Copyright (c) 2009 Carnegie Mellon University All rights reserved. http://repository.cmu.edu Recent documents in Research Showcase en-us Sun, 22 Nov 2009 05:59:56 PST 3600 http://repository.cmu.edu/statistics/42 http://repository.cmu.edu/statistics/42 Fri, 20 Nov 2009 13:49:13 PST This paper explores optimal strategies for the use of peremptory challenges in jury trials where the prospective jurors are examined and then either challenged' or seated, one by one. We assume that the lawyers for each side do not necessarily agree about the probability that each prospective juror will vote for conviction, but that the assessment of each side is available to the other. The strategies we develop are optimal non-cooperative sequential strategies in the sense that each side maximizes its expected utility at each stage under the assumption that both sides will continue to use these optimal strategies in all future decisions. Under certain regularity conditions we show that it is optimal to be the first side to decide whether to challenge any prospective juror. Necessary and sufficient conditions are given for an optimal strategy to be reversible, which means that it does not matter to either side whether it decides first or second. Specifically, the optimal strategy is reversible if the two sides always agree about the probability that each prospective juror will vote for conviction. We give an algorithm based on backward induction for finding the optimal strategies and discuss simple examples. Arthur Roth http://repository.cmu.edu/statistics/43 http://repository.cmu.edu/statistics/43 Fri, 20 Nov 2009 13:49:13 PST We examine the selection of jurors' names from multiple source lists, using statistical and optimization methodology. Five plans for sampling at random from overlapping lists of names are analyzed for their probabilistic and cost properties. In each plan the probability of a name being selected is independent of which and how many lists it appears on. We consider the optimal ordering of the frames to minimize cost and develop a heuristic for solving this problem. Although the methods are discussed in terms of juror selection, the results apply to sampling from overlapping frames in any context. For instance, if lists of equipment are kept according to possible uses, with versatile equipment listed many times, the methods of this paper can be used to draw a random sample of equipment to check for. readiness. John P. Lehoczky http://repository.cmu.edu/statistics/40 http://repository.cmu.edu/statistics/40 Fri, 20 Nov 2009 13:49:12 PST Research is growing on methods to balance two competing public purposes: the need of the public for information about society and government, and the right to privacy and confidentiality of individual information. This article presents a case study in which a governmental agency (the U.S. Department of Justice) released a report (on federal capital cases, 1995--2000) seeking to conceal certain information (the recommendations of the U.S. Attorney and the DOJ Review Committee on whether to seek the death penalty), while releasing cross-tabulations of the concealed information with other, public information about the cases. Careful study of the released cross-tabulations led to full identification of all the variables in 386 out of 682 cases. Using other public data led to full identification of another 160. For the remaining 136 cases, the space of possible values for the missing data is drastically reduced. This article explains how the inferences were made. David J. Algranati http://repository.cmu.edu/statistics/41 http://repository.cmu.edu/statistics/41 Fri, 20 Nov 2009 13:49:12 PST This paper generalizes the problems of optimal selection considered by Roth, Kadane and DeGroot by allowing a set of J items to be chosen by two decision makers, the first of whom has A challenges and the second has B challenges. The two decision makers each have an opportunity to challenge each item before it is accepted, in some arbitrary fixed order. We assume that the decision makers know the utility function of the other side as well as their own over sets of J items, and that they know the subjective distribution, assigned by the other side, of characteristics of potential items that will be observed, as well as their own. Under these conditions the other side's response to each potential item can be predicted with certainty, and backward induction defines an optimal strategy. We study an important special case we call regular, and show that it is never disadvantageous to go first in the regular case. The use of peremptory challenges in jury trials motivates our model. The basic model in which jurors are challenged one at a time is extended to a more general class of problems that includes the group system and the struck jury system. Morris H. DeGroot http://repository.cmu.edu/statistics/39 http://repository.cmu.edu/statistics/39 Fri, 20 Nov 2009 13:49:11 PST This paper explores some of the consequences of adopting a modern subjective view of probability for game theory. The consequences are substantial. The