We propose a novel framework for performing quantitative Bayesian inference based on qualitative knowledge. Here, we focus on the treatment in the case of inconsistent qualitative knowledge. A hierarchical Bayesian model is proposed for integrating inconsistent qualitative knowledge by calculating a prior belief distribution based on a vector of knowledge features. Each inconsistent knowledge c...

In this paper, Spike-and-Slab Dirichlet Process (SS-DP) priors are introduced and discussed for non-parametric Bayesian modeling and inference, especially in the mixture models context. Specifying a spike-and-slab base measure for DP priors combines the merits of Dirichlet process and spike-and-slab priors and serves as a flexible approach in Bayesian model selection and averaging. Computationa...

We propose a general MCMC method for Bayesian inference in logic-based probabilistic modeling. It covers a broad class of generative models including Bayesian networks and PCFGs. The idea is to generalize an MCMC method for PCFGs to the one for a Turing-complete probabilistic modeling language PRISM in the context of statistical abduction where parse trees are replaced with explanations. We des...

Bayesian approach using nonhomogeneous Poisson process is considered for modeling software reliability problems. A generalized gamma and lognormal order statistics models are considered to model epochs of the failures of software. Metropolis algorithms along with Gibbs steps are proposed to perform the Bayesian inference of such models. Some Bayesian model diagnostics are developed and incorpor...

This paper explores the application of Bayesian probabilistic modeling to issues of music cognition and music theory. The main concern is with the problem of key-finding: the process of inferring the key from a pattern of notes. The Bayesian perspective leads to a simple, elegant, and highly effective model of this process; the same approach can also be extended to other aspects of music percep...

Stochastic biomechanical modeling has become a useful tool most commonly implemented using Monte Carlo simulation, advanced mean value theorem, or Markov chain modeling. Bayesian networks are a novel method for probabilistic modeling in artificial intelligence, risk modeling, and machine learning. The purpose of this study was to evaluate the suitability of Bayesian networks for biomechanical m...

We present a practical implementation of a fully unsupervised disease progression model [10]. The implementation utilizes all new components we developed for generic use in Bayesian disease progression modeling. It improves upon [10] by providing a more informative fully Bayesian approach and a faster inference algorithm. The implementation is completely built on the pyMC3 open-source library m...

Modeling causal dependencies in complex or time-dependent domains often demands cyclic dependencies. Such cycles arise from local points of views on dependencies where no singular causality is identifiable, i.e., roles of causes and effects are not universally identifiable. Modeling causation instead of correlation is of utmost importance, which is why Bayesian networks are frequently used to r...

Inverse problems have been often considered ill-posed, i.e., the statement of the problem does not thoroughly constrain the solution space. In this paper we take advantage of this lack of information by adding additional informative constraints to the problem solution using Bayesian methodology. Bayesian modeling gains much of its power from its ability 2 to isolate and incorporate causal model...

We develop a dynamic Bayesian beta model for modeling and forecasting single time series of proportions. This work is related to the class of the so called dynamic generalized linear models (DGLM). We use non-conjugate priors and some forms of approximate Bayesian analysis, including Linear Bayesian estimation. Some applications to both real and simulated data are provided.