Bayesian Model Diagnostics and Reference Priors for Constrained Rate Models of Count Data." The Ohio State University, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=osu1312909127.

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Pfarrhofer, Michael, and Philipp Piribauer. "Flexible shrinkage in high-dimensional Bayesian spatial autoregressive models." Elsevier, 2019. http://epub.wu.ac.at/6839/1/1805.10822.pdf.

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Several recent empirical studies, particularly in the regional economic growth literature, emphasize the importance of explicitly accounting for uncertainty surrounding model specification. Standard approaches to deal with the problem of model uncertainty involve the use of Bayesian model-averaging techniques. However, Bayesian model-averaging for spatial autoregressive models suffers from severe drawbacks both in terms of computational time and possible extensions to more flexible econometric frameworks. To alleviate these problems, this paper presents two global-local shrinkage priors in the context of high-dimensional matrix exponential spatial specifications. A simulation study is conducted to evaluate the performance of the shrinkage priors. Results suggest that they perform particularly well in high-dimensional environments, especially when the number of parameters to estimate exceeds the number of observations. Moreover, we use pan-European regional economic growth data to illustrate the performance of the proposed shrinkage priors.

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Bitto, Angela, and Sylvia Frühwirth-Schnatter. "Achieving shrinkage in a time-varying parameter model framework." Elsevier, 2019. http://dx.doi.org/10.1016/j.jeconom.2018.11.006.

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Shrinkage for time-varying parameter (TVP) models is investigated within a Bayesian framework, with the aim to automatically reduce time-varying Parameters to staticones, if the model is overfitting. This is achieved through placing the double gamma shrinkage prior on the process variances. An efficient Markov chain Monte Carlo scheme is devel- oped, exploiting boosting based on the ancillarity-sufficiency interweaving strategy. The method is applicable both to TVP models for univariate a swell as multivariate time series. Applications include a TVP generalized Phillips curve for EU area inflation modeling and a multivariate TVP Cholesky stochastic volatility model for joint modeling of the Returns from the DAX-30index.

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Feldkircher, Martin, Florian Huber, and Gregor Kastner. "Sophisticated and small versus simple and sizeable: When does it pay off to introduce drifting coefficients in Bayesian VARs?" WU Vienna University of Economics and Business, 2018. http://epub.wu.ac.at/6021/1/wp260.pdf.

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We assess the relationship between model size and complexity in the time-varying parameter VAR framework via thorough predictive exercises for the Euro Area, the United Kingdom and the United States. It turns out that sophisticated dynamics through drifting coefficients are important in small data sets while simpler models tend to perform better in sizeable data sets. To combine best of both worlds, novel shrinkage priors help to mitigate the curse of dimensionality, resulting in competitive forecasts for all scenarios considered. Furthermore, we discuss dynamic model selection to improve upon the best performing individual model for each point in time.
Series: Department of Economics Working Paper Series

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Pirathiban, Ramethaa. "Improving species distribution modelling: Selecting absences and eliciting variable usefulness for input into standard algorithms or a Bayesian hierarchical meta-factor model." Thesis, Queensland University of Technology, 2019. https://eprints.qut.edu.au/134401/1/Ramethaa_Pirathiban_Thesis.pdf.

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This thesis explores and proposes methods to improve species distribution models. Throughout this thesis, a rich class of statistical modelling techniques has been developed to address crucial and interesting issues related to the data input into these models. The overall contribution of this research is the advancement of knowledge on species distribution modelling through an increased understanding of extraneous zeros, quality of the ecological data, variable selection that incorporates ecological theory and evaluating performance of the fitted models. Though motivated by the challenge of species distribution modelling from ecology, this research is broadly relevant to many ﬁelds, including bio-security and medicine. Speciﬁcally, this research is of potential signiﬁcance to researchers seeking to: identify and explain extraneous zeros; assess the quality of their data; or employ expert-informed variable selection.

