Related papers: From chi-squared to Bayesian model comparison and …
In the context of data modeling and comparisons between different fit models, Bayesian analysis calls that model best which has the largest evidence, the prior-weighted integral over model parameters of the likelihood function. Evidence…
The Bayesian data analysis framework has been proven to be a systematic and effective method of parameter inference and model selection for stochastic processes. In this work we introduce an information content model check which may serve…
In a thought-provoking paper, Efron (2011) investigated the merit and limitation of an empirical Bayes method to correct selection bias based on Tweedie's formula first reported by \cite{Robbins:1956}. The exceptional virtue of Tweedie's…
In this article the issues are discussed with the Bayesian approach, least-square fits, and most-likely fits. Trying to counter these issues, a method, based on weighted confidence, is proposed for estimating probabilities and other…
Bose-Einstein correlations in proton-proton collisions is an effective tool to study the space structure of the production amplitude. Usually rather simple parametrization of particle-emission distribution function has been used -…
A new empirical Bayes approach to variable selection in the context of generalized linear models is developed. The proposed algorithm scales to situations in which the number of putative explanatory variables is very large, possibly much…
Bayesian estimation is increasingly popular for performing model based inference to support policymaking. These data are often collected from surveys under informative sampling designs where subject inclusion probabilities are designed to…
A model-independent method for the analysis of the two-particle short-range correlations is presented, that can be utilized to describe e.g. Bose-Einstein (HBT), dynamical (ridge) or other correlation functions, that have a nearly L\'evy or…
Analogues of the frequentist chi-square and F tests are proposed for testing goodness-of-fit and consistency for Bayesian models. Simple examples exhibit these tests' detection of inconsistency between consecutive experiments with identical…
We introduce a flexible empirical Bayes approach for fitting Bayesian generalized linear models. Specifically, we adopt a novel mean-field variational inference (VI) method and the prior is estimated within the VI algorithm, making the…
The extraction of any physical information from quasielastic neutron scattering spectra is generally done by fitting a model to the data by means of chi-square minimization procedure. However, as pointed out by the pioneering work of D.S.…
Comparing competing mathematical models of complex natural processes is a shared goal among many branches of science. The Bayesian probabilistic framework offers a principled way to perform model comparison and extract useful metrics for…
This paper considers the objective comparison of stochastic models to solve inverse problems, more specifically image restoration. Most often, model comparison is addressed in a supervised manner, that can be time-consuming and partly…
Combining the outputs of multiple classifiers or experts into a single probabilistic classification is a fundamental task in machine learning with broad applications from classifier fusion to expert opinion pooling. Here we present a…
There has been much recent interest in modifying Bayesian inference for misspecified models so that it is useful for specific purposes. One popular modified Bayesian inference method is "cutting feedback" which can be used when the model…
A spectral approach to Bayesian inference is presented. It pursues the emulation of the posterior probability density. The starting point is a series expansion of the likelihood function in terms of orthogonal polynomials. From this…
The accuracy of least squares calibration using option premiums and particle filtering of price data to find model parameters is determined. Derivative models using exponential L\'evy processes are calibrated using regularized weighted…
Approximate Bayesian inference methods provide a powerful suite of tools for finding approximations to intractable posterior distributions. However, machine learning applications typically involve selecting actions, which -- in a Bayesian…
Bayesian Optimal Experimental Design (BOED) is a powerful tool to reduce the cost of running a sequence of experiments. When based on the Expected Information Gain (EIG), design optimization corresponds to the maximization of some…
We investigate a generalized empirical likelihood approach in a two-group setting where the constraints on parameters have a form of U-statistics. In this situation, the summands that consist of the constraints for the empirical likelihood…