BugsXLA : Bayes for the Common Man (original) (raw)

The BUGS book: A practical introduction to Bayesian analysis

2012

BUGS is a software project that began in Cambridge, England, and has been actively ongoing for more than twenty years. Its core purpose is to provide a computational companion to Bayesian statistical analyses, and the software makes extensive use of Markov chain Monte Carlo and similar simulation methods. At present the software exists in a number of versions, such as WinBUGS, OpenBUGS, and JAGS, which are available free of charge. The authors of The BUGS Book are long-standing contributors to the BUGS project.

WinBUGS - A Bayesian modelling framework: Concepts, structure, and extensibility

Statistics and Computing, 2000

WinBUGS is a fully extensible modular framework for constructing and analysing Bayesian full probability models. Models may be specified either textually via the BUGS language or pictorially using a graphical interface called DoodleBUGS. WinBUGS processes the model specification and constructs an object-oriented representation of the model. The software offers a user-interface, based on dialogue boxes and menu commands, through which the model may then be analysed using Markov chain Monte Carlo techniques. In this paper we discuss how and why various modern computing concepts, such as object-orientation and run-time linking, feature in the software's design. We also discuss how the framework may be extended. It is possible to write specific applications that form an apparently seamless interface with WinBUGS for users with specialized requirements. It is also possible to interface with WinBUGS at a lower level by incorporating new object types that may be used by WinBUGS without knowledge of the modules in which they are implemented. Neither of these types of extension require access to, or even recompilation of, the WinBUGS source-code.

Software for Bayesian Analysis: Current Status and Additional Needs

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The JASP Guidelines for Conducting and Reporting a Bayesian Analysis

2019

Despite the increasing popularity of Bayesian inference in empirical research, few practical guidelines provide detailed recommendations for how to apply Bayesian procedures and interpret the results. Here we offer specific guidelines for four different stages of Bayesian statistical reasoning in a research setting: planning the analysis, executing the analysis, interpreting the results, and reporting the results. The guidelines for each stage are illustrated with a running example. Although the guidelines are geared toward analyses performed with the open-source statistical software JASP, most guidelines extend to Bayesian inference in general.

Bayesian Inference Using Gibbs Sampling in Applications and Curricula of Decision Analysis

INFORMS Transactions on Education, 2014

Applications and curricula of decision analysis currently do not include methods to compute Bayes' rule and obtain posteriors for non-conjugate prior distributions. The current convention is to force the decision maker's belief to take the form of a conjugate distribution, leading to a suboptimal decision. BUGS software, which uses MCMC methods, is numerically capable of obtaining posteriors for non-conjugate priors. By using the decision maker's true non-conjugate belief, the problems explored suggest that BUGS is able to produce a posterior distribution which leads to optimal decision making. Other methods exist which can use nonconjugate priors, but they must be implemented ad hoc as they do not have any supporting software. BUGS offers the distinct advantage of being implemented in existing software. This software has a gradual learning curve, and with simple coding can solve a wide range of decision analysis problems. BUGS is useful in making optimal decisions, and it is reasonably easy to learn and implement, therefore there is value in including BUGS in decision analysis curricula.

An Empirical Comparison of Methods for Computing Bayes Factors in Generalized Linear Mixed Models

Journal of Computational and Graphical Statistics, 2005

Generalized linear mixed models (GLMM) are used in situations where a number of characteristics (covariates) affect a nonnormal response variable and the responses are correlated due to the existence of clusters or groups. For example, the responses in biological applications may be correlated due to common genetic factors or environmental factors. The clustering or grouping is addressed by introducing cluster effects to the model; the associated parameters are often treated as random effects parameters. In many applications, the magnitude of the variance components corresponding to one or more of the sets of random effects parameters are of interest, especially the point null hypothesis that one or more of the variance components is zero. A Bayesian approach to test the hypothesis is to use Bayes factors comparing the models with and without the random effects in questionthis work reviews a number of approaches for estimating the Bayes factor. We perform a comparative study of the different approaches to compute Bayes factors for GLMMs by applying them to two different datasets. The first example employs a probit regression model with a single variance component to data from a natural selection study on turtles. The second example uses a disease mapping model from epidemiology, a Poisson regression model with two variance components. Bridge sampling and a recent improvement known as warp bridge sampling, importance sampling, and Chib's marginal likelihood calculation are all found to be effective. The relative advantages of the different approaches are discussed.

The R Package MitISEM: Efficient and Robust Simulation Procedures for Bayesian Inference

SSRN Electronic Journal, 2000

This paper presents the R package MitISEM (mixture of t by importance sampling weighted expectation maximization) which provides an automatic and flexible two-stage method to approximate a non-elliptical target density kernel-typically a posterior density kernel-using an adaptive mixture of Student t densities as approximating density. In the first stage a mixture of Student t densities is fitted to the target using an expectation maximization algorithm where each step of the optimization procedure is weighted using importance sampling. In the second stage this mixture density is a candidate density for efficient and robust application of importance sampling or the Metropolis-Hastings (MH) method to estimate properties of the target distribution. The package enables Bayesian inference and prediction on model parameters and probabilities, in particular, for models where densities have multi-modal or other non-elliptical shapes like curved ridges. These shapes occur in research topics in several scientific fields. For instance, analysis of DNA data in bio-informatics, obtaining loans in the banking sector by heterogeneous groups in financial economics and analysis of education's effect on earned income in labor economics. The package MitISEM provides also an extended algorithm, 'sequential Mi-tISEM', which substantially decreases computation time when the target density has to be approximated for increasing data samples. This occurs when the posterior or predictive density is updated with new observations and/or when one computes model probabilities using predictive likelihoods. We illustrate the MitISEM algorithm using three canonical statistical and econometric models that are characterized by several types of non-elliptical posterior shapes and that describe well-known data patterns in econometrics and finance. We show that MH using the candidate density obtained by MitISEM outperforms, in terms of numerical efficiency, MH using a simpler candidate, as well as the Gibbs sampler. The MitISEM approach is also used for Bayesian model comparison using predictive likelihoods.

Bayesian analyses : where to start and what to report

2014

Most researchers in the social and behavioral sciences will probably have heard of Bayesian statistics in which probability is defined differently compared to classical statistics (probability as the long-run frequency versus probability as the subjective experience of uncertainty). At the same time, many may be unsure of whether they should or would like to use Bayesian methods to answer their research questions (note: all types of conventional questions can also be addressed with Bayesian statistics) . As an attempt to track how popular the methods are, we searched all papers published in 2013 in the field of Psychology (source: Scopus), and we identified 79 empirical papers that used Bayesian methods (see e.g. Dalley, Pollet, & Vidal, 2013; Fife, Weaver, Cool, & Stump, 2013; Ng, Ntoumanis, ThøgersenNtoumani, Stott, & Hindle, 2013). Although this is less than 0.5% of the total number of papers published in this particular field, the fact that ten years ago this number was only 42 ...