Importance Sampling Squared for Bayesian Inference in Latent Variable Models

Bayesian inference for latent variable models

3 Abstract Bayes’ theorem is the cornerstone of statistical inference. It provides the tools for dealing with knowledge in an uncertain world, allowing us to explain observed phenomena through the refinement of belief in model parameters. At the heart of this elegant framework lie intractable integrals, whether in computing an average over some posterior distribution, or in determining the norm...

Adaptive Importance Sampling for Bayesian Inference in Gaussian Process Models

Gaussian process (GP) models are nowadays considered among the standard tools in modern control system engineering. They are routinely used for model-based control, timeseries prediction, modelling and estimation in engineering applications. While the underlying theory is completely in line with the principles of Bayesian inference, in practice this property is lost due to approximation steps i...

Mean-field variational approximate Bayesian inference for latent variable models

The ill-posed nature of missing variable models offers a challenging testing ground for new computational techniques. This is the case for the mean-field variational Bayesian inference. The behavior of this approach in the setting of the Bayesian probit model is illustrated. It is shown that the mean-field variational method always underestimates the posterior variance and, that, for small samp...

Bayesian Inference in Nonlinear and Relational Latent Variable Models

Statistical data analysis is becoming more and more important when growingamounts of data are collected in various fields of life. Automated learning al-gorithms provide a way to discover relevant concepts and representations that canbe further used in analysis and decision making. Graphical models are an important subclass of statistical machine learning thathave clear semantic...

Efficient Nonparametric Importance Sampling for Bayesian Inference