Related papers: Bayesian comparison of latent variable models: Con…
AIC is commonly used for model selection but the precise value of AIC has no direct interpretation. We are interested in quantifying a difference of risks between two models. This may be useful for both an explanatory point of view or for…
Consider a high-dimensional linear regression problem, where the number of covariates is larger than the number of observations and the interest is in estimating the conditional variance of the response variable given the covariates. A…
Real-life statistical samples are often plagued by selection bias, which complicates drawing conclusions about the general population. When learning causal relationships between the variables is of interest, the sample may be assumed to be…
This paper considers a challenging problem of identifying a causal graphical model under the presence of latent variables. While various identifiability conditions have been proposed in the literature, they often require multiple pure…
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…
The marginal likelihood or evidence in Bayesian statistics contains an intrinsic penalty for larger model sizes and is a fundamental quantity in Bayesian model comparison. Over the past two decades, there has been steadily increasing…
This manuscript is concerned with relating two approaches that can be used to explore complex dependence structures between categorical variables, namely Bayesian partitioning of the covariate space incorporating a variable selection…
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…
When performing regression or classification, we are interested in the conditional probability distribution for an outcome or class variable Y given a set of explanatoryor input variables X. We consider Bayesian models for this task. In…
Models for dependent data are distinguished by their targets of inference. Marginal models are useful when interest lies in quantifying associations averaged across a population of clusters. When the functional form of a covariate-outcome…
We consider the Bayesian analysis of models in which the unknown distribution of the outcomes is specified up to a set of conditional moment restrictions. The nonparametric exponentially tilted empirical likelihood function is constructed…
Factorized information criterion (FIC) is a recently developed approximation technique for the marginal log-likelihood, which provides an automatic model selection framework for a few latent variable models (LVMs) with tractable inference…
Model selection in mixed models based on the conditional distribution is appropriate for many practical applications and has been a focus of recent statistical research. In this paper we introduce the R-package cAIC4 that allows for the…
Unmeasured covariates constitute one of the important problems in causal inference. Even if there are some unmeasured covariates, some instrumental variable methods such as a two-stage residual inclusion (2SRI) estimator, or a…
We develop flexible methods of deriving variational inference for models with complex latent variable structure. By splitting the variables in these models into "global" parameters and "local" latent variables, we define a class of…
The causal discovery of Bayesian networks is an active and important research area, and it is based upon searching the space of causal models for those which can best explain a pattern of probabilistic dependencies shown in the data.…
The is no other model or hypothesis verification tool in Bayesian statistics that is as widely used as the Bayes factor. We focus on generative models that are likelihood-free and, therefore, render the computation of Bayes factors…
We provide a comprehensive overview of latent Markov (LM) models for the analysis of longitudinal categorical data. The main assumption behind these models is that the response variables are conditionally independent given a latent process…
In this work, we propose a modified Bayesian Information Criterion (BIC) specifically designed for mixture models and hierarchical structures. This criterion incorporates the determinant of the Hessian matrix of the log-likelihood function,…
The application of Bayesian inference for the purpose of model selection is very popular nowadays. In this framework, models are compared through their marginal likelihoods, or their quotients, called Bayes factors. However, marginal…