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Journal articles on the topic 'Bayesian statistical analysi'

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Published: 9 March 2023

Last updated: 10 March 2023

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1

Wijayanti, Rina. "PENAKSIRAN PARAMETER ANALISIS REGRESI COX DAN ANALISIS SURVIVAL BAYESIAN." PRISMATIKA: Jurnal Pendidikan dan Riset Matematika 1, no. 2 (June 1, 2019): 16–26. http://dx.doi.org/10.33503/prismatika.v1i2.427.

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In the theory of estimation, there are two approaches, namely the classical statistical approach and global statistical approach (Bayesian). Classical statistics are statistics in which the procedure is the decision based only on the data samples taken from the population. While Bayesian statistics in making decisions based on new information from the observed data (sample) and prior knowledge. At this writing Cox Regression Analysis will be taken as an example of parameter estimation by the classical statistical approach Survival Analysis and Bayesian statistical approach as an example of global (Bayesian). Survival Bayesial parameter estimation using MCMC algorithms for model complex / complicated and difficult to resolve while the Cox regression models using the method of partial likelihood. Results of the parameter estimates do not close form that needs to be done by the method of Newton-Raphson iteration.

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2

Davidson, Russell. "An Agnostic Look at Bayesian Statistics and Econometrics." Review of Economic Analysis 2, no. 2 (August 6, 2010): 153–68. http://dx.doi.org/10.15353/rea.v2i2.1470.

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Bayesians and non-Bayesians, often called frequentists, seem to be perpetually at loggerheads on fundamental questions of statistical inference. This paper takes as agnostic a stand as is possible for a practising frequentist, and tries to elicit a Bayesian answer to questions of interest to frequentists. The argument is based on my presentation at a debate organised by the Rimini Centre for Economic Analysis, between me as the frequentist “advocate”, and Christian Robert on the Bayesian side.

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3

Ickstadt, Katja, Martin Schäfer, and Manuela Zucknick. "Toward Integrative Bayesian Analysis in Molecular Biology." Annual Review of Statistics and Its Application 5, no. 1 (March 7, 2018): 141–67. http://dx.doi.org/10.1146/annurev-statistics-031017-100438.

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4

Gelfand, Alan E., and Sudipto Banerjee. "Bayesian Modeling and Analysis of Geostatistical Data." Annual Review of Statistics and Its Application 4, no. 1 (March 7, 2017): 245–66. http://dx.doi.org/10.1146/annurev-statistics-060116-054155.

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5

Hicks, Tyler, Liliana Rodríguez-Campos, and Jeong Hoon Choi. "Bayesian Posterior Odds Ratios." American Journal of Evaluation 39, no. 2 (May 23, 2017): 278–89. http://dx.doi.org/10.1177/1098214017704302.

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To begin statistical analysis, Bayesians quantify their confidence in modeling hypotheses with priors. A prior describes the probability of a certain modeling hypothesis apart from the data. Bayesians should be able to defend their choice of prior to a skeptical audience. Collaboration between evaluators and stakeholders could make their choices more defensible. This article describes how evaluators and stakeholders could combine their expertise to select rigorous priors for analysis. The article first introduces Bayesian testing, then situates it within a collaborative framework, and finally illustrates the method with a real example.

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6

Shin, Jennifer J., and David Zurakowski. "Null Hypotheses, Interval Estimation, and Bayesian Analysis." Otolaryngology–Head and Neck Surgery 157, no. 6 (December 2017): 919–20. http://dx.doi.org/10.1177/0194599817728898.

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Hypothesis testing using a frequentist approach is the mainstay of biostatistics and forms the foundation for assessing the significance of study results. This classical method has well-understood advantages as it determines whether data are statistically improbable and provides a threshold (ie, the P value) for delineating significance. Alternative statistical approaches have been proposed, including Bayesian analysis. This technique incorporates a prior probability as to what is already known clinically with the observed data. It is important for otolaryngologists to understand the advantages and disadvantages of these 2 approaches to conduct the most appropriate analyses.

