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Nonlinear Mixed Effects models (NLME) models are widely used in pharmacometrics and related fields to analyze hierarchical and longitudinal data. However, as the number of parameters and random effects increases, traditional methods for…

In fitting a mixture of linear regression models, normal assumption is traditionally used to model the error and then regression parameters are estimated by the maximum likelihood estimators (MLE). This procedure is not valid if the normal…

Identifying signals that replicate across multiple studies is essential for establishing robust scientific evidence, yet existing methods for high-dimensional replicability analysis either rely on restrictive modeling assumptions, are…

Neural additive models (NAMs) enhance the transparency of deep neural networks by handling input features in separate additive sub-networks. However, they lack inherent mechanisms that provide calibrated uncertainties and enable selection…

Network meta-analysis (NMA) is widely used to compare multiple interventions simultaneously by synthesizing direct and indirect evidence. The general fixed or random effects contrast-based NMA model can be applied to different outcomes and…

In applications of Bayesian procedures, once a class of priors has been chosen, it may be tempting to fix the prior's hyperparameters from the data, in an empirical Bayes (EB) fashion, usually by their maximum marginal likelihood estimates…

In genome-wide association studies, hundreds of thousands of genetic features (genes, proteins, etc.) in a given case-control population are tested to verify existence of an association between each genetic marker and a specific disease. A…

In a mixture of linear regression model, the regression coefficients are treated as random vectors that may follow either a continuous or discrete distribution. We propose two Expectation-Maximization (EM) algorithms to estimate this prior…

We propose a new and computationally efficient algorithm for maximizing the observed log-likelihood for a multivariate normal data matrix with missing values. We show that our procedure based on iteratively regressing the missing on the…

The integrated nested Laplace approximation (INLA) for Bayesian inference is an efficient approach to estimate the posterior marginal distributions of the parameters and latent effects of Bayesian hierarchical models that can be expressed…

Mixtures of linear mixed models (MLMMs) are useful for clustering grouped data and can be estimated by likelihood maximization through the EM algorithm. The conventional approach to determining a suitable number of components is to compare…

Logistic linear mixed model is widely used in experimental designs and genetic analysis with binary traits. Motivated by modern applications, we consider the case with many groups of random effects and each group corresponds to a variance…

Ordinary differential equations are arguably the most popular and useful mathematical tool for describing physical and biological processes in the real world. Often, these physical and biological processes are observed with errors, in which…

We combine two important ideas in the analysis of large-scale genomics experiments (e.g. experiments that aim to identify genes that are differentially expressed between two conditions). The first is use of Empirical Bayes (EB) methods to…

The linearised Laplace method for estimating model uncertainty has received renewed attention in the Bayesian deep learning community. The method provides reliable error bars and admits a closed-form expression for the model evidence,…

Motivation: Microarray data has been recently been shown to be efficacious in distinguishing closely related cell types that often appear in the diagnosis of cancer. It is useful to determine the minimum number of genes needed to do such a…

Approximate inference methods like the Laplace method, Laplace approximations and variational methods, amongst others, are popular methods when exact inference is not feasible due to the complexity of the model or the abundance of data. In…

Mixture distributions with dynamic weights are an efficient way of modeling loss data characterized by heavy tails. However, maximum likelihood estimation of this family of models is difficult, mostly because of the need to evaluate…

Inverse Ising inference allows pairwise interactions of complex binary systems to be reconstructed from empirical correlations. Typical estimators used for this inference, such as Pseudo-likelihood maximization (PLM), are biased. Using the…

We investigate the choice of tuning parameters for a Bayesian multi-level group lasso model developed for the joint analysis of neuroimaging and genetic data. The regression model we consider relates multivariate phenotypes consisting of…