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Manandhar, Binod. "Bayesian Models for the Analyzes of Noisy Responses From Small Areas: An Application to Poverty Estimation." Digital WPI, 2017. https://digitalcommons.wpi.edu/etd-dissertations/188.

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We implement techniques of small area estimation (SAE) to study consumption, a welfare indicator, which is used to assess poverty in the 2003-2004 Nepal Living Standards Survey (NLSS-II) and the 2001 census. NLSS-II has detailed information of consumption, but it can give estimates only at stratum level or higher. While population variables are available for all households in the census, they do not include the information on consumption; the survey has the `population' variables nonetheless. We combine these two sets of data to provide estimates of poverty indicators (incidence, gap and severity) for small areas (wards, village development committees and districts). Consumption is the aggregate of all food and all non-food items consumed. In the welfare survey the responders are asked to recall all information about consumptions throughout the reference year. Therefore, such data are likely to be noisy, possibly due to response errors or recalling errors. The consumption variable is continuous and positively skewed, so a statistician might use a logarithmic transformation, which can reduce skewness and help meet the normality assumption required for model building. However, it could be problematic since back transformation may produce inaccurate estimates and there are difficulties in interpretations. Without using the logarithmic transformation, we develop hierarchical Bayesian models to link the survey to the census. In our models for consumption, we incorporate the `population' variables as covariates. First, we assume that consumption is noiseless, and it is modeled using three scenarios: the exponential distribution, the gamma distribution and the generalized gamma distribution. Second, we assume that consumption is noisy, and we fit the generalized beta distribution of the second kind (GB2) to consumption. We consider three more scenarios of GB2: a mixture of exponential and gamma distributions, a mixture of two gamma distributions, and a mixture of two generalized gamma distributions. We note that there are difficulties in fitting the models for noisy responses because these models have non-identifiable parameters. For each scenario, after fitting two hierarchical Bayesian models (with and without area effects), we show how to select the most plausible model and we perform a Bayesian data analysis on Nepal's poverty data. We show how to predict the poverty indicators for all wards, village development committees and districts of Nepal (a big data problem) by combining the survey data with the census. This is a computationally intensive problem because Nepal has about four million households with about four thousand households in the survey and there is no record linkage between households in the survey and the census. Finally, we perform empirical studies to assess the quality of our survey-census procedure.

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Egidi, Leonardo. "Developments in Bayesian Hierarchical Models and Prior Specification with Application to Analysis of Soccer Data." Doctoral thesis, Università degli studi di Padova, 2018. http://hdl.handle.net/11577/3427270.

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In the recent years the challenge for new prior specifications and for complex hierarchical models became even more relevant in Bayesian inference. The advent of the Markov Chain Monte Carlo techniques, along with new probabilistic programming languages and new algorithms, extended the boundaries of the field, both in theoretical and applied directions. In the present thesis, we address theoretical and applied tasks. In the first part we propose a new class of prior distributions which might depend on the data and specified as a mixture between a noninformative and an informative prior. The generic prior belonging to this class provides less information than an informative prior and is more likely to not dominate the inference when the data size is small or moderate. Such a distribution is well suited for robustness tasks, especially in case of informative prior misspecification. Simulation studies within the conjugate models show that this proposal may be convenient for reducing the mean squared errors and improving the frequentist coverage. Furthermore, under mild conditions this class of distributions yields some other nice theoretical properties. In the second part of the thesis we use hierarchical Bayesian models for predicting some soccer quantities and we extend the usual match goals’ modeling strategy by including the bookmakers’ information directly in the model. Posterior predictive checks on in-sample and out-of sample data show an excellent model fit, a good model calibration and, ultimately, the possibility for building efficient betting strategies.
Negli ultimi anni la sfida per la specificazione di nuove distribuzioni a priori e per l’uso di complessi modelli gerarchici è diventata ancora più rilevante all’interno dell’inferenza Bayesiana. L’avvento delle tecniche Markov Chain Monte Carlo, insieme a nuovi linguaggi di programmazione probabilistici, ha esteso i confini del campo, sia in direzione teorica che applicata. Nella presente tesi ci dedichiamo a obiettivi teorici e applicati. Nella prima parte proponiamo una nuova classe di distribuzioni a priori che dipendono dai dati e che sono specificate tramite una mistura tra una a priori non informativa e una a priori informativa. La generica distribuzione appartenente a questa nuova classe fornisce meno informazione di una priori informativa e si candida a non dominare le conclusioni inferenziali quando la dimensione campionaria è piccola o moderata. Tale distribuzione `e idonea per scopi di robustezza, specialmente in caso di scorretta specificazione della distribuzione a priori informativa. Alcuni studi di simulazione all’interno di modelli coniugati mostrano che questa proposta può essere conveniente per ridurre gli errori quadratici medi e per migliorare la copertura frequentista. Inoltre, sotto condizioni non restrittive, questa classe di distribuzioni d`a luogo ad alcune altre interessanti proprietà teoriche. Nella seconda parte della tesi usiamo la classe dei modelli gerarchici Bayesiani per prevedere alcune grandezze relative al gioco del calcio ed estendiamo l’usuale modellazione per i goal includendo nel modello un’ulteriore informazione proveniente dalle case di scommesse. Strumenti per sondare a posteriori la bontà di adattamento del modello ai dati mettono in luce un’ottima aderenza del modello ai dati in possesso, una buona calibrazione dello stesso e suggeriscono, infine, la costruzione di efficienti strategie di scommesse per dati futuri.

