Graduate Thesis Or Dissertation
 

Multi-factor information theory models and their industrial applications

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  • This dissertation treats information theory and its applications to the general area of decision making. Specifically, three areas are covered; (1) information theory applied to Bayesian analysis, (2) estimation using multi-factor information channel models, and (3) information theory applied to Markov chain analysis. A major portion of this dissertation concerns the concept of conditional information which occurs as the result of the transmission of information for an experiment (Z) when the outcomes of another experiment (Y) are known. The gain in information is measured by computing the difference between the information transmitted when one set of values is known for an experiment, and another set obtained when certain experimental parameters are allowed to vary. When only one set of experimental results is available, the information gain is computed as the difference between the transmitted information under the experimental conditions and the information transmitted assuming complete uncertainty. The latter is characterized by the condition which results when the events of the experiment are considered to be equally likely. The information theory technique appears to be especially useful in the area of sampling. The cost of gathering information may be balanced against management's willingness to pay for the information in order to arrive at an optimal number of events to sample for a particular experiment. Utilizing the concept of conditional information and information gain, estimates may be made by applying a multi-factor information channel analysis. In order to obtain the maximum amount of information from a sampling experiment, it may be desired to predict the strategies one should use. A case study is presented in which a research questionnaire was sent to prospective customers of several manufacturers of crushing and grinding equipment in an attempt to determine a particular company's standing with respect to its "image" and "progressiveness." The results of five specific questions were analyzed by the information theory approach in an attempt to predict the market shares for each of five companies. The information theory analysis showed that each of the five questions could be used independently as a market share predictor. This suggests that a person may subconsciously possess a pre-conceived opinion of a company which affects his answer to a specific question about that company. A matrix method based on the work of Muroga (1959) is presented for solving multi-factor information channel problems. In order to solve a problem of this type it is easiest to first ignore the existence of non-positive solutions and solve the information maximization equations accordingly. If a non-positive solution occurs, one or more restrictions may then be imposed in order to force only positive values on the final solution. Non-positive solutions indicate that the maximum information gain occurs outside the realm of permissible values. The solution, then, involves maximizing the information gain while insuring that the probability of each event of the experiment is positive. A multi-factor information theory analysis is applied to Markov chain problems in order to estimate at what point stochastic equilibrium occurs. This result is especially useful for computer simulations of Markov chains in which the equilibrium condition is of prime importance. By first employing the information theory analysis, the simulation may be started at or near stochastic equilibrium, thereby reducing the costs of unnecessary calculations during the transitional stages of the process. The information theory analysis shows that at least in some practical problems, stochastic equilibrium will not occur for a long period of time. In many applications, the transitional stages are of more interest than the steady-state conditions. Current research points to several areas for further investigation. Models to allow for the heterogeneity among consumers, means to identify and quantify the important factors in a multi-factor information theory model, and learning models offer unique challenges for future research. Also included in this dissertation is a computer program for solving any one-factor, two-factor or multi-factor information theory problem. A table of values for 1, 2, 3, or 4 levels of a one-factor model is also given.
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