Related papers: On the marginal likelihood and cross-validation
External information, such as prior information or expert opinions, can play an important role in the design, analysis and interpretation of clinical trials. However, little attention has been devoted thus far to incorporating external…
The future predictive performance of a Bayesian model can be estimated using Bayesian cross-validation. In this article, we consider Gaussian latent variable models where the integration over the latent values is approximated using the…
Evaluating the predictive performance of a statistical model is commonly done using cross-validation. Among the various methods, leave-one-out cross-validation (LOOCV) is frequently used. Originally designed for exchangeable observations,…
Two procedures for checking Bayesian models are compared using a simple test problem based on the local Hubble expansion. Over four orders of magnitude, p-values derived from a global goodness-of-fit criterion for posterior probability…
In applications of Bayesian procedures, once a class of priors has been chosen, it may be tempting to fix the prior's hyperparameters from the data, in an empirical Bayes (EB) fashion, usually by their maximum marginal likelihood estimates…
In this paper, we present a method for computing the marginal likelihood, also known as the model likelihood or Bayesian evidence, from Markov Chain Monte Carlo (MCMC), or other sampled posterior distributions. In order to do this, one…
Bayesian supervised predictive classifiers, hypothesis testing, and parametric estimation under Partition Exchangeability are implemented. The two classifiers presented are the marginal classifier (that assumes test data is i.i.d.) next to…
The normalized maximum likelihood (NML) is a recent penalized likelihood that has properties that justify defining the amount of discrimination information (DI) in the data supporting an alternative hypothesis over a null hypothesis as the…
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…
The standard Bayesian Information Criterion (BIC) is derived under regularity conditions which are not always satisfied by the graphical models with hidden variables. In this paper we derive the BIC score for Bayesian networks in the case…
Posterior distributions often feature intractable normalizing constants, called marginal likelihoods or evidence, that are useful for model comparison via Bayes factors. This has motivated a number of methods for estimating ratios of…
Cross-validation is one of the most popular model selection methods in statistics and machine learning. Despite its wide applicability, traditional cross validation methods tend to select overfitting models, due to the ignorance of the…
The (relevance) weighted likelihood was introduced to formally embrace a variety of statistical procedures that trade bias for precision. Unlike its classical counterpart, the weighted likelihood combines all relevant information while…
In computational mechanics, multiple models are often present to describe a physical system. While Bayesian model selection is a helpful tool to compare these models using measurement data, it requires the computationally expensive…
In Bayesian statistics, the marginal likelihood is used for model selection and averaging, yet it is often challenging to compute accurately for complex models. Approaches such as bridge sampling, while effective, may suffer from issues of…
In Bayesian accelerated life testing, the most used tool for model comparison is the deviance information criterion. An alternative and more formal approach is to use Bayes factors to compare models. However, Bayesian accelerated life…
We investigate the utility to computational Bayesian analyses of a particular family of recursive marginal likelihood estimators characterized by the (equivalent) algorithms known as "biased sampling" or "reverse logistic regression" in the…
Inference in Bayesian statistics involves the evaluation of marginal likelihood integrals. We present algebraic algorithms for computing such integrals exactly for discrete data of small sample size. Our methods apply to both uniform priors…
Bayes factors for composite hypotheses have difficulty in encoding vague prior knowledge, as improper priors cannot be used and objective priors may be subjectively unreasonable. To address these issues I revisit the posterior Bayes factor,…
In the hypothesis testing framework, p-value is often computed to determine rejection of the null hypothesis or not. On the other hand, Bayesian approaches typically compute the posterior probability of the null hypothesis to evaluate its…