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Frühwirth-Schnatter, Sylvia, and Regina Tüchler. "Bayesian parsimonious covariance estimation for hierarchical linear mixed models." Institut für Statistik und Mathematik, WU Vienna University of Economics and Business, 2004. http://epub.wu.ac.at/774/1/document.pdf.

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We considered a non-centered parameterization of the standard random-effects model, which is based on the Cholesky decomposition of the variance-covariance matrix. The regression type structure of the non-centered parameterization allows to choose a simple, conditionally conjugate normal prior on the Cholesky factor. Based on the non-centered parameterization, we search for a parsimonious variance-covariance matrix by identifying the non-zero elements of the Cholesky factors using Bayesian variable selection methods. With this method we are able to learn from the data for each effect, whether it is random or not, and whether covariances among random effects are zero or not. An application in marketing shows a substantial reduction of the number of free elements of the variance-covariance matrix. (author's abstract)
Series: Research Report Series / Department of Statistics and Mathematics

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Books on the topic "Hierarchical Bayesian Priors"

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Bera, Anil K. Estimation of systematic risk using Bayesian analysis with hierarchical and non-normal priors. [Urbana, Ill.]: College of Commerce and Business Administration, University of Illinois Urbana-Champaign, 1989.

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Kruschke, John K., and Wolf Vanpaemel. Bayesian Estimation in Hierarchical Models. Edited by Jerome R. Busemeyer, Zheng Wang, James T. Townsend, and Ami Eidels. Oxford University Press, 2015. http://dx.doi.org/10.1093/oxfordhb/9780199957996.013.13.

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Bayesian data analysis involves describing data by meaningful mathematical models, and allocating credibility to parameter values that are consistent with the data and with prior knowledge. The Bayesian approach is ideally suited for constructing hierarchical models, which are useful for data structures with multiple levels, such as data from individuals who are members of groups which in turn are in higher-level organizations. Hierarchical models have parameters that meaningfully describe the data at their multiple levels and connect information within and across levels. Bayesian methods are very flexible and straightforward for estimating parameters of complex hierarchical models (and simpler models too). We provide an introduction to the ideas of hierarchical models and to the Bayesian estimation of their parameters, illustrated with two extended examples. One example considers baseball batting averages of individual players grouped by fielding position. A second example uses a hierarchical extension of a cognitive process model to examine individual differences in attention allocation of people who have eating disorders. We conclude by discussing Bayesian model comparison as a case of hierarchical modeling.

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Butz, Martin V., and Esther F. Kutter. Top-Down Predictions Determine Perceptions. Oxford University Press, 2017. http://dx.doi.org/10.1093/acprof:oso/9780198739692.003.0009.

