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The Linearized Laplace Approximation (LLA) has been recently used to perform uncertainty estimation on the predictions of pre-trained deep neural networks (DNNs). However, its widespread application is hindered by significant computational…

Latent Gaussian models (LGMs) are perhaps the most commonly used class of models in statistical applications. Nevertheless, in areas ranging from longitudinal studies in biostatistics to geostatistics, it is easy to find datasets that…

This paper develops methodology that provides a toolbox for routinely fitting complex models to realistic spatial point pattern data. We consider models that are based on log-Gaussian Cox processes and include local interaction in these by…

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…

Regression models for circular variables are less developed, since the concept of building a linear predictor from linear combinations of covariates and various random effects, breaks the circular nature of the variable. In this paper, we…

The linearized-Laplace approximation (LLA) has been shown to be effective and efficient in constructing Bayesian neural networks. It is theoretically compelling since it can be seen as a Gaussian process posterior with the mean function…

The Laplace approximation has been one of the workhorses of Bayesian inference. It often delivers good approximations in practice despite the fact that it does not strictly take into account where the volume of posterior density lies.…

Modeling longitudinal and survival data jointly offers many advantages such as addressing measurement error and missing data in the longitudinal processes, understanding and quantifying the association between the longitudinal markers and…

Gaussian latent variable models are a key class of Bayesian hierarchical models with applications in many fields. Performing Bayesian inference on such models can be challenging as Markov chain Monte Carlo algorithms struggle with the…

Robust time series analysis is an important subject in statistical modeling. Models based on Gaussian distribution are sensitive to outliers, which may imply in a significant degradation in estimation performance as well as in prediction…

Background: We aimed to design a Bayesian adaption trial through extensive simulations to determine values for key design parameters, demonstrate error rates, and establish the expected sample size. The complexity of the proposed outcome…

Cure models in survival analysis deal with populations in which a part of the individuals cannot experience the event of interest. Mixture cure models consider the target population as a mixture of susceptible and non-susceptible…

Statistical applications often involve the calculation of intractable multidimensional integrals. The Laplace formula is widely used to approximate such integrals. However, in high-dimensional or small sample size problems, the shape of the…

Generalized additive models (GAMs) are a well-established statistical tool for modeling complex nonlinear relationships between covariates and a response assumed to have a conditional distribution in the exponential family. In this article,…

Markov chain Monte Carlo (MCMC) methods remain the mainstay of Bayesian estimation of structural equation models (SEM), though they often incur a high computational cost. We present a bespoke approximate Bayesian approach to SEM, drawing on…

State-space models are used to describe and analyse dynamical systems. They are ubiquitously used in many scientific fields such as signal processing, finance and ecology to name a few. Particle filters are popular inferential methods used…

Variational autoencoders employ an amortized inference model to approximate the posterior of latent variables. However, such amortized variational inference faces two challenges: (1) the limited posterior expressiveness of fully-factorized…

Laplace approximations are a standard tool for computationally efficient inference in latent Gaussian models, but they fail for quantile regression with the asymmetric Laplace likelihood because the observed Hessian vanishes almost…

Using an asymmetric Laplace distribution, which provides a mechanism for Bayesian inference of quantile regression models, we develop a fully Bayesian approach to fitting single-index models in conditional quantile regression. In this work,…

Variational approaches to approximate Bayesian inference provide very efficient means of performing parameter estimation and model selection. Among these, so-called variational-Laplace or VL schemes rely on Gaussian approximations to…