The probability approach in economic methodology: On the relation between Haavelmo's legacy and the methodology of economics (Revised version)

Economics

Book reviews

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45707/1/11336_2005_Article_BF02288937.pd

ARTIFICIAL INTELLIGENCE DIALECTS OF THE BAYESIAN BELIEF REVISION LANGUAGE

Rule-based expert systems must deal with uncertain data, subjective expert opinions, and inaccurate decision rules. Computer scientists and psychologists have proposed and implemented a number of belief languages widely used in applied systems, and their normative validity is clearly an important question, both on practical as well on theoretical grounds. Several well-know belief languages are reviewed, and both previous work and new insights into their Bayesian interpretations are presented. In particular, the authors focus on three alternative belief-update models the certainty factors calculus, Dempster-Shafer simple support functions, and the descriptive contrast/inertia model. Important "dialectsâ of these languages are shown to be isomorphic to each other and to a special case of Bayesian inference. Parts of this analysis were carried out by other authors; these results were extended and consolidated using an analytic technique designed to study the kinship of belief languages in general.Information Systems Working Papers Serie

Linguistic probability theory

In recent years probabilistic knowledge-based systems such as Bayesian networks and influence diagrams have come to the fore as a means of representing and reasoning about complex real-world situations. Although some of the probabilities used in these models may be obtained statistically, where this is impossible or simply inconvenient, modellers rely on expert knowledge. Experts, however, typically find it difficult to specify exact probabilities and conventional representations cannot reflect any uncertainty they may have. In this way, the use of conventional point probabilities can damage the accuracy, robustness and interpretability of acquired models. With these concerns in mind, psychometric researchers have demonstrated that fuzzy numbers are good candidates for representing the inherent vagueness of probability estimates, and the fuzzy community has responded with two distinct theories of fuzzy probabilities.This thesis, however, identifies formal and presentational problems with these theories which render them unable to represent even very simple scenarios. This analysis leads to the development of a novel and intuitively appealing alternative - a theory of linguistic probabilities patterned after the standard Kolmogorov axioms of probability theory. Since fuzzy numbers lack algebraic inverses, the resulting theory is weaker than, but generalises its classical counterpart. Nevertheless, it is demonstrated that analogues for classical probabilistic concepts such as conditional probability and random variables can be constructed. In the classical theory, representation theorems mean that most of the time the distinction between mass/density distributions and probability measures can be ignored. Similar results are proven for linguistic probabiliities.From these results it is shown that directed acyclic graphs annotated with linguistic probabilities (under certain identified conditions) represent systems of linguistic random variables. It is then demonstrated these linguistic Bayesian networks can utilise adapted best-of-breed Bayesian network algorithms (junction tree based inference and Bayes' ball irrelevancy calculation). These algorithms are implemented in ARBOR, an interactive design, editing and querying tool for linguistic Bayesian networks.To explore the applications of these techniques, a realistic example drawn from the domain of forensic statistics is developed. In this domain the knowledge engineering problems cited above are especially pronounced and expert estimates are commonplace. Moreover, robust conclusions are of unusually critical importance. An analysis of the resulting linguistic Bayesian network for assessing evidential support in glass-transfer scenarios highlights the potential utility of the approach

Survival analysis in fishery management

Economic methodology is revisited to address issues in fishery management, and survival analysis is suggested as an analytical tool to solve the uncertainty problem in evolutionary economics. Survival analysis can clarify in statistical terms the impacts of fishery regulation and economic and biological changes on the fisherman's final decisions of entry and exit from the fishery. Two types Of framework for survival analysis in fishery management are presented to show how this can be applied to fishery management. One type is the framework of the typical regression analysis for market competition and the other type is an extension to the dynamic fishery model. The evaluation of survival analysis in fishery management is provideded. An empirical application of the survival analysis, through the Icelandic trawl fishery data, is given to show how to apply the survival technique to fishery regulation

A Probabilistic Modelling Approach for Rational Belief in Meta-Epistemic Contexts

This work is part of the larger project INTEGRITY. Integrity develops a conceptual frame integrating beliefs with individual (and consensual group) decision making and action based on belief awareness. Comments and criticisms are most welcome via email. The text introduces the conceptual (internalism, externalism), quantitative (probabilism) and logical perspectives (logics for reasoning about probabilities by Fagin, Halpern, Megiddo and MEL by Banerjee, Dubois) for the framework