subjective view of probability clarifies the important distinction between normative and positive theorizing about behavior in games, a distinction that is often lost in the search for "solution concepts" which largely characterizes game theory since the work of von Neumann and Morgenstern. Many of the distinctions that appear important in conventional game theory (two-person versus n-person, zero-sum versus variable sum) appear unimportant in the subjective formulation. Other distinctions, such as single play versus repetitive-play games, appear to be more important in the subjective formulation than in the conventional formulation. Joseph B. Kadane http://repository.cmu.edu/statistics/38 http://repository.cmu.edu/statistics/38 Fri, 20 Nov 2009 13:49:11 PST Response to HARSANYI, J. C., "Subjective Probability and the Theory of Games: Comments on Kadane and Larkey's Paper," Management Science Vol. 28, No. 2 (Feb., 1982) Joseph B. Kadane http://repository.cmu.edu/statistics/36 http://repository.cmu.edu/statistics/36 Fri, 20 Nov 2009 13:49:10 PST A characterization is given of diametrically opposed interests between two players: either neither is a Bayesian, or both have a unique probability and utility function (up to the usual transformation) or both have many possible probabilities and utilities. In the second case, their utility functions must have representations that sum to zero, and they must have identical probability distributions on every uncertain event in the space. Implications of this result for negotiations and for game theory are discussed Joseph B. Kadane http://repository.cmu.edu/statistics/37 http://repository.cmu.edu/statistics/37 Fri, 20 Nov 2009 13:49:10 PST This paper explores the distinction between normative and positive theoretical statements in a game theoretic context from a Bayesian perspective. Normative and positive theoretical statements are often confused in decision making research. The confusion results from some unique epistemological and methodological problems associated with cognitive behavior as an object for scientific inquiry. The confusion persists because of poor model validation procedures which are themselves further complicated by the confusion. The confusion greatly impedes the development of more useful prescriptions for and predictions of human decision behavior. From a Bayesian perspective which acknowledges the importance of incomplete information and imperfect theories of behavior, the confusion is unnecessary. Joseph B. Kadane http://repository.cmu.edu/statistics/35 http://repository.cmu.edu/statistics/35 Fri, 20 Nov 2009 13:49:09 PST This investigation combines two questions for expected utility theory: 1. When do the shared preferences among expected utility maximizers conform to the dictates of expected utility? 2. What is the impact on expected utility theory of allowing preferences for prizes to be state-dependent? Our principal conclusion (Theorem 4) establishes very restrictive necessary and sufficient conditions for the existence of a Pareto, Bayesian compromise of preferences between two Bayesian agents, even when utilities are permitted to be state-dependent and identifiable. This finding extends our earlier result (Theorem 2, 1989a) which applies provided that all utilities are state-independent. A subsidiary theme is a decision theoretic analysis of common rules for "pooling" expert probabilities. Against the backdrop of "horse lottery" theory (Anscombe and Aumann 1963) and subject to a weak Pareto rule, we show, generally, that there is no Bayesian compromise between two Bayesian agents even when state-dependent utilities are entertained in an identifiable way. The word "identifiable" is important because, if state-dependence is permitted merely by dropping the Anscombe-Aumann axiom (Axiom 4 here) for "state-independence," though a continuum of possible Bayesian compromises emerges, also it leads to an extreme underdetermination of an agent's personal probability and utility given the agent's preferences. Instead, when state-dependence is monitored through (our version of) the approach of Karni, Schmeidler, and Vind (1983), the general impossibility of a Bayesian, Pareto compromise in preferences reappears. Mark J. Schervish http://repository.cmu.edu/statistics/34 http://repository.cmu.edu/statistics/34 Fri, 20 Nov 2009 13:49:08 PST Differences in players' skill are important determinants of relative player success in most real games such as poker, chess, basketball, business, and politics. Yet conventional game theory has concentrated primarily on games with no skill differences among players. This paper uses a simplified version of stud poker to better understand the concept of differential player skill in games. Players with very different strategies for playing this game are modeled algorithmically and pitted against one another in simulation tournaments. Patrick Larkey http://repository.cmu.edu/statistics/33 http://repository.cmu.edu/statistics/33 Fri, 20 Nov 2009 13:49:07 PST This research investigates the impact of a large-scale assortment reduction on customer retention, utilizing a model we develop to explore the effect on sales at both the store level and the category level simultaneously. We apply our model to a data set provided by an online grocer. The data contain detailed household purchase records for every category in the store. Our results indicate that the reduction in assortment reduces overall store sales, a result that contrasts with that of all of the recent studies on assortment reductions (Food Marketing Institute. 