Determining the correct sample size is of utmost importance in study design. Large samples yield classifiers or parameters with more precision and conversely, samples that are too small yield unreliable results. Fixed sample size methods, as determined by the specified level of error between the obtained parameter and population value, or a confidence level associated with the estimate, have been developed and are available. These methods are extremely useful when there is little or no cost (consequences of action), financial and time, involved in gathering the data. Alternatively, sequential sampling procedures have been developed specifically to obtain a classifier or parameter estimate that is as accurate as deemed necessary by the researcher, while sampling the least number of observations required to obtain the specified level of accuracy. This dissertation discusses a sequential procedure, derived using Martingale Limit Theory, which had been developed to train a classifier with the minimum number of observations to ensure, with a high enough probability, that the next observation sampled has a low enough probability of being misclassified. Various classification methods are discussed and tested, with multiple combinations of parameters tested. Additionally, the sequential procedure is tested on microarray data. Various advantages and shortcomings of the sequential procedure are pointed out and discussed. This dissertation also proposes a new sequential procedure that trains the classifier to such an extent as to accurately estimate the Bayes error with a high probability. The sequential procedure retains all of the advantages of the previous method, while addressing the most serious shortcoming. Ultimately, the sequential procedure developed enables the researcher to dictate how accurate the classifier should be and provides more control over the trained classifier. / Dissertation (MSc)--University of Pretoria, 2013. / Statistics / Unrestricted

Approved for public release; distribution in unlimited. / Computer simulations which forecast the performance of complicated systems are used as decision aids in many applications. For example, a ship's defensive system may use simulation to support an automated real-time response to a perceived threat, such as an incoming missile. The system uses cumulative simulation data to evaluate a set of options in order to choose the best countermeasure. Since everything happens in "real time", the system has limited time to run the simulation. Normally, a system would run the simulation an equal number of times for each option before coming to a decision. But this may cause the system to waste time on options which can be deemed non-optimal after only a few simulation runs. This time can be better used to help adjudicate between the better options. We evaluate the performance of sequential multiple comparisons algorithms to eliminate inferior options as quickly as possible, in order to have more time to dedicate to the exploration of better options, so that better decisions may be made. These algorithms allow inferior options to be dropped quickly depending on how well separated they are from others, but the algorithms differ in how well they achieve this objective. / Major, Israeli Air Force

M.Sc. (Mathematical Statistics) / Please refer to full text to view abstract

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Thesis (Ph. D.)--University of Texas at Austin, 2005. / Supervisor: John D. Leckenby. Vita. Includes bibliographical references.

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The quickest change-point detection problems with sampling right constraints are considered. Specially, an observer sequentially takes observations from a random sequence, whose distribution will change at an unknown time. Based on the observation sequence, the observer wants to identify the change-point as quickly as possible. Unlike the classic quickest detection problem in which the observer can take an observation at each time slot, we impose a causal sampling right constraint to the observer. In particular, sampling rights are consumed when the observer takes an observation and are replenished randomly by a stochastic process. The observer cannot take observations if there is no sampling right left. The causal sampling right constraint is motivated by several practical applications. For example, in the application of sensor network for monitoring the abrupt change of its ambient environment, the sensor can only take observations if it has energy left in its battery. With this additional constraint, we design and analyze the optimal detection and sampling right allocation strategies to minimize the detection delay under various problem setups. As one of our main contributions, a greedy sampling right allocation strategy, by which the observer spends sampling rights in taking observations as long as there are sampling rights left, is proposed. This strategy possesses a low complexity structure, and leads to simple but (asymptotically) optimal detection algorithms for the problems under consideration. Specially, our main results include: 1) Non-Bayesian quickest change-point detection: we consider non-Bayesian quickest detection problem with stochastic sampling right constraint. Two criteria, namely the algorithm level average run length (ARL) and the system level ARL, are proposed to control the false alarm rate. We show that the greedy sampling right allocation strategy combined with the cumulative sum (CUSUM) algorithm is optimal for Lorden's setup with the algorithm level ARL constraint and is asymptotically optimal for both Lorden's and Pollak's setups with the system level ARL constraint. 2) Bayesian quickest change-point detection: both limited sampling right constraint and stochastic sampling right constraint are considered in the Bayesian quickest detection problem. The limited sampling right constraint can be viewed as a special case of the stochastic sampling right constraint with a zero sampling right replenishing rate. The optimal solutions are derived for both sampling right constraints. However, the structure of the optimal solutions are rather complex. For the problem with the limited sampling right constraint, we provide asymptotic upper and lower bounds for the detection delay. For the problem with the stochastic sampling right constraint, we show that the greedy sampling right allocation strategy combined with Shiryaev's detection rule is asymptotically optimal. 3) Quickest change-point detection with unknown post-change parameters: we extend previous results to the quickest detection problem with unknown post-change parameters. Both non-Bayesian and Bayesian setups with stochastic sampling right constraints are considered. For the non-Bayesian problem, we show that the greedy sampling right allocation strategy combined with the M-CUSUM algorithm is asymptotically optimal. For the Bayesian setups, we show that the greedy sampling right allocation strategy combined with the proposed M-Shiryaev algorithm is asymptotically optimal.

Typescript (photocopy). / Digitized by Kansas Correctional Industries

Thesis (Ph.D.)--University of Delaware, 2006. / Principal faculty advisor: Ratna Nandakumar, School of Education. Includes bibliographical references.