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In cascaded inference tasks there is not a direct logical connection between an observable event (datum) and the hypothesis of interest. Instead there is interposed at least one logical reasoning stage, consisting of intervening variables or intermediate event states. This paper is concerned with the modification or extension of Bayes' rule to render it more specific as a normative model for cascaded inference. In particular, the work reported here is directed towards simplifying the task of the researcher who wishes to use Bayes' rule as a standard for inferential behavior and of the analyst who wishes to use task decomposition in aiding inference. This is achieved by the development of some general principles of inference, the use of concepts from graph theory for the representation of inference tasks, and the application of computer technology.

Probabilistic choice models are used by economists, psychologists, and marketing scientists in the analysis of choice behavior involving discrete, or quantal choice alternatives. The most widely-used of these is the multinomial logit model, which is a special case of the Luce model. These models are appealing for their simplicity and elegance, but have some severe flaws which have motivated continued research on more complex choice models. This has given rise to a need for efficient numerical algorithms for parameter estimation. One of the most important estimators is the maximum likelihood estimator, which historically has been avoided due to its computational difficulty. New algorithms for maximum likelihood estimation of choice models are developed which exploit the special structure inherent in the problem. The approach taken is to write the problem as a generalized regression problem; this gives rise to two formulations in which the Hessian is written as the sum of two matrices. The first is readily available from information already calculated for the gradient, and the second is expensive to calculate. The algorithms approximate the second piece by means of a least-change secant update, and solve the problem using a model/trust region approach involving model switching. Both approaches are successful, with one approach dominating the other in test examples using the multinomial logit, elimination-by-aspects, and Batsell-Polking models. Additional work includes a comparison of estimators in which it is demonstrated that the maximum likelihood and nonlinear least squares estimators have small-sample properties which are superior to other estimators proposed in the literature, especially those utilizing generalized least squares.

Many current algorithms for nonlinear constrained optimization problems determine a search direction by solving a quadratic programming subproblem. The global convergence properties are addressed by using a line search technique and a merit function to modify the length of the step obtained from the quadratic program. In unconstrained optimization, trust region strategies have been very successful. In this thesis we present a new approach for equality constrained optimization problems based on a trust region strategy. The direction selected is not necessarily the solution of the standard quadratic programming subproblem.

Multi-objective optimization problems are characterized by the need to consider multiple, and possibly conflicting, objectives in the solution process. We present an approach based on the use of interactive computer graphics to obtain qualitative information from a user about approximate solutions. We then use this qualitative information to transform the multi-objective optimization problem into a single-objective optimization problem that we may solve using standard techniques. Preliminary convergence results for the Nelder-Mead simplex algorithm are presented. Techniques for updating the single-objective problem after each piece of information is obtained from the user are described. These techniques are based on the duality theory for linear and quadratic programming. A software system for the subclass of 1-dimensional curve-fitting problems is also described.

Interior-point methods have not only shown their efficiency for linear and some nonlinear programming problems, but also for cutting plane methods and large scale optimization. The analytic center cutting plane method uses the analytic center of the current polyhedral approximation of the feasible region to add a new cutting plane. In this thesis, analytic center cutting plane and path-following interior-point methodologies are used to solve the following problems: (1) convex feasibility problems defined by a deep cut separation oracle; (2) convex optimization problems involving a nonlinear objective and a constraint set defined implicitly by a separation oracle; (3) variational inequalities involving a nonlinear operator and a convex set explicitly defined; (4) variational inequalities involving an affine operator and a constraint set defined implicitly by a deep cut separation oracle; and (5) variational inequalities involving a nonlinear operator and a constraint set defined implicitly by a deep cut separation oracle. Here, the oracle is a routine that takes as input a test point. If the point belongs to the feasible region, it answers "yes", otherwise it answers "no" and returns a cut separating the point from the feasible region. Complexity bounds are established for algorithms developed for Cases 1, 2 and 4. The algorithm developed for Case 3 will be proven to be convergent, whereas, in Case 5, the developed algorithm will be shown to find an approximate solution in finite time.

<p> This dissertation deals with the question of how to optimally execute orders for financial assets that are subject to transaction costs. We study the problem in a discrete&ndash;time model where the asset price processes of interest are subject to stochastic volatility and liquidity. </p><p> First, we consider the case for the execution of a single asset. We find predictable strategies that minimize the expectation, mean&ndash;variance and expected exponential of the implementation cost. </p><p> Second, we extend the single asset case to incorporate a dark pool where the orders can be crossed at the mid-price depending on the liquidity available. The orders submitted to the dark pool face execution uncertainty and are assumed to be subject to adverse selection risk. We find strategies that minimize the expectation and the expected exponential of the implementation shortfall and show that one can incur less costs by also making use of the dark pool. </p><p> Next chapter studies a multi asset setting in the presence of a dark pool. We find strategies that minimize the expectation and expected exponential of a cost functional that consists of the implementation shortfall and an aversion term that penalizes the orders crossed in the dark pool. In the expected exponential of the cost case, the dimensionality of the problem does not allow for the numerical computation of optimal strategies. Therefore, we first solve the expected exponential case for a second order Taylor approximation and then provide a framework via a duality argument which can be used to generate approximate strategies. </p><p> Lastly, we treat the case where the single asset execution problem exhibits ambiguity for the distribution of stochastic liquidity and volatility. We see the implementation cost as the sum of risk terms arising at each execution period. We consider the problem obtained from aggregating worst case expectations of these risk terms, by penalizing the distributions used with dynamic indicator, relative entropy and Gini indices. Next, we formulate the problem as the multi&ndash;prior first order certainty equivalent of the exponential cost and lastly we consider a second order certainty equivalence formulation.</p>

Diss. Stockholm : Handelshögsk.

Diss. (sammanfattning) Uppsala : Sveriges lantbruksuniv. / Härtill 5 uppsatser.