1993. Variety or duplication: A process to know where you stand. Prepared by Willard Bishop Consulting and Information resources, Inc., in cooperation with Frito Lay; Drèze, Xavier, Stephen J. Hoch, Mary E. Purk. 1994. Shelf management and space elasticity. J. Retailing 70(4) 301-326; Broniarczyk, Susan M., Wayne D. Hoyer, Leigh McAlister. 1998. Consumers' perceptions of the assortment offered in a grocery category: The impact of item reduction. J. Marketing Res. 35(May) 166-176; Boatwright, Peter, Joseph C. Nunes. 2001. Reducing assortment: An attribute-based approach. J. Marketing 65(July) 50-63; Boatwright, Peter, Joseph C. Nunes. 2004. Correction note for "Reducing assortment: An attribute-based approach." J. Marketing. Forthcoming). We find the reduction had a negative effect on both shopping frequency and purchase quantity, and we find that the decline in shopping frequency resulted in a greater loss than did the reduction in purchase quantities. We also find that the impact of the assortment cut varies widely by category, with less-frequently purchased categories more adversely affected. The variation in the assortment reduction's impact across categories suggests that managers compare select categories in order to moderate the overall loss in sales. Sharad Borle http://repository.cmu.edu/statistics/32 http://repository.cmu.edu/statistics/32 Fri, 20 Nov 2009 13:49:06 PST Count data arise in various organizational settings. When the release of such data is sensitive, organizations need information-disclosure policies that protect data confidentiality while still providing data access. In contrast to extant disclosure policies, we describe a new policy for count tables that is based on disclosing only the sufficient statistics of a flexible discrete distribution. This distribution, the COM-Poisson, well approximates Poisson counts but also under- and over-dispersed counts. The sufficient statistics mask the exact cell counts and often also the table size. Under the scenario of a data holding agency and a data snooper, we show that this policy has low disclosure risk with no loss of data utility: Usually, many count tables correspond to the disclosed sufficient statistics. Furthermore, these count tables are equally likely to be the undisclosed table. Finding these solutions requires solving a system of linear equations, which are underdetermined for tables with more than three cells, and can be computationally prohibitive for even small tables. We also consider cell-specific interval bounds, a commonly used disclosure limitation policy, and compare them to our policy. We describe several types of snooper knowledge, their integration with the disclosed statistics, and implications. Applying this policy to three real data sets, we illustrate the low associated disclosure risk. Joseph B. Kadane http://repository.cmu.edu/lib_science/66 http://repository.cmu.edu/lib_science/66 Fri, 20 Nov 2009 12:42:52 PST Science librarians, as well as other librarians, have seen ample new technologies come and go over the years. Librarians experiment and try to find ways to employ the new tools in our libraries. A driving force in our decision making about what tools to use should always be our patrons and whether the tools can help us do a better job of delivering services. This paper discusses what technologies have proven to be successful, as well as other thoughts to bear in mind as librarians evaluate Web 2.0 tools for science libraries. Melissa J. Harvey Articles http://repository.cmu.edu/lib_science/67 http://repository.cmu.edu/lib_science/67 Fri, 20 Nov 2009 12:42:52 PST Tolkien's Cauldron studies the sources of J.R.R. Tolkien's The Lord of the Rings. Tolkien was a scholar of Old Norse literature and much of his work in the Lord of the Rings is informed by his knowledge of old Norse mythology, Eddic poetry, and saga. Tolkien's use of these sources enriched this complex story of Middle-earth. Gloriana St. Clair Lord of the Rings http://repository.cmu.edu/statistics/31 http://repository.cmu.edu/statistics/31 Thu, 19 Nov 2009 14:12:14 PST Stability of Bayes decision problems under uniform convergence of losses is revisited and sufficient conditions for stability are obtained. The results generalize and complement the earlier works of Kadane and Chuang, Chuang, and Salinetti. General conditions are also given for the equivalence of two definitions of stability. Joseph B. Kadane http://repository.cmu.edu/statistics/30 http://repository.cmu.edu/statistics/30 Thu, 19 Nov 2009 14:12:13 PST We consider how an unconditional, finite-valued, finitely additive probability P on a countable set may localize its non-conglomerability (non-disintegrability). Non-conglomerability, a characteristic of merely finitely additive probability, occurs when the unconditional probability of an event P(E) lies outside the closed interval of conditional probability values, [infhe pi P(E|h), suphe pp(E|h)], taken from a countable partition p = hj:j=1,...