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7

Donnison, J. R., and M. P. Wiper. "Bayesian statistical analysis of asteroid rotation rates." Monthly Notices of the Royal Astronomical Society 302, no. 1 (January 1, 1999): 75–80. http://dx.doi.org/10.1046/j.1365-8711.1999.02075.x.

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8

Brophy, James M., and Lawrence Joseph. "Bayesian interim statistical analysis of randomised trials." Lancet 349, no. 9059 (April 1997): 1166–68. http://dx.doi.org/10.1016/s0140-6736(96)06377-5.

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9

CLINTON, JOSHUA, SIMON JACKMAN, and DOUGLAS RIVERS. "The Statistical Analysis of Roll Call Data." American Political Science Review 98, no. 2 (May 2004): 355–70. http://dx.doi.org/10.1017/s0003055404001194.

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We develop a Bayesian procedure for estimation and inference for spatial models of roll call voting. This approach is extremely flexible, applicable to any legislative setting, irrespective of size, the extremism of the legislators' voting histories, or the number of roll calls available for analysis. The model is easily extended to let other sources of information inform the analysis of roll call data, such as the number and nature of the underlying dimensions, the presence of party whipping, the determinants of legislator preferences, and the evolution of the legislative agenda; this is especially helpful since generally it is inappropriate to use estimates of extant methods (usually generated under assumptions of sincere voting) to test models embodying alternate assumptions (e.g., log-rolling, party discipline). A Bayesian approach also provides a coherent framework for estimation and inference with roll call data that eludes extant methods; moreover, via Bayesian simulation methods, it is straightforward to generate uncertainty assessments or hypothesis tests concerning any auxiliary quantity of interest or to formally compare models. In a series of examples we show how our method is easily extended to accommodate theoretically interesting models of legislative behavior. Our goal is to provide a statistical framework for combining the measurement of legislative preferences with tests of models of legislative behavior.

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10

Fang, Kai-Tai, and Runze Li. "Bayesian Statistical Inference on Elliptical Matrix Distributions." Journal of Multivariate Analysis 70, no. 1 (July 1999): 66–85. http://dx.doi.org/10.1006/jmva.1998.1816.

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11

Cohen, Andrew L., Tanya L. Leise, and David K. Welsh. "Bayesian statistical analysis of circadian oscillations in fibroblasts." Journal of Theoretical Biology 314 (December 2012): 182–91. http://dx.doi.org/10.1016/j.jtbi.2012.08.038.

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12

Lauret, Philippe, John Boland, and Barbara Ridley. "Bayesian statistical analysis applied to solar radiation modelling." Renewable Energy 49 (January 2013): 124–27. http://dx.doi.org/10.1016/j.renene.2012.01.049.

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13

Serna, A., and P. Parrado. "Statistical Bayesian analysis of the brachytherapy source position." Physica Medica 32 (September 2016): 208. http://dx.doi.org/10.1016/j.ejmp.2016.07.704.

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14

Landes, Reid D., Peter G. Loutzenhiser, and Stephen B. Vardeman. "Hierarchical Bayesian Statistical Analysis for a Calibration Experiment." IEEE Transactions on Instrumentation and Measurement 55, no. 6 (December 2006): 2165–71. http://dx.doi.org/10.1109/tim.2006.884128.

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15

Gottardo, R. "Statistical analysis of microarray data: a Bayesian approach." Biostatistics 4, no. 4 (October 1, 2003): 597–620. http://dx.doi.org/10.1093/biostatistics/4.4.597.

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16

Mathai, A. M., and H. J. Haubold. "A pathway from Bayesian statistical analysis to superstatistics." Applied Mathematics and Computation 218, no. 3 (October 2011): 799–804. http://dx.doi.org/10.1016/j.amc.2011.03.027.

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17

Seo, Young-Min, Ki-Bum Park, and Sung-Won Kim. "Uncertainty Analysis of Parameters of Spatial Statistical Model Using Bayesian Method for Estimating Spatial Distribution of Probability Rainfall." Journal of the Environmental Sciences 20, no. 12 (December 31, 2011): 1541–51. http://dx.doi.org/10.5322/jes.2011.20.12.1541.

