Bayesian inference is a theoretically well-founded and conceptually simple approach to data analysis. The computations in practical problems are anything but simple though, and thus approximations are almost always a necessity. The topic of this thesis is approximate Bayesian inference and its applications in three intertwined problem domains. Variational Bayesian learning is one type of approx...

We consider the problem of deriving Bayesian inference procedures via the concept of relative surprise. The mathematical concept of surprise has been developed by I.J. Good in a long sequence of papers. We make a modiÞcation to this development that permits the avoidance of a serious defect; namely, the change of variable problem. We apply relative surprise to the development of estimation, hyp...

OBJECTIVE There is evidence of substantial subnational variation in the HIV epidemic. However, robust spatial HIV data are often only available at high levels of geographic aggregation and not at the finer resolution needed for decision making. Therefore, spatial analysis methods that leverage available data to provide local estimates of HIV prevalence may be useful. Such methods exist but have...

The principles behind the interface to continuous domain spatial models in the RINLA software package for R are described. The Integrated Nested Laplace Approximation (INLA) approach proposed by Rue, Martino, and Chopin (2009) is a computationally effective alternative to MCMC for Bayesian inference. INLA is designed for latent Gaussian models, a very wide and flexible class of models ranging f...

Parameter estimation is generally based upon the maximum likelihood approach and often involves regularization. Typically it is desired that the results be unbiased and of minimum variance. However, it is often better to accept biased estimates that have minimum mean square error. Bayesian inference is an attractive approach that achieves this goal and incorporates regularization automatically....

Meta-learning allows an intelligent agent to leverage prior learning episodes as a basis for quickly improving performance on a novel task. Bayesian hierarchical modeling provides a theoretical framework for formalizing meta-learning as inference for a set of parameters that are shared across tasks. Here, we reformulate the model-agnostic meta-learning algorithm (MAML) of Finn et al. (2017) as ...

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...

Bayesian inference is a vital tool for consistent manipulation of the uncertainty that is present in many military scenarios. However, in some highly complex environments, it is hard to write down an analytic form for the likelihood function that underlies Bayesian inference. Approximate Bayesian computation (ABC) algorithms address this difficulty by enabling one to proceed without analyticall...