}. The problem we address is how to identify events and partitions where a finite-valued, finitely additive probability fails to satisfy conglomerability. We focus on the extreme case of 2-valued finitely additive probabilities that are not countably additive. These are, equivalently, non-principal ultrafilters. Evidently, the challenge we face is that given a countable partition, at most one of its elements has positive probability under P. Thus, we must find ways of regulating the coherent conditional probabilities, given null events, that cohere with the unconditional probability P. Our analysis of P proceeds by the use of combinatorial properties of the associated non-principal ultrafilter UP. We show that when ultrafilter UP is not minimal in the Rudin-Keisler partial order of b(w)\w, we may locate a partition in which P fails to satisfy the conglomerability principle by examining (at most) countably many partitions. This result is then applied to finitely additive probabilities that assume only finitely many values. By contrast, if ultrafilter UP is Rudin-Keisler minimal, then P is simultaneously conglomerable in each finite collection of partitions, though not simultaneously conglomerable in all partitions. Teddy Seidenfeld http://repository.cmu.edu/statistics/29 http://repository.cmu.edu/statistics/29 Thu, 19 Nov 2009 14:12:12 PST The degree of incoherence, when previsions are not made in accordance with a probability measure, is measured by the rate at which an incoherent bookie can be made a sure loser. Each bet is rescaled by one of several normalizations to account for the overall sizes of bets. For each normalization, the sure loss for incoherent previsions is divided by the normalization to determine the rate of incoherence. We study several properties of normalizations and degrees of incoherence and present some examples. Potential applications include the degree of incoherence of classical statistical procedures. Mark J. Schervish http://repository.cmu.edu/statistics/28 http://repository.cmu.edu/statistics/28 Thu, 19 Nov 2009 14:12:12 PST It has long been known that the practice of testing all hypotheses at the same level (such as 0.05), regardless of the distribution of the data, is not consistent with Bayesian expected utility maximization. According to de Finetti's "Dutch Book" argument, procedures that are not consistent with expected utility maximization are incoherent and they lead to gambles that are sure to lose no matter what happens. In this paper, we use a method to measure the rate at which incoherent procedures are sure to lose, so that we can distinguish slightly incoherent procedures from grossly incoherent ones. We present an analysis of testing a simple hypothesis against a simple alternative as a case‐study of how the method can work Mark J. Schervish http://repository.cmu.edu/statistics/27 http://repository.cmu.edu/statistics/27 Thu, 19 Nov 2009 14:12:11 PST The number of calls in a telephone survey is used as an indicator of how difficult an intended respondent is to reach. This permits a probabilistic division of the nonrespondents into nonsusceptibles (those who will always refuse to respond), and the susceptible nonrespondents (those who were not available to respond) in a model of the nonresponse. Further, it permits stochastic estimation of the views of the latter group and an evaluation of whether the nonresponse is ignorable for inference about the dependent variable. These ideas are implemented on the data from a survey in Metropolitan Toronto of attitudes toward smoking in the workplace. Using a Bayesian model, the posterior distribution of the model parameters is sampled by Markov Chain Monte Carlo methods. The results reveal that the nonresponse is not ignorable and those who do not respond are twice as likely to favor unrestricted smoking in the workplace as are those who do. Louis T. Mariano http://repository.cmu.edu/statistics/25 http://repository.cmu.edu/statistics/25 Thu, 19 Nov 2009 14:12:10 PST A dynamic sampling plan among strata is a permutation of sampled items specifying which stratum is to receive the next item to be included in the sample. An optimal such plan has the property of achieving minimum variance for its cost whenever it is truncated. This article shows that optimal dynamic sampling plans exist under very general conditions, and gives a simple algorithm for constructing them. The well-known Neyman allocation is compared to the dynamic optimum, both statically and dynamically. The theorems rely on a version of the Neyman-Pearson Lemma adapted for use in search theory. Joseph B. Kadane http://repository.cmu.edu/statistics/26 http://repository.cmu.edu/statistics/26 Thu, 19 Nov 2009 