Related papers: On the large-sample limits of some Bayesian model …
We explore the arguments for maximizing the `evidence' as an algorithm for model selection. We show, using a new definition of model complexity which we term `flexibility', that maximizing the evidence should appeal to both Bayesian and…
This paper considers data-driven chance-constrained stochastic optimization problems in a Bayesian framework. Bayesian posteriors afford a principled mechanism to incorporate data and prior knowledge into stochastic optimization problems.…
We develop an algorithm for model selection which allows for the consideration of a combinatorially large number of candidate models governing a dynamical system. The innovation circumvents a disadvantage of standard model selection which…
We introduce a new criterion to determine the order of an autoregressive model fitted to time series data. It has the benefits of the two well-known model selection techniques, the Akaike information criterion and the Bayesian information…
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…
Consider the Gaussian sequence model under the additional assumption that a fixed fraction of the means is known. We study the problem of variance estimation from a frequentist Bayesian perspective. The maximum likelihood estimator (MLE)…
The efficacy of family-based approaches to mixture model-based clustering and classification depends on the selection of parsimonious models. Current wisdom suggests the Bayesian information criterion (BIC) for mixture model selection.…
We consider the use of randomised forward models and log-likelihoods within the Bayesian approach to inverse problems. Such random approximations to the exact forward model or log-likelihood arise naturally when a computationally expensive…
In statistical modeling area, the Akaike information criterion AIC, is a widely known and extensively used tool for model choice. The {\phi}-divergence test statistic is a recently developed tool for statistical model selection. The…
Bayesian model selection poses two main challenges: the specification of parameter priors for all models, and the computation of the resulting Bayes factors between models. There is now a large literature on automatic and objective…
We consider the use of Bayesian information criteria for selection of the graph underlying an Ising model. In an Ising model, the full conditional distributions of each variable form logistic regression models, and variable selection…
Claeskens and Hjort (2003) constructed the focused information criterion (FIC) and developed frequentist model averaging methods using maximum likelihood estimators assuming the observations to be independent and identically distributed.…
We propose a new parameter-adaptive uncertainty-penalized Bayesian information criterion (UBIC) to prioritize the parsimonious partial differential equation (PDE) that sufficiently governs noisy spatial-temporal observed data with few…
We introduce a novel Information Criterion (IC), termed Learning under Singularity (LS), designed to enhance the functionality of the Widely Applicable Bayes Information Criterion (WBIC) and the Singular Bayesian Information Criterion…
Deep learning is renowned for its theory-practice gap, whereby principled theory typically fails to provide much beneficial guidance for implementation in practice. This has been highlighted recently by the benign overfitting phenomenon:…
Generalised Bayesian Inference (GBI) attempts to address model misspecification in a standard Bayesian setup by tempering the likelihood. The likelihood is raised to a fractional power, called the learning rate, which reduces its importance…
This paper presents a study of the large-sample behavior of the posterior distribution of a structural parameter which is partially identified by moment inequalities. The posterior density is derived based on the limited information…
After experimenting with a number of non-probabilistic methods for dealing with uncertainty many researchers reaffirm a preference for probability methods [1] [2], although this remains controversial. The importance of being able to form…
In objective Bayesian model selection, no single criterion has emerged as dominant in defining objective prior distributions. Indeed, many criteria have been separately proposed and utilized to propose differing prior choices. We first…
This paper studies the model selection problem in a large class of causal time series models, which includes both the ARMA or AR($\infty$) processes, as well as the GARCH or ARCH($\infty$), APARCH, ARMA-GARCH and many others processes. We…