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While bottom-up visual processing is important, the brain integrates this information with top-down, generative expectations from very early on in the visual processing hierarchy. Indeed, our brain should not be viewed as a classification system, but rather as a generative system, which perceives something by integrating sensory evidence with the available, learned, predictive knowledge about that thing. The involved generative models continuously produce expectations over time, across space, and from abstracted encodings to more concrete encodings. Bayesian information processing is the key to understand how information integration must work computationally – at least in approximation – also in the brain. Bayesian networks in the form of graphical models allow the modularization of information and the factorization of interactions, which can strongly improve the efficiency of generative models. The resulting generative models essentially produce state estimations in the form of probability densities, which are very well-suited to integrate multiple sources of information, including top-down and bottom-up ones. A hierarchical neural visual processing architecture illustrates this point even further. Finally, some well-known visual illusions are shown and the perceptions are explained by means of generative, information integrating, perceptual processes, which in all cases combine top-down prior knowledge and expectations about objects and environments with the available, bottom-up visual information.

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Book chapters on the topic "Hierarchical Bayesian Priors"

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Wang, Jian, and Miaomiao Zhang. "Bayesian Atlas Building with Hierarchical Priors for Subject-Specific Regularization." In Medical Image Computing and Computer Assisted Intervention – MICCAI 2021, 76–86. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-87202-1_8.

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Aoki, Kohta, and Hiroshi Nagahashi. "Bayesian Image Segmentation Using MRF’s Combined with Hierarchical Prior Models." In Image Analysis, 65–74. Berlin, Heidelberg: Springer Berlin Heidelberg, 2005. http://dx.doi.org/10.1007/11499145_8.

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Mohammad-Djafari, Ali. "Variational Bayesian Approximation for Linear Inverse Problems with a Hierarchical Prior Models." In Lecture Notes in Computer Science, 669–76. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-40020-9_74.

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Congdon, Peter D. "Time Structured Priors." In Bayesian Hierarchical Models, 165–211. Chapman and Hall/CRC, 2019. http://dx.doi.org/10.1201/9780429113352-5.

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Congdon, Peter D. "Regression Techniques Using Hierarchical Priors." In Bayesian Hierarchical Models, 253–315. Chapman and Hall/CRC, 2019. http://dx.doi.org/10.1201/9780429113352-7.

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"Regression Techniques Using Hierarchical Priors." In Applied Bayesian Hierarchical Methods, 207–55. Chapman and Hall/CRC, 2010. http://dx.doi.org/10.1201/9781584887218-c5.

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Congdon, Peter D. "Factor Analysis, Structural Equation Models, and Multivariate Priors." In Bayesian Hierarchical Models, 339–403. Chapman and Hall/CRC, 2019. http://dx.doi.org/10.1201/9780429113352-9.

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"Structured Priors Recognizing Similarity over Time and Space." In Applied Bayesian Hierarchical Methods, 141–205. Chapman and Hall/CRC, 2010. http://dx.doi.org/10.1201/9781584887218-c4.

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"Multivariate Priors, with a Focus on Factor and Structural Equation Models." In Applied Bayesian Hierarchical Methods, 281–336. Chapman and Hall/CRC, 2010. http://dx.doi.org/10.1201/9781584887218-c7.

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Bloetscher, Frederick. "Applications of Hierarchical Bayesian Methods to Answer Multilayer Questions with Limited Data." In Bayesian Inference [Working Title]. IntechOpen, 2022. http://dx.doi.org/10.5772/intechopen.104784.