14:12:10 PST We contrast three decision rules that extend Expected Utility to contexts where a convex set of probabilities is used to depict uncertainty: Γ-Maximin, Maximality, and E-admissibility. The rules extend Expected Utility theory as they require that an option is inadmissible if there is another that carries greater expected utility for each probability in a (closed) convex set. If the convex set is a singleton, then each rule agrees with maximizing expected utility. We show that, even when the option set is convex, this pairwise comparison between acts may fail to identify those acts which are Bayes for some probability in a convex set that is not closed. This limitation affects two of the decision rules but not E-admissibility, which is not a pairwise decision rule. E-admissibility can be used to distinguish between two convex sets of probabilities that intersect all the same supporting hyperplanes. Mark J. Schervish http://repository.cmu.edu/statistics/24 http://repository.cmu.edu/statistics/24 Thu, 19 Nov 2009 14:12:09 PST This article explores a Bayesian analysis of a generalization of the Poisson distribution. By choice of a second parameter v, both under-dispersed and over-dispersed data can be modeled. The Conway-Maxwell-Poisson distribution forms an exponential family of distributions, so it has sufficient statistics of fixed dimension as the sample size varies, and a conjugate family of prior distributions. The article displays and proves a necessary and sufficient condition on the hyperparameters of the conjugate family for the prior to be proper, and it discusses methods of sampling from the conjugate distribution. An elicitation program to find the hyperparameters from the predictive distribution is also discussed. Joseph B. Kadane http://repository.cmu.edu/statistics/19 http://repository.cmu.edu/statistics/19 Thu, 19 Nov 2009 12:41:55 PST In a paired comparison experiment n judges give a preference in some or all of the (t/2) pairs of t items. Frequently the purpose of the experiment is to test the null hypothesis that every preference is equally likely against a vaguely defined alternative of consistency. Our purpose is to study several of the tests used, from the point of view of a natural equivalence relation which arises in graph theory. In the first section we introduce graph theory notation, the equivalence relation, and some results on partial and strict orderings on the equivalence classes. The succeeding section applies these notions to Kendall and Babington Smith's statistic in detail (hereafter simply referred to as Kendall's statistic), and mentions applications in the Bradley-Terry model, and the strong-stochastic ordering model. Joseph B. Kadane http://repository.cmu.edu/statistics/23 http://repository.cmu.edu/statistics/23 Thu, 19 Nov 2009 12:41:08 PST As a first step toward developing statistical models based on upper and lower probabilities, we study upper probabilities and upper expectations on the unit interval that are symmetric, by which we mean invariant with respect to equimeasurability. These upper probabilities are generalizations of uniform probability measures. We give some characterizations of these upper probabilities. Specifically, we show that symmetry of the upper expectation functional is equivalent to the underlying set of densities being closed under majorization. We also show that a function is the upper distribution for a symmetric upper probability if and only if its lower graph is star-shaped with respect to the origin and to the point (1, 1). We derive inner and outer approximations to symmetric classes of probabilities based on the upper probability. The class of symmetric upper expectations that are completely determined by their values on the indicator functions is characterized. We provide a geometric characterization of a hierarchy of upper probabilities including Fine's generalized upper probabilities and 2-alternating Choquet capacities. In particular, we establish a 1-1 correspondence between symmetric, 2-alternating capacities and non-increasing density functions. We prove that undominated generalized upper probabilities do not exist in the symmetric case. Examples from robust statistics are considered. An example is given that shows that symmetry of upper probabilities does not imply symmetry of upper expectations. A corollary is that symmetry of the Choquet integral does not imply symmetry of the upper expectation functional. Larry Wasserman http://repository.cmu.edu/statistics/22 http://repository.cmu.edu/statistics/22 Thu, 19 Nov 2009 12:41:07 PST This essay considers decision-theoretic foundations for robust Bayesian statistics. We modify the approach of Ramsey, de Finetti, Savage and Anscombe and Aumann in giving axioms for a theory of robust preferences. We establish that preferences which satisfy axioms for robust preferences can be represented by a set of expected utilities. In the presence of two axioms relating to state-independent utility, robust preferences are represented by a set of probability/utility pairs, where the utilities are