In this paper we prove that a recent Bayesian approximation of belief functions, the relative belief of singletons, meets a number of properties with respect to Dempster’s rule of combination which mirrors those satisfied by the relative plausibility of singletons. In particular, its operator commutes with Dempster’s sum of plausibility functions, while perfectly representing a plausibility fun...

Bayesian inference is a process of eliminating parameter values that do not explain the data and shifting posteriors towards values that do explain them. There is no room in it for ‘discovery’. I study belief processes that allow for discovery. I then ask when one can approximate discovery-induced beliefs by a Bayesian belief mechanism. This allows us to define optimal decisions and rational va...

PANSOMBUT, TATDOW. Advanced Learning Techniques for Improved Inference of Bayesian Belief Networks from Uncertain and High-dimensional Data. (Under the direction of Prof. Nagiza F. Samatova and Prof. Dennis R. Bahler.) A Bayesian Belief Network (BBN) is a powerful probabilistic learning model, it has been used successfully in many problem domains, such as medical diagnostics, computational biol...

The fuzzy belief Petri net we propose in this paper propagates fuzzy beliefs from observations at nodes that represent measured parameters to fuzzy beliefs of the truths of parameters at hidden and decision nodes. The fuzzy influences spread from the observation nodes throughout our new enhanced bidirectional fuzzy belief Petri net. Compared with Bayesian belief networks, it is simpler and fast...

Decision tree induction systems are being used for knowledge acquisition. Yet they have been developed without proper regard for the subjective Bayesian theory of inductive inference. This paper examines the problem tackled by these systems from the Bayesian view in order to interpret the systems and the heuristic methods they use. It is shown that decision tree systems depart from the usual Ba...

105 WORDS) This paper introduces the use of Bayesian Belief Networks for the analysis of survey data to investigate the relationship between land use and transportation. Bayesian statistics are used to reason under uncertainty and provide the basis for a methodological approach that does not require stringent a priori assumptions about the statistical model used to analyze the data. This study ...

This paper presents a Bayesian method for constructing Bayesian belief networks from a database of cases. Potential applications include computer-assisted hypothesis testing, automated scientific discovery, and automated construction of probabilistic expert systems. Results are presented of a preliminary evaluation of an algorithm for constructing a belief network from a database of cases. We r...

We describe an environment that considerably simplifies the process of generating Bayesian belief networks. The system has been implemented on readily available, inexpensive hardware, and provides clarity and high performance. We present an introduction to Bayesian belief networks, discuss algorithms for inference with these networks, and delineate the classes of problems that can be solved wit...

In a teaching and learning environment Bayesian network fits well because it can adjust its structure as per data presented to it. When a Bayesian network learns with a huge number of data, its belief value is updated even if the change in belief is not significant. This causes a problem when the user’s preference changes over time. The learning process cannot catch up rapidly enough to handle ...

In this letter we prove that the relative belief of singletons, one of the possible Bayesian approximations of a belief function, commutes with respect to Dempster’s orthogonal sum, and meets a number of properties which are indeed the duals of those met by the relative plausibility of singletons. This highlights a classification of Bayesian approximations in two families, according to the oper...