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18

Helu, Amal, and Hani Samawi. "Statistical Analysis Based on Adaptive Progressive Hybrid Censored Data From Lomax Distribution." Statistics, Optimization & Information Computing 9, no. 4 (November 30, 2021): 789–808. http://dx.doi.org/10.19139/soic-2310-5070-1330.

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In this article, we consider statistical inferences about the unknown parameters of the Lomax distribution basedon the Adaptive Type-II Progressive Hybrid censoring scheme, this scheme can save both the total test time and the cost induced by the failure of the units and increases the efficiency of statistical analysis. The estimation of the parameters is derived using the maximum likelihood (MLE) and the Bayesian procedures. The Bayesian estimators are obtained based on the symmetric and asymmetric loss functions. There are no explicit forms for the Bayesian estimators, therefore, we propose Lindley’s approximation method to compute the Bayesian estimators. A comparison between these estimators is provided by using extensive simulation. A real-life data example is provided to illustrate our proposed estimators.

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19

Sosa, Juan, and Lina Buitrago. "Illustrating advantages and challenges of Bayesian statistical modelling: An empirical perspective." Model Assisted Statistics and Applications 17, no. 3 (August 26, 2022): 175–87. http://dx.doi.org/10.3233/mas-221342.

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We provide four case studies that use Bayesian machinery to making inductive reasoning. Our main motivation relies in offering several instances where the Bayesian approach to data analysis is exploited at its best to perform complex tasks, such as description, testing, estimation, and prediction. This work is not meant to be either a reference text or a survey in Bayesian statistical inference. Our goal is simply to provide several examples that use Bayesian methodology to solve data-driven problems. The topics we cover here include analysis of times series and analysis of spatial data.

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20

CUNHA FILHO, Moacyr, David Venancio da CRUZ, Emídio Cantídio Almeida de OLIVEIRA, Victor Cassimiro PISCOYA, Guilherme Rocha MOREIRA, Ana Luiza Xavier CUNHA, and Renisson Neponuceno de ARAÚJO FILHO. "STATISTICAL ANALYSIS WITH A BAYESIAN APPROACH TO THE HARDY-WEINBERG EQUILIBRIUM." REVISTA BRASILEIRA DE BIOMETRIA 38, no. 1 (March 28, 2020): 69. http://dx.doi.org/10.28951/rbb.v38i1.427.

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In population genetics, it is very common to use statistical analysis to test the Hardy-Weinberg genetic equilibrium in a given population. The classical method of approaching this problem is done through the chi-square test that often leads to the verification of the equilibrium hypothesis. In the present work, a Bayesian analysis was developed involving hypothesis testing, estimation and credibility intervals to test this balance. Data on M, MN and N blood groups from the MNS system were used on samples from two populations, one from Brazilians and one from North Americans, obtained by Beiguelman (1977). The HardyWeinberg equilibrium adhesion chi-square test was performed, where the acceptance of the Hardy-Weinberg equilibrium hypothesis was confirmed. By Bayesian analysis, the rejection of the Hardy-Weinberg equilibrium hypothesis was confirmed, mainly by the Bayes factor. Our primary concern was to develop a Bayesian technique as an alternative to testing HardyWeinberg equilibrium using the MNSs blood sample data. The result obtained may encourage researchers mainly in the field of biological sciences to practice Bayesian Methodology, as an alternative in statistical tests.

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21

Matsuzoe, Hiroshi, Jun-ichi Takeuchi, and Shun-ichi Amari. "Equiaffine structures on statistical manifolds and Bayesian statistics." Differential Geometry and its Applications 24, no. 6 (December 2006): 567–78. http://dx.doi.org/10.1016/j.difgeo.2006.02.003.

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22

Halloran, M. Elizabeth, Andrew Gelman, John B. Carlin, Hal S. Stern, Donald B. Rubin, Bradley P. Carlin, and Thomas A. Louis. "Bayesian Data Analysis." Journal of the American Statistical Association 92, no. 440 (December 1997): 1640. http://dx.doi.org/10.2307/2965436.

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23

Yan, Jun. "Bayesian Survival Analysis." Journal of the American Statistical Association 99, no. 468 (December 2004): 1202–3. http://dx.doi.org/10.1198/jasa.2004.s359.

