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The behavior of many Bayesian models used in machine learning critically depends on the choice of prior distributions, controlled by some hyperparameters that are typically selected by Bayesian optimization or cross-validation. This…
Regularized system identification is the major advance in system identification in the last decade. Although many promising results have been achieved, it is far from complete and there are still many key problems to be solved. One of them…
We study a nonparametric Bayesian approach to linear inverse problems under discrete observations. We use the discrete Fourier transform to convert our model into a truncated Gaussian sequence model, that is closely related to the classical…
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…
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…
Beliefs inform the behavior of forward-thinking agents in complex environments. Recently, sequential Bayesian inference has emerged as a mechanism to study belief formation among agents adapting to dynamical conditions. However, we lack…
Bayesian inference is attractive for its coherence and good frequentist properties. However, it is a common experience that eliciting a honest prior may be difficult and, in practice, people often take an {\em empirical Bayes} approach,…
We investigate Bayesian non-parametric inference of the $\Lambda$-measure of $\Lambda$-coalescent processes with recurrent mutation, parametrised by probability measures on the unit interval. We give verifiable criteria on the prior for…
Bayesian inference and uncertainty quantification in a general class of non-linear inverse regression models is considered. Analytic conditions on the regression model $\{\mathscr G(\theta): \theta \in \Theta\}$ and on Gaussian process…
Bayesian neural networks (BNNs) have recently regained a significant amount of attention in the deep learning community due to the development of scalable approximate Bayesian inference techniques. There are several advantages of using…
Which neural networks are similar is a fundamental question for both machine learning and neuroscience. Here, it is proposed to base comparisons on the predictive distributions of linear readouts from intermediate representations. In…
Estimation of the covariance matrix for high-dimensional multivariate datasets is a challenging and important problem in modern statistics. In this paper, we focus on high-dimensional Gaussian DAG models where sparsity is induced on the…
Much is now known about the consistency of Bayesian updating on infinite-dimensional parameter spaces with independent or Markovian data. Necessary conditions for consistency include the prior putting enough weight on the correct…
We consider the problem of learning parameters of latent variable models from mixed (continuous and ordinal) data with missing values. We propose a novel Bayesian Gaussian copula factor (BGCF) approach that is consistent under certain…
We consider Bayesian sample size determination using a criterion that utilizes the first two moments of the expected posterior variance. We study the resulting sample size in dependence on the chosen prior and explore the success rate for…
This paper investigates the {\em nonasymptotic} properties of Bayes procedures for estimating an unknown distribution from $n$ i.i.d.\ observations. We assume that the prior is supported by a model $(\scr{S},h)$ (where $h$ denotes the…
In this paper, we derive a Bayesian model order selection rule by using the exponentially embedded family method, termed Bayesian EEF. Unlike many other Bayesian model selection methods, the Bayesian EEF can use vague proper priors and…
Bayesian model selection is a tool to decide whether the introduction of a new parameter is warranted by data. I argue that the usual sampling statistic significance tests for a null hypothesis can be misleading, since they do not take into…
We discuss Bayesian inference for parameters selected using the data. First, we provide a critical analysis of the existing positions in the literature regarding the correct Bayesian approach under selection. Second, we propose two types of…
We outline a Bayesian model-averaged meta-analysis for standardized mean differences in order to quantify evidence for both treatment effectiveness $\delta$ and across-study heterogeneity $\tau$. We construct four competing models by…