almost state-independent (in a sense which we make precise). Our goal is to focus on preference alone and to extract whatever probability and/or utility information is contained in the preference relation when that is merely a partial order. This is in contrast with the usual approach to Bayesian robustness that begins with a class of "priors" or "likelihoods," and a single loss function, in order to derive preferences from these probability/utility assumptions. Teddy Seidenfeld http://repository.cmu.edu/statistics/21 http://repository.cmu.edu/statistics/21 Thu, 19 Nov 2009 12:40:36 PST Choquet capacities are a generalization of probability measures that arise in robustness, decision theory and game theory. Many capacities that arise in robustness are symmetric or can be transformed into symmetric capacities. We characterize the extreme points of the set of upper distribution functions corresponding to coherent, symmetric Choquet capacities on [0,1]. We also show that the set of 2-alternating capacities is a simplex and we give a Choquet representation of this set. Larry Wasserman http://repository.cmu.edu/statistics/20 http://repository.cmu.edu/statistics/20 Thu, 19 Nov 2009 12:40:35 PST Improper regular conditional distributions (rcd's) given a σ-field .A have the following anomalous property. For sets A ∈, Pr(A I A) is not always equal to the indicator of A. Such a property makes the conditional probability puzzling as a representation of uncertainty. When rcd's exist and the σ-field A is countably generated, then almost surely the rcd is proper. We give sufficient conditions for an rcd to be improper in a maximal sense, and show that these conditions apply to the tail σ-field and the σ-field of symmetric events Teddy Seidenfeld http://repository.cmu.edu/sds/92 http://repository.cmu.edu/sds/92 Thu, 19 Nov 2009 11:23:46 PST Recent research has demonstrated that choices between gambles are systematically influenced by the way they are expressed. Kahneman and Tversky's Prospect Theory (1979) explains many of these "framing" effects as shifts in the point of reference from which prospects are evaluated. This paper demonstrates the applicability of the reference point concept to intertemporal choice. Three experiments demonstrate that when people choose between immediate and delayed consumption, the reference point used to evaluate alternatives can significantly influence choice. The first study elicited relative preference for immediate and delayed consumption using three methods, each of which differently framed choices between alternatives offering identical end-state consumption. The conventional discounted utility model predicts that the three methods of elicitation should yield similar estimates of time preference, but preferences were found to differ in accordance with a reference point model. The second and third studies extend and replicate the results from the first, the third using real rather than hypothetical choices. George Loewenstein http://repository.cmu.edu/sds/91 http://repository.cmu.edu/sds/91 Thu, 19 Nov 2009 11:23:45 PST Research on decision making under uncertainty has been strongly influenced by the documentation of numerous expected utility (EU) anomalies-behaviors that violate the expected utility axioms. The relative lack of progress on the closely related topic of intertemporal choice is partly due to the absence ofan analogous set of discounted utility (DU) anomalies. We enumerate a set of DU anomalies analogous to the EU anomalies and propose a model that accounts for the anomalies, as well as other intertemporal choice phenomena incompatible with DU. We discuss implications for savings behavior, estimation of discount rates, and choice framing effects. George Loewenstein http://repository.cmu.edu/sds/90 http://repository.cmu.edu/sds/90 Thu, 19 Nov 2009 11:23:44 PST This paper develops a sequential learning estimator of production functions and productivity dynamics for unbalanced establishment panels. Extending an idea from the literature on dynamic industry models, establishments are uncertain about their own idiosyncratic productivities and update productivity beliefs using information revealed by their production experience. The estimator relies on the structure of this iterative learning process and thereby avoids placing any restriction on establishment strategic behavior. Consequently, the estimator is suitable for comparative studies of the behavioral sources of technological change across all types of industry. Estimation of productivity dynamics and of behavioral decision rules are separated into recursive stages. Using sequential learning estimates of productivity beliefs from the first stage, decision rules for exit, investment, and innovation effort can be estimated in a second stage. A test application with four Chilean industries confirms that the estimator produces plausible estimates with small standard errors. Decision rule estimates show that productivity beliefs affect investment and exit hazards in the expected direction. David Greenstreet http://repository.cmu.edu/sds/89 