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24

Hill, Bruce M., Harry F. Martz, and Ray A. Waller. "Bayesian Reliability Analysis." Journal of the American Statistical Association 80, no. 389 (March 1985): 253. http://dx.doi.org/10.2307/2288105.

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25

Souayeh, Basma, Zulqurnain Sabir, Najib Hdhiri, Wael Al-Kouz, Mir Waqas Alam, and Tarfa Alsheddi. "A Stochastic Bayesian Regularization Approach for the Fractional Food Chain Supply System with Allee Effects." Fractal and Fractional 6, no. 10 (September 29, 2022): 553. http://dx.doi.org/10.3390/fractalfract6100553.

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This motive of current research is to provide a stochastic platform based on the artificial neural networks (ANNs) along with the Bayesian regularization approach for the fractional food chain supply system (FFSCS) with Allee effects. The investigations based on the fractional derivatives are applied to achieve the accurate and precise results of FFSCS. The dynamical FFSCS is divided into special predator category P(η), top-predator class Q(η), and prey population dynamics R(η). The computing numerical performances for three different variations of the dynamical FFSCS are provided by using the ANNs along with the Bayesian regularization approach. The data selection for the dynamical FFSCS is selected for train as 78% and 11% for both test and endorsement. The accuracy of the proposed ANNs along with the Bayesian regularization method is approved using the comparison performances. For the rationality, ability, reliability, and exactness are authenticated by using the ANNs procedure enhanced by the Bayesian regularization method through the regression measures, correlation values, error histograms, and transition of state performances.

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26

Kamedulska, Agnieszka, Łukasz Kubik, and Paweł Wiczling. "Statistical analysis of isocratic chromatographic data using Bayesian modeling." Analytical and Bioanalytical Chemistry 414, no. 11 (March 28, 2022): 3471–81. http://dx.doi.org/10.1007/s00216-022-03968-x.

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27

Aslam, Muhammad, Dildar Hussain, and Ghausia Masood Gilani. "STATISTICAL ANALYSIS OF THE TM- MODEL VIA BAYESIAN APPROACH." Pakistan Journal of Statistics and Operation Research 8, no. 4 (November 8, 2012): 849. http://dx.doi.org/10.18187/pjsor.v8i4.174.

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28

Fackler, Cameron J., Alistair Hurrell, Douglas Beaton, and Ning Xiang. "Statistical analysis of multilayer porous absorbers with Bayesian inference." Journal of the Acoustical Society of America 139, no. 4 (April 2016): 2070. http://dx.doi.org/10.1121/1.4950139.

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29

Dennis, Samuel Y. "A Bayesian analysis of tree-structured statistical decision problems." Journal of Statistical Planning and Inference 53, no. 3 (August 1996): 323–44. http://dx.doi.org/10.1016/0378-3758(95)00112-3.

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30

Berliner, L. M., N. Cressie, K. Jezek, Y. Kim, C. Q. Lam, and C. J. van der Veen. "Equilibrium dynamics of ice streams: a Bayesian statistical analysis." Statistical Methods and Applications 17, no. 2 (December 1, 2007): 145–65. http://dx.doi.org/10.1007/s10260-007-0077-1.

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31

Yang, Dongyan, Stanislav O. Zakharkin, Grier P. Page, Jacob P. L. Brand, Jode W. Edwards, Alfred A. Bartolucci, and David B. Allison. "Applications of Bayesian Statistical Methods in Microarray Data Analysis." American Journal of PharmacoGenomics 4, no. 1 (2004): 53–62. http://dx.doi.org/10.2165/00129785-200404010-00006.

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32

Edwards, Thomas H., and Stefan Stoll. "Bayesian Statistical Methods in the Analysis of DEER Data." Biophysical Journal 110, no. 3 (February 2016): 153a. http://dx.doi.org/10.1016/j.bpj.2015.11.859.

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33

Dunbrack, Roland L., and Fred E. Cohen. "Bayesian statistical analysis of protein side-chain rotamer preferences." Protein Science 6, no. 8 (August 1997): 1661–81. http://dx.doi.org/10.1002/pro.5560060807.