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There are many types of problems that include variables that are not well defined. Seeking answers to complex problems that involve many variables becomes mathematically challenging. Instead, many investigators use methods like principal component analysis to reduce the number of variables, or linear or logistic regression to rank the impact of the variables and eliminating those with the limited impact. However, eliminating variables can create a loss of integrity, especially for variables that might be associated with low likelihood but have high impact events. The use of hierarchical Bayesian methods resolves this issue by utilizing the benefits of information theory to help answer questions by incorporating a series of prior distributions for a number of variables used to solve an equation. The concept is to create distributions for the range and likelihood for each variable, and then create additional distributions to define the mean and shape values. At least three levels of analysis are required, but the hierarchical solution can include added levels beyond the initial variables (i.e., distributions related to the priors for the shape parameters). The results incorporate uncertainty, variability, and the ability to update the confidence in the values of the variables based on the receipt of new data.

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Conference papers on the topic "Hierarchical Bayesian Priors"

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Wang, Zhen, and Chao Lan. "Towards a Hierarchical Bayesian Model of Multi-View Anomaly Detection." In Twenty-Ninth International Joint Conference on Artificial Intelligence and Seventeenth Pacific Rim International Conference on Artificial Intelligence {IJCAI-PRICAI-20}. California: International Joint Conferences on Artificial Intelligence Organization, 2020. http://dx.doi.org/10.24963/ijcai.2020/335.

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Traditional anomaly detectors examine a single view of instances and cannot discover multi-view anomalies, i.e., instances that exhibit inconsistent behaviors across different views. To tackle the problem, several multi-view anomaly detectors have been developed recently, but they are all transductive and unsupervised thus may suffer some challenges. In this paper, we propose a novel inductive semi-supervised Bayesian multi-view anomaly detector. Specifically, we first present a generative model for normal data. Then, we build a hierarchical Bayesian model, by first assigning priors to all parameters and latent variables, and then assigning priors over the priors. Finally, we employ variational inference to approximate the posterior of the model and evaluate anomalous scores of multi-view instances. In the experiment, we show the proposed Bayesian detector consistently outperforms state-of-the-art counterparts across several public data sets and three well-known types of multi-view anomalies. In theory, we prove the inferred Bayesian estimator is consistent and derive a proximate sample complexity for the proposed anomaly detector.

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Stahlhut, Carsten, Hagai T. Attias, Kensuke Sekihara, David Wipf, Lars K. Hansen, and Srikantan S. Nagarajan. "A hierarchical Bayesian M/EEG imagingmethod correcting for incomplete spatio-temporal priors." In 2013 IEEE 10th International Symposium on Biomedical Imaging (ISBI 2013). IEEE, 2013. http://dx.doi.org/10.1109/isbi.2013.6556536.

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Giri, Ritwik, and Bhaskar D. Rao. "Hierarchical Bayesian formulation of Sparse Signal Recovery algorithms using scale mixture priors." In 2015 49th Asilomar Conference on Signals, Systems and Computers. IEEE, 2015. http://dx.doi.org/10.1109/acssc.2015.7421083.

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Lesouple, J., J. Y. Tourneret, M. Sahmoudi, F. Barbiero, and F. Faurie. "Multipath Mitigation in Global Navigation Satellite Systems Using a Bayesian Hierarchical Model With Bernoulli Laplacian Priors." In 2018 IEEE Statistical Signal Processing Workshop (SSP). IEEE, 2018. http://dx.doi.org/10.1109/ssp.2018.8450818.

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Abaei, Mohammad Mahdi, Nu Rhahida Arini, Philipp R. Thies, and Johanning Lars. "Failure Estimation of Offshore Renewable Energy Devices Based on Hierarchical Bayesian Approach." In ASME 2019 38th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/omae2019-95099.