http://repository.cmu.edu/sds/89 Thu, 19 Nov 2009 11:23:43 PST Why do consumers sometimes act against their own better judgment, engaging in behavior that is often regretted after the fact and that would have been rejected with adequate forethought? More generally, how do consumers attempt to maintain self-control in the face of time-inconsistent preferences? This article addresses consumer impatience by developing a decision-theoretic model based on reference points. The model explains how and why consumers experience sudden increases in desire for a product, increases that can result in the temporary overriding of longterm preferences. Tactics that consumers use to control their own behavior are also discussed. Consumer self-control is framed as a struggle between two psychological forces, desire and willpower. Finally, two general classes of self-control strategies are described: those that directly reduce desire, and those that overcome desire through willpower. Steven J. Hoch http://repository.cmu.edu/sds/88 http://repository.cmu.edu/sds/88 Wed, 18 Nov 2009 13:41:22 PST We describe an instance-based model of decision-making for repeated binary choice. The model provides an accurate account of existing data of aggregate choice probabilities and individual differences, as well as newly collected data on learning and choice interdependency. In particular, the model provides a general emergent account of the risk aversion effect that does not require any metacognitive assumptions. Advantages of the model include its simplicity, its compatibility with previous models of choice and dynamic control, and the strong constraints it inherits from the underlying cognitive architecture. Christian Lebiere http://repository.cmu.edu/sds/86 http://repository.cmu.edu/sds/86 Wed, 18 Nov 2009 13:41:21 PST Similarity and preference theories face similar effects but their methodologies vary enormously. In this paper, we present an explanation of decoy effects using semantic (nonnumerical) stimuli. People had to choose from a set of news the closest to a reference one. We discuss the consequences of the assumptions made by the JDM and similarity communities in explaining context effects. Jose Quesada http://repository.cmu.edu/sds/87 http://repository.cmu.edu/sds/87 Wed, 18 Nov 2009 13:41:21 PST 'Cognitive architectures' are computer algorithms designed to model human behavior and to function in a way similar to the workings of the human mind. The breadth of cognitive architectures is one of their primary strengths. Rather than serving as special-purpose models engineered specifically for individual tasks, cognitive architectures provide general computational mechanisms and constraints that are applicable to the development of models for all kinds of tasks. Cleotilde Gonzalez http://repository.cmu.edu/sds/84 http://repository.cmu.edu/sds/84 Wed, 18 Nov 2009 13:41:20 PST Sterman (1989) proposed that decision makers misperceive the feedback provided by dynamically complex environments, and questioned whether people can learn to make effective decisions in such environments. We provide empirical evidence of learning in a well-known dynamic environment called the beer game. We then describe a preliminary version of an instance-based, dynamic decision making model built using the ACT-R cognitive architecture. The model mimics the general patterns of human behavior observed for aggregate performance across trials and local performance within trials. Implications for research on dynamic decision making are summarized. Michael K. Martin http://repository.cmu.edu/sds/85 http://repository.cmu.edu/sds/85 Wed, 18 Nov 2009 13:41:20 PST This paper discusses a computational model of situation awareness (SA) for military command and control in complex battle situations. Cognitive modeling is a research method that does not forgive vagueness. How do military commanders create awareness in a highly complex and uncertain world? The model described in this paper simulates computationally some of the cognitive operations performed by commanders during the evaluation of a complex battle situation. Although the set of cognitive processes that support SA are still not well understood, we have hypothesized a metaarchitecture involving: information gathering, assessment, and alternative generation. The cognitive model reported here paves the road towards a more complete and valid representation. The model was implemented using ACT-R, a cognitive architecture, and tested with scenarios running in OTB, a simulation tool for war scenarios. Octavio Juarez-Espinosa http://repository.cmu.edu/sds/83 http://repository.cmu.edu/sds/83 Wed, 18 Nov 2009 13:41:19 PST This study presents the results from the analyses of verbal protocols elicited from inexperienced and experienced participants of a real-time, Dynamic Decision-Making (DDM) task. This research intends to complement a series of studies performed in DDM environments analyzing the cognitive structures and processes involved in learning in DDM. Results show that inexperienced and experienced participants differ in several