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Bayesian inference

About: Bayesian inference is a research topic. Over the lifetime, 22485 publications have been published within this topic receiving 820403 citations. The topic is also known as: Bayesian analysis & Bayes' solution.


Papers
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BookDOI
TL;DR: The Markov Chain Monte Carlo Implementation Results Summary and Discussion MEDICAL MONITORING Introduction Modelling Medical Monitoring Computing Posterior Distributions Forecasting Model Criticism Illustrative Application Discussion MCMC for NONLINEAR HIERARCHICAL MODELS.
Abstract: INTRODUCING MARKOV CHAIN MONTE CARLO Introduction The Problem Markov Chain Monte Carlo Implementation Discussion HEPATITIS B: A CASE STUDY IN MCMC METHODS Introduction Hepatitis B Immunization Modelling Fitting a Model Using Gibbs Sampling Model Elaboration Conclusion MARKOV CHAIN CONCEPTS RELATED TO SAMPLING ALGORITHMS Markov Chains Rates of Convergence Estimation The Gibbs Sampler and Metropolis-Hastings Algorithm INTRODUCTION TO GENERAL STATE-SPACE MARKOV CHAIN THEORY Introduction Notation and Definitions Irreducibility, Recurrence, and Convergence Harris Recurrence Mixing Rates and Central Limit Theorems Regeneration Discussion FULL CONDITIONAL DISTRIBUTIONS Introduction Deriving Full Conditional Distributions Sampling from Full Conditional Distributions Discussion STRATEGIES FOR IMPROVING MCMC Introduction Reparameterization Random and Adaptive Direction Sampling Modifying the Stationary Distribution Methods Based on Continuous-Time Processes Discussion IMPLEMENTING MCMC Introduction Determining the Number of Iterations Software and Implementation Output Analysis Generic Metropolis Algorithms Discussion INFERENCE AND MONITORING CONVERGENCE Difficulties in Inference from Markov Chain Simulation The Risk of Undiagnosed Slow Convergence Multiple Sequences and Overdispersed Starting Points Monitoring Convergence Using Simulation Output Output Analysis for Inference Output Analysis for Improving Efficiency MODEL DETERMINATION USING SAMPLING-BASED METHODS Introduction Classical Approaches The Bayesian Perspective and the Bayes Factor Alternative Predictive Distributions How to Use Predictive Distributions Computational Issues An Example Discussion HYPOTHESIS TESTING AND MODEL SELECTION Introduction Uses of Bayes Factors Marginal Likelihood Estimation by Importance Sampling Marginal Likelihood Estimation Using Maximum Likelihood Application: How Many Components in a Mixture? Discussion Appendix: S-PLUS Code for the Laplace-Metropolis Estimator MODEL CHECKING AND MODEL IMPROVEMENT Introduction Model Checking Using Posterior Predictive Simulation Model Improvement via Expansion Example: Hierarchical Mixture Modelling of Reaction Times STOCHASTIC SEARCH VARIABLE SELECTION Introduction A Hierarchical Bayesian Model for Variable Selection Searching the Posterior by Gibbs Sampling Extensions Constructing Stock Portfolios With SSVS Discussion BAYESIAN MODEL COMPARISON VIA JUMP DIFFUSIONS Introduction Model Choice Jump-Diffusion Sampling Mixture Deconvolution Object Recognition Variable Selection Change-Point Identification Conclusions ESTIMATION AND OPTIMIZATION OF FUNCTIONS Non-Bayesian Applications of MCMC Monte Carlo Optimization Monte Carlo Likelihood Analysis Normalizing-Constant Families Missing Data Decision Theory Which Sampling Distribution? Importance Sampling Discussion STOCHASTIC EM: METHOD AND APPLICATION Introduction The EM Algorithm The Stochastic EM Algorithm Examples GENERALIZED LINEAR MIXED MODELS Introduction Generalized Linear Models (GLMs) Bayesian Estimation of GLMs Gibbs Sampling for GLMs Generalized Linear Mixed Models (GLMMs) Specification of Random-Effect Distributions Hyperpriors and the Estimation of Hyperparameters Some Examples Discussion HIERARCHICAL LONGITUDINAL MODELLING Introduction Clinical Background Model Detail and MCMC Implementation Results Summary and Discussion MEDICAL MONITORING Introduction Modelling Medical Monitoring Computing Posterior Distributions Forecasting Model Criticism Illustrative Application Discussion MCMC FOR NONLINEAR HIERARCHICAL MODELS Introduction Implementing MCMC Comparison of Strategies A Case Study from Pharmacokinetics-Pharmacodynamics Extensions and Discussion BAYESIAN MAPPING OF DISEASE Introduction Hypotheses and Notation Maximum Likelihood Estimation of Relative Risks Hierarchical Bayesian Model of Relative Risks Empirical Bayes Estimation of Relative Risks Fully Bayesian Estimation of Relative Risks Discussion MCMC IN IMAGE ANALYSIS Introduction The Relevance of MCMC to Image Analysis Image Models at Different Levels Methodological Innovations in MCMC Stimulated by Imaging Discussion MEASUREMENT ERROR Introduction Conditional-Independence Modelling Illustrative examples Discussion GIBBS SAMPLING METHODS IN GENETICS Introduction Standard Methods in Genetics Gibbs Sampling Approaches MCMC Maximum Likelihood Application to a Family Study of Breast Cancer Conclusions MIXTURES OF DISTRIBUTIONS: INFERENCE AND ESTIMATION Introduction The Missing Data Structure Gibbs Sampling Implementation Convergence of the Algorithm Testing for Mixtures Infinite Mixtures and Other Extensions AN ARCHAEOLOGICAL EXAMPLE: RADIOCARBON DATING Introduction Background to Radiocarbon Dating Archaeological Problems and Questions Illustrative Examples Discussion Index

