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State-space models are successfully used in many areas of science, engineering and economics to model time series and dynamical systems. We present a fully Bayesian approach to inference \emph{and learning} (i.e. state estimation and system…
Bayesian model selection provides a powerful framework for objectively comparing models directly from observed data, without reference to ground truth data. However, Bayesian model selection requires the computation of the marginal…
Gaussian process regression is a powerful Bayesian nonlinear regression method. Recent research has enabled the capture of many types of observations using non-Gaussian likelihoods. To deal with various tasks in spatial modeling, we benefit…
We review an established Bayesian sampling method called sampling/importance resampling and highlight situations in nuclear theory when it can be particularly useful. To this end we both analyse a toy problem and demonstrate realistic…
We develop a unifying framework for Bayesian nonparametric regression to study the rates of contraction with respect to the integrated $L_2$-distance without assuming the regression function space to be uniformly bounded. The framework is…
In Bayesian inference, the approximation of integrals of the form $\psi = \mathbb{E}_{F}{l(X)} = \int_{\chi} l(\mathbf{x}) d F(\mathbf{x})$ is a fundamental challenge. Such integrals are crucial for evidence estimation, which is important…
This paper proposes a novel Bayesian framework for solving Poisson inverse problems by devising a Monte Carlo sampling algorithm which accounts for the underlying non-Euclidean geometry. To address the challenges posed by the Poisson…
A new Riemannian geometry for the Compound Gaussian distribution is proposed. In particular, the Fisher information metric is obtained, along with corresponding geodesics and distance function. This new geometry is applied on a change…
We study location-scale mixture priors for nonparametric statistical problems, including multivariate regression, density estimation and classification. We show that a rate-adaptive procedure can be obtained if the prior is properly…
An important problem in shape analysis is to match configurations of points in space filtering out some geometrical transformation. In this paper we introduce hierarchical models for such tasks, in which the points in the configurations are…
We develop a Bayesian graphical modeling framework for functional data for correlated multivariate random variables observed over a continuous domain. Our method leads to graphical Markov models for functional data which allows the graphs…
Statistical estimates from survey samples have traditionally been obtained via design-based estimators. In many cases, these estimators tend to work well for quantities such as population totals or means, but can fall short as sample sizes…
Bayesian methods have been widely used in the last two decades to infer statistical properties of spatially variable coefficients in partial differential equations from measurements of the solutions of these equations. Yet, in many cases…
Observational astrophysics consists of making inferences about the Universe by comparing data and models. The credible intervals placed on model parameters are often as important as the maximum a posteriori probability values, as the…
Calibration or parameter identification is used with computational mechanics models related to observed data of the modeled process to find model parameters such that good similarity between model prediction and observation is achieved. We…
A nonparametric Bayes approach is proposed for the problem of estimating a sparse sequence based on Gaussian random variables. We adopt the popular two-group prior with one component being a point mass at zero, and the other component being…
Both Approximate Bayesian Computation (ABC) and composite likelihood methods are useful for Bayesian and frequentist inference, respectively, when the likelihood function is intractable. We propose to use composite likelihood score…
We develop scalable methods for producing conformal Bayesian predictive intervals with finite sample calibration guarantees. Bayesian posterior predictive distributions, $p(y \mid x)$, characterize subjective beliefs on outcomes of…
The geographically weighted regression (GWR) is a well-known statistical approach to explore spatial non-stationarity of the regression relationship in spatial data analysis. In this paper, we discuss a Bayesian recourse of GWR. Bayesian…
Several approaches have been proposed in the literature for clustering multivariate ordinal data. These methods typically treat missing values as absent information, rather than recognizing them as valuable for profiling population…