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34

BEST, NICKY. "BAYESIAN DATA ANALYSIS." Statistics in Medicine 15, no. 19 (October 15, 1996): 2123–24. http://dx.doi.org/10.1002/(sici)1097-0258(19961015)15:19<2123::aid-sim364>3.0.co;2-k.

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35

Zellner, Arnold. "S. James Press and Bayesian Analysis." Review of Economic Analysis 1, no. 1 (November 22, 2009): 98–118. http://dx.doi.org/10.15353/rea.v1i1.1481.

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S. James Press’s many contributions to statistical research, lecturing, mentoring students, the statistics profession, etc. are summarized. Then some new developments in Bayesian analysis are described and remarks on the future of Bayesian analysis are presented.

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36

ZELLNER, ARNOLD. "S. JAMES PRESS AND BAYESIAN ANALYSIS." Macroeconomic Dynamics 10, no. 5 (October 13, 2006): 667–84. http://dx.doi.org/10.1017/s1365100506050383.

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S. James Press's many contributions to statistical research, lecturing, mentoring students, the statistics profession, etc., are summarized. Then some new developments in Bayesian analysis are described and remarks on the future of Bayesian analysis are presented.

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37

Hanley, Kevin E., A. Reed Gibby, and Thomas C. Ferrara. "Analysis of Accident-Reduction Factors on California State Highways." Transportation Research Record: Journal of the Transportation Research Board 1717, no. 1 (January 2000): 37–45. http://dx.doi.org/10.3141/1717-06.

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Accident reduction factors (ARFs) are mechanisms that the California Department of Transportation employs in calculating Traffic Safety Index values, which are used to prioritize safety-improvement projects on California state highways. Many factors that affect motorist safety have changed over the nearly 30 years in which ARFs have been used in the Traffic Safety Index Program. It is therefore appropriate to review and update, as needed, these accident-reduction factors. The research focused on four accident-reduction factors that are currently in use (rumble-strip installation, shoulder widening, superelevation correction, and curve correction). An accident-reduction factor was developed for a fifth treatment category (wet-pavement treatments). Data were gathered for all projects proposed for funding in the state of California’s Safety Improvement Program from 1985 through 1995. Projects completed from 1988 through 1992 were considered for inclusion in a before-and-after study that employed empirical Bayesian statistical analysis. A Bayesian statistical software package, BEATS (Bayesian Estimation of Accidents in Transportation Studies), was used in the analysis. The study reviewed scope of work for each of the projects of interest that were completed from 1988 to 1992. Thirty projects—the most frequently occurring individual treatments and treatment combinations—were categorized by treatment type and analyzed. Accident-reduction factors of sufficient statistically significant strength were found for wet-pavement treatments, rumble-strip installations, and shoulder-widening projects. Data for shoulder widening, superelevation correction, and curve correction projects also are presented, but small sample size hampered statistical significance for these projects. Results of the study revealed the importance of improving curve radius during superelevation correction and lane- and/or shoulder-widening treatments.

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38

Mathai, A. M. "Mellin convolutions, statistical distributions and fractional calculus." Fractional Calculus and Applied Analysis 21, no. 2 (April 25, 2018): 376–98. http://dx.doi.org/10.1515/fca-2018-0022.

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Abstract This paper shows that meaningful interpretations for Mellin convolutions of products and ratios involving two, three or more functions, can be given through statistical distribution theory of products and ratios involving two, three or more real scalar random variables or general multivariate situations. This paper shows that the approach through statistical distributions can also establish connection to fractional integrals, reaction-rate probability integrals in nuclear reaction-rate theory, Krätzel integrals and Krätzel transform in applied analysis, continuous mixtures, Bayesian analysis etc. This paper shows that the theory of Mellin convolutions, currently available for two functions, can be extended to many functions through statistical distributions. As illustrative examples, products and ratios of generalized gamma variables, which lead to Krätzel integrals, reaction-rate probability integrals, inverse Gaussian density etc, and type-1 beta variables, which lead to various types of fractional integrals and fractional calculus in general, are considered.

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39

Chaudhary, A. K. "Bayesian Analysis of Two Parameter Complementary Exponential Power Distribution." NCC Journal 3, no. 1 (June 14, 2018): 1–23. http://dx.doi.org/10.3126/nccj.v3i1.20244.