7,399 citations

Journal ArticleDOI
TL;DR: In this article, a Bayesian approach to hypothesis testing, model selection, and accounting for model uncertainty is presented, which is straightforward through the use of the simple and accurate BIC approximation, and it can be done using the output from standard software.
Abstract: It is argued that P-values and the tests based upon them give unsatisfactory results, especially in large samples. It is shown that, in regression, when there are many candidate independent variables, standard variable selection procedures can give very misleading results. Also, by selecting a single model, they ignore model uncertainty and so underestimate the uncertainty about quantities of interest. The Bayesian approach to hypothesis testing, model selection, and accounting for model uncertainty is presented. Implementing this is straightforward through the use of the simple and accurate BIC approximation, and it can be done using the output from standard software. Specific results are presented for most of the types of model commonly used in sociology. It is shown that this approach overcomes the difficulties with P-values and standard model selection procedures based on them. It also allows easy comparison of nonnested models, and permits the quantification of the evidence for a null hypothesis of interest, such as a convergence theory or a hypothesis about societal norms.

6,100 citations

Book
22 Dec 2012
TL;DR: An overview of statistical decision theory, which emphasizes the use and application of the philosophical ideas and mathematical structure of decision theory.
Abstract: 1. Basic concepts 2. Utility and loss 3. Prior information and subjective probability 4. Bayesian analysis 5. Minimax analysis 6. Invariance 7. Preposterior and sequential analysis 8. Complete and essentially complete classes Appendices.

5,573 citations

Journal ArticleDOI
TL;DR: The software package Tracer is presented, for visualizing and analyzing the MCMC trace files generated through Bayesian phylogenetic inference, which provides kernel density estimation, multivariate visualization, demographic trajectory reconstruction, conditional posterior distribution summary, and more.
Abstract: Bayesian inference of phylogeny using Markov chain Monte Carlo (MCMC) plays a central role in understanding evolutionary history from molecular sequence data. Visualizing and analyzing the MCMC-generated samples from the posterior distribution is a key step in any non-trivial Bayesian inference. We present the software package Tracer (version 1.7) for visualizing and analyzing the MCMC trace files generated through Bayesian phylogenetic inference. Tracer provides kernel density estimation, multivariate visualization, demographic trajectory reconstruction, conditional posterior distribution summary, and more. Tracer is open-source and available at http://beast.community/tracer.

5,492 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20251
2023584
20221,268
20211,618
20201,740
20191,724