ways: in the way they distribute attention to different parts of the system, in their awareness of the relationship of the attributes involved in the decision making process, and in their coordination to make decisions in real time. These results have been used to support the refinement of a cognitive model developed to explain how people learn in DDM tasks. Cleotilde Gonzalez http://repository.cmu.edu/statistics/18 http://repository.cmu.edu/statistics/18 Tue, 17 Nov 2009 14:35:56 PST The hyper-geometric function is shown to be logarithmically concave in integer values of one of its parameters. The methods used are probabilistic. Joseph B. Kadane http://repository.cmu.edu/statistics/16 http://repository.cmu.edu/statistics/16 Tue, 17 Nov 2009 14:35:55 PST We give an upper bound for the posterior probability of a measurable set A when the prior lies in a class of probability measures P. The bound is a rational function of two Choquet integrals. If P is weakly compact and is closed with respect to majorization, then the bound is sharp if and only if the upper prior probability is 2-alternating. The result is used to compute -bounds for several sets of priors used in robust Bayesian inference. The result may be regarded as a characterization of 2-alternating Choquet capacities. Larry A. Wasserman http://repository.cmu.edu/statistics/17 http://repository.cmu.edu/statistics/17 Tue, 17 Nov 2009 14:35:55 PST Joseph B. Kadane http://repository.cmu.edu/statistics/15 http://repository.cmu.edu/statistics/15 Tue, 17 Nov 2009 14:35:54 PST Necessary and sufficient conditions are given for a triangular array of numbers to be expectations of order statistics of some nonnegative random variable. Using well-known recurrence relations, the expectations of all order statistics of the largest sample size, n, in the triangular array, or the expectations of the smallest of every sample size up to and including n are sufficient to determine the whole array. The former are reduced to a Stieltjes moment problem, the latter to a Hausdorff moment problem. These results are applied to show that for every sample size, there is a positive random variable with geometrically increasing expectations of order statistics with arbitrary ratio and expectation of smallest order statistic. However, only the degenerate distributions have geometrically increasing expectations of order statistics for more than one sample size, even when the ratio and mean of the smallest order statistic can depend on the sample size. These results were required for a study of participation in discussion groups. Joseph B. Kadane http://repository.cmu.edu/statistics/14 http://repository.cmu.edu/statistics/14 Tue, 17 Nov 2009 10:08:46 PST Scanning activity is a common activity on the Internet today, representing malicious activity such as information gathering by a motivated adversary or automated tools searching for vulnerable hosts (e.g., worms). Many scan detection techniques have been developed; however, their focus has been on smaller networks where packet-level information is available, or where internal characteristics of the network are known. For large networks, such as those of ISPs, large corporations or government organizations, this information might not be available. This paper presents a model of scans that can be used given only unidirectional flow data. The model uses a Bayesian logistic regression, which was developed using a combination of expert opinion and manually-classified training data. It is shown to have a detection rate of 95.5% with a false positive rate of 0.4% overall when tested against a set of 300 TCP events. Carrie Gates http://repository.cmu.edu/statistics/13 http://repository.cmu.edu/statistics/13 Mon, 16 Nov 2009 13:20:02 PST Scans are often used by adversaries to determine the potential weaknesses in a target network or system prior to an intrusion attempt. In other cases, exploits are packaged with the scans themselves. This report presents a novel approach to detecting scans (including very stealthy scans) against, or passing through, very large networks. It meets operational requirements that are particular to detecting scans in ISP level networks.This scan-detection approach performs an ongoing, incremental analysis of flow-level data regarding traffic inbound to a network. It is multi-dimensional and flexible, based on up to 21 characteristics describing traffic collected from any single source. The report describes in detail a method developed to provide a probability that a particular traffic sample contains a scan. In validation testing using a manual analysis of traffic collected from a high-volume network, this method correctly classified 99.3% of TCP traffic samples.This report also compares this new approach to other scan approaches, particularly a naïve scan approach, based on simple thresholding, and a modified version of the threshold random walk approach, to which it performed comparably. Combining the random walk approach with the new approach produced very good results, reducing the number of false negatives to zero. Carrie Gates