Related papers: Bayesian sequential parameter estimation with a La…
Using a hierarchical construction, we develop methods for a wide and flexible class of models by taking a fully parametric approach to generalized linear mixed models with complex covariance dependence. The Laplace approximation is used to…
We propose a general method to carry out a valid Bayesian analysis of a finite-dimensional `targeted' parameter in the presence of a finite-dimensional nuisance parameter. We apply our methods to causal inference based on estimating…
We consider Bayesian inference problems with computationally intensive likelihood functions. We propose a Gaussian process (GP) based method to approximate the joint distribution of the unknown parameters and the data. In particular, we…
We consider the problem of estimating a variable number of parameters with a dynamic nature. A familiar example is finding the position of moving targets using sensor array observations. The problem is challenging in cases where either the…
Variational inference techniques based on inducing variables provide an elegant framework for scalable posterior estimation in Gaussian process (GP) models. Besides enabling scalability, one of their main advantages over sparse…
In this work the issue of Bayesian inference for stationary data is addressed. Therefor a parametrization of a statistically suitable subspace of the the shift-ergodic probability measures on a Cartesian product of some finite state space…
Bayesian modelling of dynamic systems must achieve a compromise between providing a complete mechanistic specification of the process while retaining the flexibility to handle those situations in which data is sparse relative to model…
In Bayesian inference, making deductions about a parameter of interest requires one to sample from or compute an integral against a posterior distribution. A popular method to make these computations cheaper in high-dimensional settings is…
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…
Various computational challenges arise when applying Bayesian inference approaches to complex hierarchical models. Sampling-based inference methods, such as Markov Chain Monte Carlo strategies, are renowned for providing accurate results…
The likelihood for the parameters of a generalized linear mixed model involves an integral which may be of very high dimension. Because of this intractability, many approximations to the likelihood have been proposed, but all can fail when…
Latent force models are a class of hybrid models for dynamic systems, combining simple mechanistic models with flexible Gaussian process (GP) perturbations. An extension of this framework to include multiplicative interactions between the…
Variational inference is a general framework to obtain approximations to the posterior distribution in a Bayesian context. In essence, variational inference entails an optimization over a given family of probability distributions to choose…
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…
This work considers estimation and forecasting in a multivariate, possibly high-dimensional count time series model constructed from a transformation of a latent Gaussian dynamic factor series. The estimation of the latent model parameters…
Approximate Bayesian computation methods can be used to evaluate posterior distributions without having to calculate likelihoods. In this paper we discuss and apply an approximate Bayesian computation (ABC) method based on sequential Monte…
Although linear regression models are fundamental tools in statistical science, the estimation results can be sensitive to outliers. While several robust methods have been proposed in frequentist frameworks, statistical inference is not…
Latent Gaussian process (GP) models are flexible probabilistic non-parametric function models. Vecchia approximations are accurate approximations for GPs to overcome computational bottlenecks for large data, and the Laplace approximation is…
We consider the problem of sampling from a product-of-experts-type model that encompasses many standard prior and posterior distributions commonly found in Bayesian imaging. We show that this model can be easily lifted into a novel latent…
Dynamic factor models are often estimated by point-estimation methods, disregarding parameter uncertainty. We propose a method accounting for parameter uncertainty by means of posterior approximation, using variational inference. Our…