Abstract:
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.