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A staple of Bayesian model comparison and hypothesis testing, Bayes factors are often used to quantify the relative predictive performance of two rival hypotheses. The computation of Bayes factors can be challenging, however, and this has…
The Rician distribution, a well-known statistical distribution frequently encountered in fields like magnetic resonance imaging and wireless communications, is particularly useful for describing many real phenomena such as signal process…
Bayesian learning is a powerful learning framework which combines the external information of the data (background information) with the internal information (training data) in a logically consistent way in inference and prediction. By…
Motivated by the statistical evaluation of complex computer models, we deal with the issue of objective prior specification for the parameters of Gaussian processes. In particular, we derive the Jeffreys-rule, independence Jeffreys and…
In this paper, we consider objective Bayesian inference of the generalized exponential distribution using the independence Jeffreys prior and validate the propriety of the posterior distribution under a family of structured priors. We…
We focus on variational inference in dynamical systems where the discrete time transition function (or evolution rule) is modelled by a Gaussian process. The dominant approach so far has been to use a factorised posterior distribution,…
We propose a framework for general Bayesian inference. We argue that a valid update of a prior belief distribution to a posterior can be made for parameters which are connected to observations through a loss function rather than the…
In this study we explore a new simulation scheme for partial differential equations known as Information Field Dynamics (IFD). Information field dynamics attempts to improve on existing simulation schemes by incorporating Bayesian field…
Bayesian filtering serves as the mainstream framework of state estimation in dynamic systems. Its standard version utilizes total probability rule and Bayes' law alternatively, where how to define and compute conditional probability is…
Post-data statistical inference concerns making probability statements about model parameters conditional on observed data. When a priori knowledge about parameters is available, post-data inference can be conveniently made from Bayesian…
Ising models originated in statistical physics and are widely used in modeling spatial data and computer vision problems. However, statistical inference of this model remains challenging due to intractable nature of the normalizing constant…
Forecasting techniques for assessing the power of future experiments to discriminate between theories or discover new laws of nature are of great interest in many areas of science. In this paper, we introduce a Bayesian forecasting method…
Bayesian methods are increasingly applied in these days in the theory and practice of statistics. Any Bayesian inference depends on a likelihood and a prior. Ideally one would like to elicit a prior from related sources of information or…
We show that the mathematical form of the information measure of Fisher's I for a Gibbs' canonical probability distribution (the most important one in statistical mechanics) incorporates important features of the intrinsic structure of…
Bayes' rule has enabled innumerable powerful algorithms of statistical signal processing and statistical machine learning. However, when model misspecifications exist in prior and/or data distributions, the direct application of Bayes' rule…
The random dot product graph is a popular model for network data with extensions that accommodate dynamic (time-varying) networks. However, two significant deficiencies exist in the dynamic random dot product graph literature: (1) no…
Bayes' theorem incorporates distinct types of information through the likelihood and prior. Direct observations of state variables enter the likelihood and modify posterior probabilities through consistent updating. Information in terms of…
We develop an efficient Bayesian sequential inference framework for factor analysis models observed via various data types, such as continuous, binary and ordinal data. In the continuous data case, where it is possible to marginalise over…
The formalism of quantum estimation theory with a specific focus on classical data postprocessing is applied to a two-level system driven by an external gyrating magnetic field. We employed both Bayesian and frequentist approaches to…
We study belief revision when information is represented by a set of probability distributions, or general information. General information extends the standard event notion while including qualitative information (A is more likely than B),…