Related papers: Computational methods for Bayesian model choice
This paper surveys some well-established approaches on the approximation of Bayes factors used in Bayesian model choice, mostly as covered in Chen et al. (2000). Our focus here is on methods that are based on importance sampling strategies…
This paper focuses on utilizing two different Bayesian methods to deal with a variety of toy problems which occur in data analysis. In particular we implement the Variational Bayesian and Nested Sampling methods to tackle the problems of…
In this paper we review the concepts of Bayesian evidence and Bayes factors, also known as log odds ratios, and their application to model selection. The theory is presented along with a discussion of analytic, approximate and numerical…
We develop a Bayesian approach for selecting the model which is the most supported by the data within a class of marginal models for categorical variables formulated through equality and/or inequality constraints on generalised logits…
Quality by design in pharmaceutical manufacturing hinges on computational methods and tools that are capable of accurate quantitative prediction of the design space. This paper investigates Bayesian approaches to design space…
Importance sampling is used to approximate Bayes' rule in many computational approaches to Bayesian inverse problems, data assimilation and machine learning. This paper reviews and further investigates the required sample size for…
This paper introduces a feasible and practical Bayesian method for unit root testing in financial time series. We propose a convenient approximation of the Bayes factor in terms of the Bayesian Information Criterion as a straightforward and…
The choice of the summary statistics used in Bayesian inference and in particular in ABC algorithms has bearings on the validation of the resulting inference. Those statistics are nonetheless customarily used in ABC algorithms without…
Bayesian inference affords scientists with powerful tools for testing hypotheses. One of these tools is the Bayes factor, which indexes the extent to which support for one hypothesis over another is updated after seeing the data. Part of…
Bayes Factors, the Bayesian tool for hypothesis testing, are receiving increasing attention in the literature. Compared to their frequentist rivals ($p$-values or test statistics), Bayes Factors have the conceptual advantage of providing…
Astronomers are often confronted with funky populations and distributions of objects: brighter objects are more likely to be detected; targets are selected based on colour cuts; imperfect classification yields impure samples. Failing to…
Bayesian model selection provides a powerful framework for objectively comparing models directly from observed data, without reference to ground truth data. However, Bayesian model selection requires the computation of the marginal…
We describe a new method for evaluating Bayes factors. The key idea is to introduce a hypermodel in which the competing models are components of a mixture distribution. Inference for the mixing probabilities then yields estimates of the…
Implementing Bayesian inference is often computationally challenging in applications involving complex models, and sometimes calculating the likelihood itself is difficult. Synthetic likelihood is one approach for carrying out inference…
The Bayes factor, the data-based updating factor of the prior to posterior odds of two hypotheses, is a natural measure of statistical evidence for one hypothesis over the other. We show how Bayes factors can also be used for parameter…
One of the main problems of importance sampling in Bayesian networks is representation of the importance function, which should ideally be as close as possible to the posterior joint distribution. Typically, we represent an importance…
Hypothesis testing and model choice are quintessential questions for statistical inference and while the Bayesian paradigm seems ideally suited for answering these questions, it faces difficulties of its own ranging from prior modelling to…
The measurement of the efficiency of an event selection is always an important part of the analysis of experimental data. The statistical techniques which are needed to determine the efficiency and its uncertainty are reviewed. Frequentist…
This introduction to Bayesian statistics presents the main concepts as well as the principal reasons advocated in favour of a Bayesian modelling. We cover the various approaches to prior determination as well as the basis asymptotic…
Computing the exact likelihood of data in large Bayesian networks consisting of thousands of vertices is often a difficult task. When these models contain many deterministic conditional probability tables and when the observed values are…