The usual approach to solving the Multiple Criteria Decision Making (MCDM) problem is by either using a weighted objective function based on each individual objective or by optimizing one objective while setting constraints on the others. These approaches try to find a point on the efficient frontier or the Pareto optimal set based on the preferences of the decision maker. Here, a new algorithm...

Animal models are generalized linear mixed models used in evolutionary biology and animal breeding to identify the genetic part of traits. Integrated Nested Laplace Approximation (INLA) is a methodology for making fast, nonsampling-based Bayesian inference for hierarchical Gaussian Markov models. In this article, we demonstrate that the INLA methodology can be used for many versions of Bayesian...

This paper presents an extension of Bayesian networks (BN) applied to reliability analysis. We developed a general methodology for modelling reliability of complex systems based on Bayesian networks. A reliability structure represented as a reliability block diagram is transformed to a Bayesian network representation, and with this, the reliability of the system can be obtained using probabilit...

This paper describes a structure of a standalone Intrusion Detection System (IDS) based on a large Bayesian network. To implement the IDS we develop the design methodology of large Bayesian networks. A small number of natural templates (idioms) are defined which make the design of Bayesian network easier. They are related to specific fragments of Bayesian networks representing the basic element...

Bayesian methodology continues to be widely used in statistical applications. As a result, it is increasingly important to introduce students to Bayesian thinking at early stages in their mathematics and statistics education. While many students in upper level probability courses can recite the differences in the Frequentist and Bayesian inferential paradigms, these students often struggle usin...

Inference in popular nonparametric Bayesian models typically relies on sampling or other approximations. This paper presents a general methodology for constructing novel tractable nonparametric Bayesian methods by applying the kernel trick to inference in a parametric Bayesian model. For example, Gaussian process regression can be derived this way from Bayesian linear regression. Despite the su...