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Abstract Improving the reliability of marine renewable energy devices such as wave and tidal energy convertors is an important task, primarily to minimize the perceived risks and reduce the associated cost for operation and maintenance. Marine systems involve a wide range of uncertainties, due to the complexity of failure mechanism of the marine components, scarcity of data, human interactions and randomness of the sea environment. The fundamental element of a probabilistic risk analysis necessarily needs to rely on operational information and observation data to quantify the performance of the system. However, in reality it is difficult to ascertain observation of the precursor data according to the number of component failures that have occurred, mainly as a result of imprecision in the failure criterion, record keeping, or experimental and physical modelling of the process. Traditional reliability estimation approaches such as Fault Tree, Event Tree and Reliability Block Diagram analysis offer simplified, rarely realistic models of this complex reliability problem. The main reason is that they all rely on accurate prior information as a perquisite for performing reliability assessment. In this paper, a hierarchical Bayesian framework is developed for modelling marine renewable component failures encountered the uncertainty. The proposed approach is capable to incorporate the conditions, which lack reliable observation data (e.g. unknown/uncertain failure rate of a component). The hierarchical Bayesian framework provides a platform for the propagation of uncertainties through the reliability assessment of the system, via Markov Chain Monte Carlo (MCMC) sampling. The advantages of using MCMC sampling has proliferated Bayesian inference for conducting risk and reliability assessment of engineering system. It is able to use hyper-priors to represent prior parameters as a subjective observations for probability estimation of the failure events and enable an updating process for quantitative reasoning of interdependence between parameters. The developed framework will be an assistive tool for a better monitoring of the operation in terms of evaluating performance of marine renewable system under the risk of failure. The paper illustrates the approach using a tidal energy convertor as a case study for estimating components failure rates and representing the uncertainties of system reliability. The paper will be of interest to reliability practitioners and researchers, as well as tidal energy technology and project developers, seeking a more accurate reliability estimation framework.

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Lopez-Martinez, Daniel, Ke Peng, Arielle Lee, David Borsook, and Rosalind Picard. "Pain Detection with fNIRS-Measured Brain Signals: A Personalized Machine Learning Approach Using the Wavelet Transform and Bayesian Hierarchical Modeling with Dirichlet Process Priors." In 2019 8th International Conference on Affective Computing and Intelligent Interaction Workshops and Demos (ACIIW). IEEE, 2019. http://dx.doi.org/10.1109/aciiw.2019.8925076.

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Liu, Yuhang, Wenyong Dong, Lei Zhang, Dong Gong, and Qinfeng Shi. "Variational Bayesian Dropout With a Hierarchical Prior." In 2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR). IEEE, 2019. http://dx.doi.org/10.1109/cvpr.2019.00729.

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Feng, Wei, Qiaofeng Li, and Qiuhai Lu. "A Hierarchical Bayesian Method for Time Domain Structure Damage Detection." In ASME 2019 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/detc2019-97026.

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Abstract A time domain structural damage detection method based on hierarchical Bayesian framework is proposed. Due to local stiffness reductions, the responses of damaged structures vary from those in undamaged status under the same external excitation. In this paper, the responses of damaged structures are assumed as the result of a summation of known external forces and unknown virtual forces exerted on corresponding undamaged structures. The damages can thus be detected, located, and quantified by the identification of associated virtual forces. A hierarchical Bayesian formulation considering all undetermined damage-related variables is adopted for the identification of virtual forces. The reasonable values of the variables and their uncertainties are depicted by their posterior distributions, sampled by Markov chain Monte Carlo method. Compared with traditional Bayesian formulations, manual choice of prior parameters is avoided and less prior information is required. The proposed virtual force indicator provides a more intuitive perspective for damage detection tasks and is potentially more operable in engineering practice. These advantages are illustrated by simulation of a cantilever beam under various damage conditions.

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Wang, Li, Ali Mohammad-Djafari, and Nicolas Gac. "Bayesian X-ray computed tomography using a three-level hierarchical prior model." In BAYESIAN INFERENCE AND MAXIMUM ENTROPY METHODS IN SCIENCE AND ENGINEERING: Proceedings of the 36th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering (MaxEnt 2016). Author(s), 2017. http://dx.doi.org/10.1063/1.4985361.

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Pedersen, Niels Lovmand, Carles Navarro Manchon, Dmitriy Shutin, and Bernard Henri Fleury. "Application of Bayesian hierarchical prior modeling to sparse channel estimation." In ICC 2012 - 2012 IEEE International Conference on Communications. IEEE, 2012. http://dx.doi.org/10.1109/icc.2012.6363847.

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