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Generalized linear models (GLMs) -- such as logistic regression, Poisson regression, and robust regression -- provide interpretable models for diverse data types. Probabilistic approaches, particularly Bayesian ones, allow coherent…

Generating large-scale samples of stationary random fields is of great importance in the fields such as geomaterial modeling and uncertainty quantification. Traditional methodologies based on covariance matrix decomposition have the…

A method for sequential inference of the fixed parameters of a dynamic latent Gaussian models is proposed and evaluated that is based on the iterated Laplace approximation. The method provides a useful trade-off between computational…

Transformed Generalized Autoregressive Moving Average (TGARMA) models were recently proposed to deal with non-additivity, non-normality and heteroscedasticity in real time series data. In this paper, a Bayesian approach is proposed for…

Latent force models (LFMs) are hybrid models combining mechanistic principles with non-parametric components. In this article, we shall show how LFMs can be equivalently formulated and solved using the state variable approach. We shall also…

Studying conditional independence among many variables with few observations is a challenging task. Gaussian Graphical Models (GGMs) tackle this problem by encouraging sparsity in the precision matrix through $l_q$ regularization with…

Gaussian process-based latent variable models are flexible and theoretically grounded tools for nonlinear dimension reduction, but generalizing to non-Gaussian data likelihoods within this nonlinear framework is statistically challenging.…

Traditional spatio-temporal models for areal data typically begin with spatial structure imposed at the level of random effects and later extend to include temporal dynamics. We propose an alternative hierarchical modeling framework that…

The integrated nested Laplace approximation (INLA) method has become a popular approach for computationally efficient approximate Bayesian computation. In particular, by leveraging sparsity in random effect precision matrices, INLA is…

We put forward a new Bayesian modeling strategy for spatiotemporal count data that enables efficient posterior sampling. Most previous models for such data decompose logarithms of the response Poisson rates into fixed effects and spatial…

Coming up with Bayesian models for spatial data is easy, but performing inference with them can be challenging. Writing fast inference code for a complex spatial model with realistically-sized datasets from scratch is time-consuming, and if…

The general linear model (GLM) is a widely popular and convenient tool for estimating the functional brain response and identifying areas of significant activation during a task or stimulus. However, the classical GLM is based on a massive…

This article is concerned with learning and stochastic control in physical systems which contain unknown input signals. These unknown signals are modeled as Gaussian processes (GP) with certain parametrized covariance structures. The…

Generalizing robot trajectories from human demonstrations to new contexts remains a key challenge in Learning from Demonstration (LfD), particularly when only single-context demonstrations are available. We present a novel Gaussian Mixture…

The Gaussian process latent variable model (GP-LVM) provides a flexible approach for non-linear dimensionality reduction that has been widely applied. However, the current approach for training GP-LVMs is based on maximum likelihood, where…

Distributed lag non-linear models (DLNM) have gained popularity for modeling nonlinear lagged relationships between exposures and outcomes. When applied to spatially referenced data, these models must account for spatial dependence, a…

Geographic distribution shift arises when the distribution of locations on Earth in a training dataset is different from what is seen at inference time. Using standard empirical risk minimization (ERM) in this setting can lead to uneven…

The Laplace approximation (LA) has been proposed as a method for approximating the marginal likelihood of statistical models with latent variables. However, the approximate maximum likelihood estimators (MLEs) based on the LA are often…

Bayesian Generalized Nonlinear Models (BGNLM) offer a flexible nonlinear alternative to GLM while still providing better interpretability than machine learning techniques such as neural networks. In BGNLM, the methods of Bayesian Variable…

Generalized linear models (GLMs) are routinely used for modeling relationships between a response variable and a set of covariates. The simple form of a GLM comes with easy interpretability, but also leads to concerns about model…