Bayesian and Dempster-Shafer fusion

The Kalman Filter is traditionally viewed as a prediction-correction filtering algorithm. In this work we show that it can be viewed as a Bayesian fusion algorithm and derive it using Bayesian arguments. We begin with an outline of Bayes theory, using it to discuss well-known quantities such as priors, likelihood and posteriors, and we provide the basic Bayesian fusion equation. We derive the Kalman Filter from this equation using a novel method to evaluate the Chapman-Kolmogorov prediction integral. We then use the theory to fuse data from multiple sensors. Vying with this approach is the Dempster-Shafer theory, which deals with measures of “belief”, and is based on the nonclassical idea of “mass” as opposed to probability. Although these two measures look very similar, there are some differences. We point them out through outlining the ideas of the Dempster-Shafer theory and presenting the basic Dempster-Shafer fusion equation. Finally we compare the two methods, and discuss the relative merits and demerits using an illustrative example.     

A Bayesian model for measurements on a set of instruments

A Bayesian model is proposed based on randomizing the systematic errors of the instruments. Conditions are identified under which the randomization reduces the expected bias in estimating a measured quantity. __________ Translated from Izmeritel’naya Tekhnika, No. 3, pp. 22–25, March, 2007.     

Reconstruction of a discontinuous function from a few fourier coefficients using bayesian estimation

The goal of this paper is the application of spectral methods to the numerical solution of conservation law equations. Spectral methods furnish estimates of the firstn Fourier coefficients of the solution. But since the solutions of conservation law equations can have discontinuities, the estimate of the solution by summing the firstn terms of the Fourier series will haveO(1/n) error, even if the Fourier coefficients are known to high accuracy. But if the solution could be accurately reconstructed from its Fourier coefficients, spectral methods could be used effectively in these problems. A method for doing this is to assume a probability distribution for functions. Functions which are smooth away from the discontinuity are assumed to be likely, and those which are not smooth away from the discontinuity are assumed to be unlikely. Then a reconstruction algorithm is chosen by minimizing the expected error over all algorithms. It is possible to put the smoothness assumptions mentioned earlier into an infinite-dimensional Gaussian probability distribution, and then the minimum-error algorithm is well-known and fairly simple to construct and apply. If the Fourier coefficients of the reconstructed function are known exactly, then this approach gives very good results. But when used with Fourier coefficients obtained from a spectral approximation to Burgers' equation, the results were much less impressive, probably because the coefficients were not known very accurately. It is possible to construct filters that reconstruct a function using Legendre or Chebyshev coefficients for information instead Fourier coefficients. It is found that the performance of these filters is similar to the Fourier case.     

Mixture of probability distributions as a basic component in simulating measurement accuracy

A stochastic model is proposed for a basic mechanism in the formation of uncertainties in physical quantity measurements. __________ Translated from Izmeritel'naya Tekhnika, No. 1, pp. 12–17, January, 2006.     

Simulation-based sequential analysis of Markov switching stochastic volatility models

We propose a simulation-based algorithm for inference in stochastic volatility models with possible regime switching in which the regime state is governed by a first-order Markov process. Using auxiliary particle filters we developed a strategy to sequentially learn about states and parameters of the model. The methodology is tested against a synthetic time series and validated with a real financial time series: the IBOVESPA stock index (São Paulo Stock Exchange).     

Complex system reliability modelling with Dynamic Object Oriented Bayesian Networks (DOOBN)

Nowadays, the complex manufacturing processes have to be dynamically modelled and controlled to optimise the diagnosis and the maintenance policies. This article presents a methodology that will help developing Dynamic Object Oriented Bayesian Networks (DOOBNs) to formalise such complex dynamic models. The goal is to have a general reliability evaluation of a manufacturing process, from its implementation to its operating phase. The added value of this formalisation methodology consists in using the a priori knowledge of both the system's functioning and malfunctioning. Networks are built on principles of adaptability and integrate uncertainties on the relationships between causes and effects. Thus, the purpose is to evaluate, in terms of reliability, the impact of several decisions on the maintenance of the system. This methodology has been tested, in an industrial context, to model the reliability of a water (immersion) heater system.     

Enhancing cognitive radio systems with robust reasoning

Cognitive radio systems dynamically reconfigure the algorithms and parameters they use, in order to adapt to the changing environment conditions. However, reaching proper reconfiguration decisions presupposes a way of knowing, with high enough assurance, the capabilities of the alternate configurations, especially in terms of achievable transmission capacity and coverage. The present paper addresses this problem, firstly, by specifying a complete process for extracting estimations of the capabilities of candidate configurations, in terms of transmission capacity and coverage, and, secondly, by enhancing these estimations with the employment of a machine learning technique. The technique is based on the use of Bayesian Networks, in conjunction with an effective learning and adaptation strategy, and aims at extracting and exploiting knowledge and experience, in order to reach robust (i.e. stable and reliable) estimations of the configurations' capabilities. Comprehensive results of the proposed method are presented, in order to validate its functionality. Copyright © 2007 John Wiley & Sons, Ltd.     

Decision support in early development phases—A case study from machine engineering

In the case study presented in this paper we consider early development phases of a mechanical product. We want to evaluate different concepts and decide which one(s) to pursue. A problem in early phases is that usually no test runs are available. In our case study, based on a standard, there are ways to compute the lifetime distributions of the components of the different concepts. Some parameters needed for these computations are not known precisely. Unfortunately, the lifetime distributions of the components are highly sensitive to these parameters. Our approach is to equip these parameters with distributions. These distributions would be called prior distributions in Bayesian terminology, but no update is possible since no test runs are available. Our approach implies that the distribution of the system lifetime for each concept is random, i.e. we get random elements in the space of lifetime distributions. Using Monte-Carlo simulations, we demonstrate several ways to compare the random lifetime distributions of the concepts. Some of these comparisons use stochastic orderings. We also introduce a new stochastic ordering which is particularly suitable for reliability purposes. Our case study, consisting of three scenarios, allows us to demonstrate some conclusions that can be reached.     

Can being scared cause tummy aches? Naive theories, ambiguous evidence, and preschoolers' causal inferences.

Causal learning requires integrating constraints provided by domain-specific theories with domain-general statistical learning. In order to investigate the interaction between these factors, the authors presented preschoolers with stories pitting their existing theories against statistical evidence. Each child heard 2 stories in which 2 candidate causes co-occurred with an effect. Evidence was presented in the form: AB→E; CA→E; AD→E; and so forth. In 1 story, all variables came from the same domain; in the other, the recurring candidate cause, A, came from a different domain (A was a psychological cause of a biological effect). After receiving this statistical evidence, children were asked to identify the cause of the effect on a new trial. Consistent with the predictions of a Bayesian model, all children were more likely to identify A as the cause within domains than across domains. Whereas 3.5-year-olds learned only from the within-domain evidence, 4- and 5-year-olds learned from the cross-domain evidence and were able to transfer their new expectations about psychosomatic causality to a novel task. (PsycINFO Database Record (c) 2010 APA, all rights reserved)