Fuzzy Bayesian inference

Bayesian methods provide formalism for reasoning about partial beliefs under conditions of uncertainty. Given a set of exhaustive and mutually exclusive hypotheses, one can compute the probability of a hypothesis for a given evidence using the Bayesian inversion formula. In Bayesian's inference, the evidence could be a single atomic proposition or multi-valued one. For the multi-valued evidence, these values could be discrete, continuous, or fuzzy. For the continuous-valued evidence, the density functions used in the Bayesian inference are difficult to be determined in many practical situations. Complicated laboratory testing and advance statistical techniques are required to estimate the parameters of the assumed type of distribution. Using the proposed fuzzy Bayesian approach, a formulation is derived to estimate the density function from the conditional probabilities of the fuzzy-supported values. It avoids the complicated testing and analysis, and it does not require the assumption of a particular type of distribution. The estimated density function in our approach is proved to conform to two axioms in the theorem of probability. Example is provided in the paper.published_or_final_versio

Fuzzy reasoning in confidence evaluation of speech recognition

Confidence measures represent a systematic way to express reliability of speech recognition results. A common approach to confidence measuring is to take profit of the information that several recognition-related features offer and to combine them, through a given compilation mechanism , into a more effective way to distinguish between correct and incorrect recognition results. We propose to use a fuzzy reasoning scheme to perform the information compilation step. Our approach opposes the previously proposed ones because ours treats the uncertainty of recognition hypotheses in terms ofPeer ReviewedPostprint (published version

Frequentist tests for Bayesian models

Analogues of the frequentist chi-square and F tests are proposed for testing goodness-of-fit and consistency for Bayesian models. Simple examples exhibit these tests' detection of inconsistency between consecutive experiments with identical parameters, when the first experiment provides the prior for the second. In a related analysis, a quantitative measure is derived for judging the degree of tension between two different experiments with partially overlapping parameter vectors.Comment: 8 pages, 4 figures. Section 8 rewritten. Additional references. Accepted by Astronomy & Astrophysic

Ensemble evaluation of hydrological model hypotheses

It is demonstrated for the first time how model parameter, structural and data uncertainties can be accounted for explicitly and simultaneously within the Generalized Likelihood Uncertainty Estimation (GLUE) methodology. As an example application, 72 variants of a single soil moisture accounting store are tested as simplified hypotheses of runoff generation at six experimental grassland field-scale lysimeters through model rejection and a novel diagnostic scheme. The fields, designed as replicates, exhibit different hydrological behaviors which yield different model performances. For fields with low initial discharge levels at the beginning of events, the conceptual stores considered reach their limit of applicability. Conversely, one of the fields yielding more discharge than the others, but having larger data gaps, allows for greater flexibility in the choice of model structures. As a model learning exercise, the study points to a “leaking” of the fields not evident from previous field experiments. It is discussed how understanding observational uncertainties and incorporating these into model diagnostics can help appreciate the scale of model structural error

A Manifesto for the Equifinality Thesis.

This essay discusses some of the issues involved in the identification and predictions of hydrological models given some calibration data. The reasons for the incompleteness of traditional calibration methods are discussed. The argument is made that the potential for multiple acceptable models as representations of hydrological and other environmental systems (the equifinality thesis) should be given more serious consideration than hitherto. It proposes some techniques for an extended GLUE methodology to make it more rigorous and outlines some of the research issues still to be resolved

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

Economics