This thesis considers two distinct aspects of the empirical Bayes decision problem. The first aspect considered is the problem or point estimation and hypothesis testing. The second aspect considered is that of estimating the prior distribution and then the estimation of posterior distribution and confidence intervals. In the first aspect considered we assume that there exists an unobservable parameter space 𝔏={λ} on which is defined a prior distribution G(λ). For any action a from a class A there is a loss, L(a,λ) ≥ 0, which we incur when we take action a and the true parameter is λ. There exists an observable random vector X̰=(X₁,...X_k), k ≥ 1, which admits of a sufficient statistic T=T(X̰) for λ. The conditional density function (c.d.f.) of T is f(t(λ). We assume that there exists a decision function δ_ɢ(t) from a class D (δεD) implies that δ(t)εA for all t) such that the expected loss, R(δ,G) = ∫∫L(δ(t),λ) f(t|λ)dtdG(λ), is minimized. This minimizing decision function is called a Bayes decision function and the associated minimum expected loss is called the Bayes risk R(G). We assume that there exists a sequence or independent identically distributed random vectors <(X₁,...,X_k,λ)_n> (or <(T,λ)_n >) with each element distributed independently of and identically to (X₁,...,X_𝗄,λ) (or (T,λ). The problem is to construct sequential decision functions, δ_n(t;t₁,t₂,...,t_n)=δ_n(t), which are asymptotically optimal (a.o.), that is which satisfy lim_n→∞ R(δ_n(T),G) = R(G). We extend a theorem or Robbins (Ann. Math. Statist. 35,1-20) to provide a simple method for the construction or a.o. point estimators of λ with a squared-error loss function when f(t|λ) is continuous. We extend the results or Samuel (Ann. Math. Statist., 34, 1370-1385) to provide a.o. tests of certain parametric hypotheses with loss functions which are polynomials in λ. The c.d.f.'s which are considered are all continuous and include some or those of the exponential class and some whose range depends upon the parameter. This latter result is applied to the problem or the one-sided truncation of density functions. The usefulness of all or these results is predicated upon the tact that the forms or the Bayes decision functions can be determined in such a way that the construction or the analogous a.o. empirical Bayes decision functions is simple. Two manipulative techniques, which provide the desired forms of the Bayes decision function, are introduced. These techniques are applied to several examples, and a.o. decision functions are defined. To estimate the prior distribution we assume that there exists a sequence of independent identically distributed random vectors <(T,λ)_n>) each distributed according to the joint density function J(t,λ)=G(λ)F(t|λ). The sequence <λ_n> of <(T,λ)_n> is unobservable. G(λ) belongs to a subclass g of a class G_p(g) and F(t|λ) belongs to a class F. G_p(g) is determined by the conditions: (a) G(λ) is absolutely continuous with with respect to Lebesgum measure; (b) its density function, g(λ), is determined completely by a continuous function of its first p moments, p ≥ 2; (c) the first p moments are finite; (d) the subclass g contains those density functions which are determined by a particular known continuous function. The class F is determined by the condition that there exist known functions h_𝗸(.), k=1,...,p, such that E[h_𝗸(T)|λ] = λᵏ. Under these conditions we construct an estimate, Gn(λ), of G(λ) such that lim_n→∞ E[(G_n(λ) - G(λ))²] = 0, a.e.λ. Estimates of the posterior distribution and of confidence intervals are constructed using G_n(λ). / Ph. D.

This dissertation explores and analyzes the performance of several Bayesian anytime inference algorithms for dynamic influence diagrams. These algorithms are compared on the On-Line Maintenance Agent testbed, a software artifact permitting comparison of dynamic reasoning algorithms used by an agent on a variety of simulated maintenance and monitoring tasks. Analysis of their performance suggests that a particular algorithmic property, which I term sampling kurtosis, may be responsible for successful reasoning in the tested half-adder domain. A new algorithm is devised and evaluated which permits testing of sampling kurtosis, revealing that it may not be the most significant algorithm property but suggesting new lines of inquiry. Peculiarities in the observed data lead to a detailed analysis of agent-simulator interaction, resulting in an equation model and a Stochastic Automata Network model for a random action algorithm. The model analyses are extended to show that some of the anytime reasoning algorithms perform remarkably near optimally. The research suggests improvements for the design and development of reasoning testbeds. / Graduation date: 2002

Thesis (Ph. D.)--Ohio State University, 2006. / Title from first page of PDF file. Includes bibliographical references (p. 126-130).

Thesis (Ph. D.)--Ohio State University, 2006. / Title from first page of PDF file. Includes bibliographical references (p. 94-103).

Thesis (Ph. D.)--Ohio State University, 2004. / Title from first page of PDF file. Document formatted into pages; contains xii, 138 p.; also includes graphics. Includes abstract and vita. Advisor: Greg M. Allenby, Dept. of Business Admnistration. Includes bibliographical references (p. 134-138).

Thesis (Ph. D.)--University of Missouri-Columbia, 2002. / Typescript. Vita. Includes bibliographical references (leaves 192-195). Also available on the Internet.

Thesis (Ph. D.)--University of Missouri-Columbia, 2002. / Typescript. Vita. Includes bibliographical references (leaves 192-195). Also available on the Internet.

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Due to the nature of survey design, the estimation of parameters associated with small areas is extremely problematic. In this study, techniques for the estimation of small area proportions are proposed and implemented. More specifically, empirical Bayes estimation methodologies, where random effects which reflect the complex structure of a multi-stage sample design are incorporated into logistic regression models, are derived and studied. / The proposed techniques are applied to data from the 1950 United States Census to predict local labor force participation rates of females. Results are compared with those obtained using unbiased and synthetic estimation approaches. / Using the proposed methodologies, a sensitivity analysis concerning the prior distribution assumption, conducted with a view toward outlier detection, is performed. The use of bootstrap techniques to correct measures of uncertainty is also studied.