An overview of the essential differences and similarities of system identification techniques

Information is given in the form of outlines, graphs, tables and charts. Topics include system identification, Bayesian statistical decision theory, Maximum Likelihood Estimation, identification methods, structural mode identification using a stochastic realization algorithm, and identification results regarding membrane simulations and X-29 flutter flight test data

Testing the Bayesian brain hypothesis in visual perception

Dissertation supervisor: Dr. Jeffrey N. Rouder.Includes vita.Bayesian ideal observer theory describes perception as an ideal integration of sensory information with prior knowledge to produce optimal responses. Bayesian ideal perception models are popular in sensory domains; however, these models often prove unfalsifiable because of excessive distributional assumptions and post-hoc estimation of participant beliefs. Three visual perception tasks were designed to test Bayesian ideal observer theory under minimal assumptions using the Bayesian Decision Theory framework. Prior distributions of stimuli were specified, likelihoods were manipulated across four stimulus reliability levels, and loss functions were established so that participants could choose posterior point estimates which minimize loss. In each experiment, a Bayesian ideal observer model was fit against a Bayesian posterior matching model (adapted from the probability matching phenomenon) and one or more non-Bayesian mixture models. Results from two experiments in which participants were making location-based judgments overwhelmingly supported the posterior matching models. Data from a third experiment in which participants made estimations about the number of items in an array were fit best by a non-Bayesian mixture model. Overall, Bayesian ideal observer theory was not supported in three experiments of visual perception.Includes bibliographical references (pages 128-134)

Decision-theoretical formulation of the calibration problem

The choice of calibration policy is of basic importance in analytical chemistry. A prototype of the practical calibration problem is formulated as a mathematical task and a Bayesian solution of the resulting decision problem is presented. The optimum feedback calibration policy can then be found by dynamic programming. The underlying parameter estimation and filtering are solved by updating relevant conditional distributions. In this way: the necessary information is specified (for instance, the need for knowledge of the probability distribution of unknown samples is clearly recognized as the conceptually unavoidable informational source); the relationship of the information gained from a calibration experiment to the ultimate goal of calibration, i.e., to the estimation of unknown samples, is explained; an ideal solution is given which can serve for comparing various ways of calibration; and a consistent and conceptually simple guideline is given for using decision theory when solving problems of analytical chemistry containing uncertain data. The abstract formulation is systematically illustrated by an example taken from gas chromatography

Value of Information: Sensitivity Analysis and Research Design in Bayesian Evidence Synthesis.

Suppose we have a Bayesian model that combines evidence from several different sources. We want to know which model parameters most affect the estimate or decision from the model, or which of the parameter uncertainties drive the decision uncertainty. Furthermore, we want to prioritize what further data should be collected. These questions can be addressed by Value of Information (VoI) analysis, in which we estimate expected reductions in loss from learning specific parameters or collecting data of a given design. We describe the theory and practice of VoI for Bayesian evidence synthesis, using and extending ideas from health economics, computer modeling and Bayesian design. The methods are general to a range of decision problems including point estimation and choices between discrete actions. We apply them to a model for estimating prevalence of HIV infection, combining indirect information from surveys, registers, and expert beliefs. This analysis shows which parameters contribute most of the uncertainty about each prevalence estimate, and the expected improvements in precision from specific amounts of additional data. These benefits can be traded with the costs of sampling to determine an optimal sample size. Supplementary materials for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement

An Application of Statistical Decision Theory to Farm Management in Sevier County, Utah

The major purpose of this study is to present selected empirical results of a study employing decision-making theory as a framework for considering decision making under risk. The particular problem involves choices between alternative crop rotations for Sevier County farmers. The study demonstrates the usefulness of the Bayesian theory that gives more than a point estimation. A multiple regression model using two linear terms was employed to determine the influence of s now pack and reservoir storage on water availability for irrigation purposes during July, August, and September. The Bayesian approach was employed. The optima l action or decision was first determined where only the knowledge of the a priori probabilities of the states of nature was available. Optimal strategies were then determined where run-off observation was available and the a posteriori probabilities of the states of nature were determined. Study results indicate that the expected value of the additional information is substantial and come out very close to the expected value of a perfect predictor and higher than the expected value of t he no data problems . It means that the Bayesian approach gives more than a point estimation and is useful for farm management decision making under risk