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We consider the estimation of parametric fractional time series models in which not only is the memory parameter unknown, but one may not know whether it lies in the stationary/invertible region or the nonstationary or noninvertible…

Within a Bayesian decision theoretic framework we investigate some asymptotic optimality properties of a large class of multiple testing rules. A parametric setup is considered, in which observations come from a normal scale mixture model…

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…

Implementing Bayesian inference is often computationally challenging in applications involving complex models, and sometimes calculating the likelihood itself is difficult. Synthetic likelihood is one approach for carrying out inference…

Preferential sampling is a common feature in geostatistics and occurs when the locations to be sampled are chosen based on information about the phenomena under study. In this case, point pattern models are commonly used as the probability…

In practical situations, most experimental designs often yield unbalanced data which have different numbers of observations per unit because of cost constraints, or missing data, etc. In this paper, we consider the Bayesian approach to…

Approximate Bayesian computation (ABC) methods have become increasingly prevalent of late, facilitating as they do the analysis of intractable, or challenging, statistical problems. With the initial focus being primarily on the practical…

The standard approach to Bayesian inference is based on the assumption that the distribution of the data belongs to the chosen model class. However, even a small violation of this assumption can have a large impact on the outcome of a…

Bayesian learning is built on an assumption that the model space contains a true reflection of the data generating mechanism. This assumption is problematic, particularly in complex data environments. Here we present a Bayesian…

In this paper, we consider Bayesian hypothesis testing for the balanced one-way random effects model. A special choice of the prior formulation for the ratio of variance components is shown to yield an explicit closed-form Bayes factor…

In Bayesian inference, an unknown measurement uncertainty is often quantified in terms of a Gamma distributed precision parameter, which is impractical when prior information on the standard deviation of the measurement uncertainty shall be…

Bayesian inference typically relies on specifying a parametric model that approximates the data-generating process. However, misspecified models can yield poor convergence rates and unreliable posterior calibration. Bayesian empirical…

Distribution regression has recently attracted much interest as a generic solution to the problem of supervised learning where labels are available at the group level, rather than at the individual level. Current approaches, however, do not…

Bayesian statistics has gained popularity in psychological research due to its intuitive uncertainty quantification and convenient information-updating rules. In many applications, however, prior distributions are introduced merely as…

Mathematical models are routinely applied to interpret biological data, with common goals that include both prediction and parameter estimation. A challenge in mathematical biology, in particular, is that models are often complex and…

Bayesian variable selection often assumes normality, but the effects of model misspecification are not sufficiently understood. There are sound reasons behind this assumption, particularly for large $p$: ease of interpretation, analytical…

Like mean, quantile and variance, mode is also an important measure of central tendency and data summary. Many practical questions often focus on "Which element (gene or file or signal) occurs most often or is the most typical among all…

Model misspecification is ubiquitous in data analysis because the data-generating process is often complex and mathematically intractable. Therefore, assessing estimation uncertainty and conducting statistical inference under a possibly…

Bayesian field theory denotes a nonparametric Bayesian approach for learning functions from observational data. Based on the principles of Bayesian statistics, a particular Bayesian field theory is defined by combining two models: a…

We consider the asymptotic behavior of posterior distributions and Bayes estimators based on observations which are required to be neither independent nor identically distributed. We give general results on the rate of convergence of the…