Exact Solution of Bayes and Minimax Change-Detection Problems

The challenge of detecting a change in the distribution of data is a sequential decision problem that is relevant to many engineering solutions, including quality control and machine and process monitoring. This dissertation develops techniques for exact solution of change-detection problems with discrete time and discrete observations. Change-detection problems are classified as Bayes or minimax based on the availability of information on the change-time distribution. A Bayes optimal solution uses prior information about the distribution of the change time to minimize the expected cost, whereas a minimax optimal solution minimizes the cost under the worst-case change-time distribution. Both types of problems are addressed. The most important result of the dissertation is the development of a polynomial-time algorithm for the solution of important classes of Markov Bayes change-detection problems. Existing techniques for epsilon-exact solution of partially observable Markov decision processes have complexity exponential in the number of observation symbols. A new algorithm, called constellation induction, exploits the concavity and Lipschitz continuity of the value function, and has complexity polynomial in the number of observation symbols. It is shown that change-detection problems with a geometric change-time distribution and identically- and independently-distributed observations before and after the change are solvable in polynomial time. Also, change-detection problems on hidden Markov models with a fixed number of recurrent states are solvable in polynomial time. A detailed implementation and analysis of the constellation-induction algorithm are provided. Exact solution methods are also established for several types of minimax change-detection problems. Finite-horizon problems with arbitrary observation distributions are modeled as extensive-form games and solved using linear programs. Infinite-horizon problems with linear penalty for detection delay and identically- and independently-distributed observations can be solved in polynomial time via epsilon-optimal parameterization of a cumulative-sum procedure. Finally, the properties of policies for change-detection problems are described and analyzed. Simple classes of formal languages are shown to be sufficient for epsilon-exact solution of change-detection problems, and methods for finding minimally sized policy representations are described.

The influence of past behavior on future behavior: a mind-set perspective

A behavioral mind-set refers to the effect of performing a behavior in one situation (e.g., deciding which animals jump higher, dolphins or sea lions) on the likelihood of performing a conceptually similar behavior in subsequent, unrelated situations (e.g., deciding which of two candies to purchase). It reflects the activation and persistence of procedural knowledge. My dissertation circumscribes the construct of a behavioral mind-set and proposes a theoretical framework describing how mind-sets operate as well as their cognitive and motivational determinants. Three sets of studies investigated the role of mind-sets in different domains. The first set of studies explored the influence of making comparative judgments on subsequent decision making. Specifically, I found that making comparative judgment in one situation activates a which-to-buy mind-set that increases the willingness to decide which of two products to purchase in a later situation without considering the option of not buying anything at all. This mind-set can be activated not only by stating preferences for one of two products but also by comparing the relative attractiveness of wild animals, comparing the animals with respect to physical attributes, and estimating how similar one object is to another. Furthermore, the mind-set, once activated, influences not only purchase intentions in hypothetical situations but the actual decisions to purchase one of different types of products that are on sale after the experiment. The second set of studies investigated whether generating supportive elaborations or counterarguments in one situation will influence people’s tendency to engage in similar behavior in a subsequent, unrelated situation. I found that making supportive elaborations in one situation gives rise to a bolstering mind-set that, once activated, increases participants’ disposition to generate supportive thoughts in response to persuasive communications that they receive later and, therefore, increases the effectiveness of persuasion. Correspondingly, generating opposing arguments in an initial situation activates a counterarguing mind-set that increases the tendency to argue against the persuasive communications and decreases its effectiveness. However, a counterarguing mind-set may increase the effectiveness of persuasion if the messages are difficult to be refuted. The third set of studies distinguished between the influence of motivation on consumer behavior and the influence of a mind-set that is activated by this motivation. Specifically, I found that appetitive motivation, which naturally increases people’s tendency to acquire food products, can give rise to a cognition-based acquisition mind-set that increases people’s disposition to acquire non-food products as well. This acquisition mind-set may persist even when the appetitive motivation that gave rise to it is satiated by eating. Moreover, the disposition to acquire non-food products is not mediated by the products’ attractiveness. The studies suggest that motivation and mind-sets may independently influence consumers’ evaluation of a product and their dispositions to acquire it. Motivation is more likely to influence product evaluations whereas a mind-set is more likely to influence consumers’ acquisition dispositions. In summary, a behavioral mind-set can be activated in the process of performing a behavior. And the mind-set may influence people’s subsequent behaviors in unrelated situations in which the activated procedure is applicable. Moreover, motivation to engage in one behavior could also elicit a cognition-based mind-set, which may change people’s subsequent behaviors.