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The generalized linear mixed model (GLMM) is widely used for analyzing correlated data, particularly in large-scale biomedical and social science applications. Scalable Bayesian inference for GLMMs is challenging because the marginal…

We present a sequential Monte Carlo sampler algorithm for the Bayesian analysis of generalised linear mixed models (GLMMs). These models support a variety of interesting regression-type analyses, but performing inference is often extremely…

As the amount and complexity of available data increases, the need for robust statistical learning becomes more pressing. To enhance resilience against model misspecification, the generalized posterior inference method adjusts the…

We propose a random-effects approach to missing values for generalized linear mixed model (GLMM) analysis. The method converts a GLMM with missing covariates to another GLMM without missing covariates. The standard GLMM analysis tools for…

Exact MLE for generalized linear mixed models (GLMMs) is a long-standing problem unsolved until today. The proposed research solves the problem. In this problem, the main difficulty is caused by intractable integrals in the likelihood…

In the realm of statistical learning, the increasing volume of accessible data and increasing model complexity necessitate robust methodologies. This paper explores two branches of robust Bayesian methods in response to this trend. The…

Sliced Inverse Regression (SIR) is an effective method for dimension reduction in high-dimensional regression problems. The original method, however, requires the inversion of the predictors covariance matrix. In case of collinearity…

Ill-posed linear inverse problems arise frequently in various applications, from computational photography to medical imaging. A recent line of research exploits Bayesian inference with informative priors to handle the ill-posedness of such…

This paper deals with some computational aspects in the Bayesian analysis of statistical models with intractable normalizing constants. In the presence of intractable normalizing constants in the likelihood function, traditional MCMC…

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…

Estimating the predictive uncertainty of a Bayesian learning model is critical in various decision-making problems, e.g., reinforcement learning, detecting adversarial attack, self-driving car. As the model posterior is almost always…

The advantages of sequential Monte Carlo (SMC) are exploited to develop parameter estimation and model selection methods for GARCH (Generalized AutoRegressive Conditional Heteroskedasticity) style models. It provides an alternative method…

By formulating the inverse problem of partial differential equations (PDEs) as a statistical inference problem, the Bayesian approach provides a general framework for quantifying uncertainties. In the inverse problem of PDEs, parameters are…

Discrete state spaces represent a major computational challenge to statistical inference, since the computation of normalisation constants requires summation over large or possibly infinite sets, which can be impractical. This paper…

The statistical inverse problem of estimating the probability distribution of an infinite-dimensional unknown given its noisy indirect observation is studied in the Bayesian framework. In practice, one often considers only…

The Bayesian approach has proved to be a coherent approach to handle ill posed Inverse problems. However, the Bayesian calculations need either an optimization or an integral calculation. The maximum a posteriori (MAP) estimation requires…

Generalized linear mixed models (GLMMs) are commonly used to analyze correlated discrete or continuous response data. In Bayesian GLMMs, the often-used improper priors may yield undesirable improper posterior distributions. Thus, verifying…

In this work, we adopt a general framework based on the Gibbs posterior to update belief distributions for inverse problems governed by partial differential equations (PDEs). The Gibbs posterior formulation is a generalization of standard…

While the Matrix Generalized Inverse Gaussian ($\mathcal{MGIG}$) distribution arises naturally in some settings as a distribution over symmetric positive semi-definite matrices, certain key properties of the distribution and effective ways…

We propose a sequential Monte Carlo (SMC) method to efficiently and accurately compute cut-Bayesian posterior quantities of interest, variations of standard Bayesian approaches constructed primarily to account for model misspecification. We…