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In this paper, the Markov chain Monte Carlo (MCMC) method is used to estimate the parameters of CEP distribution based on a complete sample. A procedure is developed to obtain Bayes estimates of the parameters of the CEP distribution using Markov Chain Monte Carlo (MCMC) simulation method in OpenBUGS, established software for Bayesian analysis using Markov Chain Monte Carlo (MCMC) methods. The MCMC methods have been shown to be easier to implement computationally, the estimates always exist and are statistically consistent, and their probability intervals are convenient to construct. The R functions are developed to study the statistical properties, model validation and comparison tools of the distribution and the output analysis of MCMC samples generated from OpenBUGS. A real data set is considered for illustration under uniform and gamma sets of priors. NCC Journal Vol. 3, No. 1, 2018, Page: 1-23

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40

Fearnhead, Paul, and Despina Vasileiou. "Bayesian Analysis of Isochores." Journal of the American Statistical Association 104, no. 485 (March 2009): 132–41. http://dx.doi.org/10.1198/jasa.2009.0009.

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41

Besag, Julian. "Towards Bayesian image analysis." Journal of Applied Statistics 20, no. 5-6 (January 1993): 107–19. http://dx.doi.org/10.1080/02664769300000061.

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42

Perez Ruiz, Diego Andres. "Bayesian Nonparametric Data Analysis." International Statistical Review 84, no. 1 (April 2016): 157–58. http://dx.doi.org/10.1111/insr.12168.

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43

Leddy, J., S. Madireddy, E. Howell, and S. Kruger. "Single Gaussian process method for arbitrary tokamak regimes with a statistical analysis." Plasma Physics and Controlled Fusion 64, no. 10 (August 26, 2022): 104005. http://dx.doi.org/10.1088/1361-6587/ac89ab.

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Abstract Gaussian process regression is a Bayesian method for inferring profiles based on input data. The technique is increasing in popularity in the fusion community due to its many advantages over traditional fitting techniques including intrinsic uncertainty quantification and robustness to over-fitting. This work investigates the use of a new method, the change-point method, for handling the varying length scales found in different tokamak regimes. The use of the Student’s t-distribution for the Bayesian likelihood probability is also investigated and shown to be advantageous in providing good fits in profiles with many outliers. To compare different methods, synthetic data generated from analytic profiles is used to create a database enabling a quantitative statistical comparison of which methods perform the best. Using a full Bayesian approach with the change-point method, Matérn kernel for the prior probability, and Student’s t-distribution for the likelihood is shown to give the best results.

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44

Cook, Peyton. "Bayesian autoregressive spectral analysis." Communications in Statistics - Theory and Methods 14, no. 5 (January 1985): 1001–18. http://dx.doi.org/10.1080/03610928508828959.

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45

Alvarez, Enrique E., and Dipak K. Dey. "Bayesian isotonic changepoint analysis." Annals of the Institute of Statistical Mathematics 61, no. 2 (August 18, 2007): 355–70. http://dx.doi.org/10.1007/s10463-007-0148-y.

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46

Engeland, K., and L. Gottschalk. "Bayesian estimation of parameters in a regional hydrological model." Hydrology and Earth System Sciences 6, no. 5 (October 31, 2002): 883–98. http://dx.doi.org/10.5194/hess-6-883-2002.

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Abstract. This study evaluates the applicability of the distributed, process-oriented Ecomag model for prediction of daily streamflow in ungauged basins. The Ecomag model is applied as a regional model to nine catchments in the NOPEX area, using Bayesian statistics to estimate the posterior distribution of the model parameters conditioned on the observed streamflow. The distribution is calculated by Markov Chain Monte Carlo (MCMC) analysis. The Bayesian method requires formulation of a likelihood function for the parameters and three alternative formulations are used. The first is a subjectively chosen objective function that describes the goodness of fit between the simulated and observed streamflow, as defined in the GLUE framework. The second and third formulations are more statistically correct likelihood models that describe the simulation errors. The full statistical likelihood model describes the simulation errors as an AR(1) process, whereas the simple model excludes the auto-regressive part. The statistical parameters depend on the catchments and the hydrological processes and the statistical and the hydrological parameters are estimated simultaneously. The results show that the simple likelihood model gives the most robust parameter estimates. The simulation error may be explained to a large extent by the catchment characteristics and climatic conditions, so it is possible to transfer knowledge about them to ungauged catchments. The statistical models for the simulation errors indicate that structural errors in the model are more important than parameter uncertainties. Keywords: regional hydrological model, model uncertainty, Bayesian analysis, Markov Chain Monte Carlo analysis

