Abductive Reasoning in Multiple Fault Diagnosis

Abductive reasoning involves generating an explanation for a given set of observations about the world. Abduction provides a good reasoning framework for many AI problems, including diagnosis, plan recognition and learning. This paper focuses on the use of abductive reasoning in diagnostic systems in which there may be more than one underlying cause for the observed symptoms. In exploring this topic, we will review and compare several different approaches, including Binary Choice Bayesian, Sequential Bayesian, Causal Model Based Abduction, Parsimonious Set Covering, and the use of First Order Logic. Throughout the paper we will use as an example a simple diagnostic problem involving automotive troubleshooting

Solving Two Sided Incomplete Information Games with Bayesian Iterative Conjectures Approach

This paper proposes a way to solve two (and multiple) sided incomplete information games which generally generates a unique equilibrium. The approach uses iterative conjectures updated by game theoretic and Bayesian statistical decision theoretic reasoning. Players in the games form conjectures about what other players want to do, starting from first order uninformative conjectures and keep updating with games theoretic and Bayesian statistical decision theoretic reasoning until a convergence of conjectures is achieved. The resulting convergent conjectures and the equilibrium (which is named Bayesian equilibrium by iterative conjectures) they supported form the solution of the game. The paper gives two examples which show that the unique equilibrium generated by this approach is compellingly intuitive and insightful. The paper also solves an example of a three sided incomplete information simultaneous game

Helping with inquiries: theory and practice in forensic science

This thesis investigates the reasoning practices of forensic scientists, with specific focus on the application of the Bayesian form of probabilistic reasoning to forensic science matters. Facilitated in part by the insights of evidence scholarship, Bayes Theorem has been advocated as an essential resource for the interpretation and evaluation of forensic evidence, and has been used to support the production of specific technologies designed to aid forensic scientists in these processes. In the course of this research I have explored the ways in which Bayesian reasoning can be regarded as a socially constructed collection of practices, despite proposals that it is simply a logical way to reason about evidence. My data are drawn from two case studies. In the first, I demonstrate how the Bayesian algorithms used for the interpretation of complex DNA profiles are themselves elaborately constructed devices necessary for the anchoring of scientific practice to forensic contexts. In the second case study, an investigation of a more generalised framework of forensic investigation known as the Case Assessment and Interpretation (CAI) model, I show how the enactment of Bayesian reasoning is dependent on a series of embodied, experiential and intersubjective knowledge-forming activities. Whilst these practices may seem to be largely independent of theoretical representations of Bayesian reasoning, they are nonetheless necessary to bring the latter into being. This is at least partially due to the ambiguities and liminalities encountered in the process of applying Bayesianism to forensic investigation, and also may result from the heavy informational demands placed on the reasoner. I argue that these practices, or 'forms of Bayes', are necessary in order to negotiate areas of ontological uncertainty. The results of this thesis therefore challenge prevailing conceptions of Bayes Theorem as a universal, immutable signifier, able to be put to work unproblematically in any substantive domain, Instead, I have been able to highlight the diverse range of practices required for 'Bayesian' reasoners to negotiate the sociomaterial contingencies exposed in the process of its application

Bayesian Theory of Games: A Statistical Decision Theoretic Based Analysis of Strategic Interactions

Bayesian rational prior equilibrium requires agent to make rational statistical predictions and decisions, starting with first order non informative prior and keeps updating with statistical decision theoretic and game theoretic reasoning until a convergence of conjectures is achieved. The main difference between the Bayesian theory of games and the current games theory are: I. It analyzes a larger set of games, including noisy games, games with unstable equilibrium and games with double or multiple sided incomplete information games which are not analyzed or hardly analyzed under the current games theory. II. For the set of games analyzed by the current games theory, it generates far fewer equilibria and normally generates only a unique equilibrium and therefore functions as an equilibrium selection and deletion criterion and, selects the most common sensible and statistically sound equilibrium among equilibria and eliminates insensible and statistically unsound equilibria. III. It differentiates between simultaneous move and imperfect information. The Bayesian theory of games treats sequential move with imperfect information as a special case of sequential move with observational noise term. When the variance of the noise term approaches its maximum such that the observation contains no informational value, there is imperfect information (with sequential move). IV. It treats games with complete and perfect information as special cases of games with incomplete information and noisy observation whereby the variance of the prior distribution function on type and the variance of the observation noise term tend to zero. Consequently, there is the issue of indeterminacy in statistical inference and decision making in these games as the equilibrium solution depends on which variances tends to zero first. It therefore identifies equilibriums in these games that have so far eluded the classical theory of games.Games Theory, Bayesian Statistical Decision Theory, Prior Distribution Function, Conjectures, Subjective Probabilities

Uncovering deterministic causal structures: a Boolean approach

While standard procedures of causal reasoning as procedures analyzing causal Bayesian networks are custom-built for (non-deterministic) probabilistic structures, this paper introduces a Boolean procedure that uncovers deterministic causal structures. Contrary to existing Boolean methodologies, the procedure advanced here successfully analyzes structures of arbitrary complexity. It roughly involves three parts: first, deterministic dependencies are identified in the data; second, these dependencies are suitably minimalized in order to eliminate redundancies; and third, one or—in case of ambiguities—more than one causal structure is assigned to the minimalized deterministic dependencie