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47

Fryback, Dennis G., James O. Chinnis, and Jacob W. Ulvila. "BAYESIAN COST-EFFECTIVENESS ANALYSIS." International Journal of Technology Assessment in Health Care 17, no. 1 (January 2001): 83–97. http://dx.doi.org/10.1017/s0266462301104083.

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A desirable element of cost-effectiveness analysis (CEA) modeling is a systematic way to relate uncertainty about input parameters to uncertainty in the computational results of the CEA model. Use of Bayesian statistical estimation and Monte Carlo simulation provides a natural way to compute a posterior probability distribution for each CEA result. We demonstrate this approach by reanalyzing a previously published CEA evaluating the incremental cost-effectiveness of tissue plasminogen activator compared to streptokinase for thrombolysis in acute myocardial infarction patients using data from the GUSTO trial and other auxiliary data sources. We illustrate Bayesian estimation for proportions, mean costs, and mean quality-of-life weights. The computations are performed using the Bayesian analysis software WinBUGS, distributed by the MRC Biostatistics Unit, Cambridge, England.

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48

Karimnezhad, Ali, and Ahmad Parsian. "Bayesian and robust Bayesian analysis in a general setting." Communications in Statistics - Theory and Methods 48, no. 15 (October 30, 2018): 3899–920. http://dx.doi.org/10.1080/03610926.2018.1482344.

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49

Louzada, Francisco, Diego Carvalho do Nascimento, and Osafu Augustine Egbon. "Spatial Statistical Models: An Overview under the Bayesian Approach." Axioms 10, no. 4 (November 17, 2021): 307. http://dx.doi.org/10.3390/axioms10040307.

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Spatial documentation is exponentially increasing given the availability of Big Data in the Internet of Things, enabled by device miniaturization and data storage capacity. Bayesian spatial statistics is a useful statistical tool to determine the dependence structure and hidden patterns in space through prior knowledge and data likelihood. However, this class of modeling is not yet well explored when compared to adopting classification and regression in machine-learning models, in which the assumption of the spatiotemporal independence of the data is often made, that is an inexistent or very weak dependence. Thus, this systematic review aims to address the main models presented in the literature over the past 20 years, identifying the gaps and research opportunities. Elements such as random fields, spatial domains, prior specification, the covariance function, and numerical approximations are discussed. This work explores the two subclasses of spatial smoothing: global and local.

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Bronk Ramsey, Christopher. "Bayesian Analysis of Radiocarbon Dates." Radiocarbon 51, no. 1 (2009): 337–60. http://dx.doi.org/10.1017/s0033822200033865.

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Abstract:

If radiocarbon measurements are to be used at all for chronological purposes, we have to use statistical methods for calibration. The most widely used method of calibration can be seen as a simple application of Bayesian statistics, which uses both the information from the new measurement and information from the 14C calibration curve. In most dating applications, however, we have larger numbers of 14C measurements and we wish to relate those to events in the past. Bayesian statistics provides a coherent framework in which such analysis can be performed and is becoming a core element in many 14C dating projects. This article gives an overview of the main model components used in chronological analysis, their mathematical formulation, and examples of how such analyses can be performed using the latest version of the OxCal software (v4). Many such models can be put together, in a modular fashion, from simple elements, with defined constraints and groupings. In other cases, the commonly used “uniform phase” models might not be appropriate, and ramped, exponential, or normal distributions of events might be more useful. When considering analyses of these kinds, it is useful to be able run simulations on synthetic data. Methods for performing such tests are discussed here along with other methods of diagnosing possible problems with statistical models of this kind.

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