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INTRODUCTION 1654 I. RULE 104: MABRUS AND ZORGS 1657 II. BOURJAILY AND HUDDLESTON 1660 III. A BRIEF ACCOUNT OF THE PROOF DEBATES 1664 A. Possibility One: Objective Probabilities 1666 B. [...], An unfortunate disconnect exists in modern evidence scholarship. On one hand, a rich literature has explored the process of legal proof in general and legal standards of proof in particular. Call this the "macro level" of legal proof. On the other hand, a rich literature has explored the admissibility rules that regulate the admission or exclusion of particular types of evidence (such as hearsay, character evidence, expert testimony, and so on). Call this the "micro level" of legal proof. Little attention, however, has focused on how the issues discussed in these two distinct strands of evidence scholarship intertwine. One important connection concerns the process and the standards for proving admissibility or exclusion when admissibility or exclusion depends on disputed facts. This Article illustrates how the theoretical debates regarding the proof process as a whole also apply to questions of admissibility. Federal Rule of Evidence 104 creates a two-part structure for the admissibility of evidence that largely mirrors proof issues that apply to a case as a whole--some issues are decided by a fact finder, and some issues are decided under a "reasonable jury" standard. A classic article by John Kaplan coined the terms "mabrus" and "zorgs" to refer to these different types of admissibility determinations. Extending Kaplan's analysis, this Article argues that the best account of what grounds the proof process as a whole (the macro level)--that is, an explanatory account that focuses on the relationships between the evidence and the competing explanations of the parties--also applies to admissibility determinations (the micro level).

Relations between moments and cumulants play a central role in both classical and non-commutative probability theory. The latter allows for several distinct families of cumulants corresponding to different types of independences: free, Boolean and monotone. Relations among those cumulants have been studied recently. In this work, we focus on the problem of expressing with a closed formula multivariate monotone cumulants in terms of free and Boolean cumulants. In the process, we introduce various constructions and statistics on non-crossing partitions. Our approach is based on a pre-Lie algebra structure on cumulant functionals. Relations among cumulants are described in terms of the pre-Lie Magnus expansion combined with results on the continuous Baker-Campbell-Hausdorff formula due to A. Murua., Author(s): Adrian Celestino [sup.1], Kurusch Ebrahimi-Fard [sup.1], Frédéric Patras [sup.2], Daniel Perales [sup.3] Author Affiliations: (1) grid.5947.f, 0000 0001 1516 2393, Department of Mathematical Sciences, Norwegian University of Science and [...]

This paper provides a brief overview of various definitions of multivariate regularly varying functions and some of their applications in probability theory and related fields., 1. Introduction The concept of univariate regularly varying functions was introduced by J. Karamata [10]. Namely, a positive measurable function f (t) defined for t [??] C [??] 0 is [...]

V. APPLICATION TO PEOPLE V. PUCKETT On February 21, 2008, John Puckett was found guilty of first-degree murder for the 1972 death of Diana Sylvester. (70) Sylvester was a twenty-two-year-old [...]

The Supreme Court has held that a plaintiff can have Article III standing based on a fear of future harm, or fear-based injury. The Court's approach to fear-based injury, however, [...]

B. Accuracy Through Communication: Penalties, Anti-Abuse Doctrines, Covered Opinions, and Informed Written Consent to Conflicts In elevating the standard of care on tax shelter opinions in 1984, the Treasury imposed [...]

Several of our colleagues asked, 'Why is this article necessary? Shouldn't the American Statistical Association's (ASA) statement on p-values be enough?' Our answer to this is affirmative; the ASA's statement [...]

INTRODUCTION The World Series is tied at three games apiece. Going into the decisive seventh game, which players would you prefer to have in the line-up? If it is the [...]

We model a system that consists of a stream of customers processed through three steps by two resources. The first resource, an investigator, handles the first step, in which she collects information from the customer and decides what work will be done in the second step by the second resource, the back office. In the third step, the investigator returns to the customer armed with the additional information or analysis done by the back office and provides the customer with a conclusion, solution, or diagnosis. The investigator has to prioritize either seeing a new customer or completing the work with a customer already in the system. While serving one customer, the investigator may be interrupted by requests from the other customers in the system. Our main objective is to understand the impact of the investigator's choices on system throughput. In addition, we are interested in the occupancy of the system (and thus the flow time of customers). We create a stylized queueing model to examine the investigator's decisions and show that, when interruptions are not an issue, the investigator should prioritize new customers to maximize throughput, keeping the system as full as possible. If customers who have been in the system for a long time generate interruptions and thus additional work for the investigator, we show that it is asymptotically optimal for the investigator to keep the system occupancy low and prioritize discharging customers. Our conclusions are based on a model of a re-entrant queue with dedicated servers serving multiple stations, with two novel features: a buffer that is shared between stations, and jobs in the system generating additional work for the servers. Key words: dynamic programming; optimal control; Markov; healthcare; hospitals; probability; Markov processes; stochastic; queues; limit theorems History: Received September 28, 2010; accepted July 12, 2012, by Assaf Zeevi, stochastic models and simulation. Published online in Articles in Advance January 8, 2013., 1. Introduction We model a system that consists of a stream of customers processed through three steps by two resources. The first resource, an investigator, handles the first step, in [...]

In this paper we focus on robust linear optimization problems with uncertainty regions defined by ∅-divergences (for example, chi-squared, Hellinger, Kullback--Leibler). We show how uncertainty regions based on ∅-divergences arise in a natural way as confidence sets if the uncertain parameters contain elements of a probability vector. Such problems frequently occur in, for example, optimization problems in inventory control or finance that involve terms containing moments of random variables, expected utility, etc. We show that the robust counterpart of a linear optimization problem with ∅-divergences uncertainty is tradable for most of the choices of ∅typically considered in the literature. We extend the results to problems that are nonlinear in the optimization variables. Several applications, including an asset pricing example and a numerical multiitem newsvendor example, illustrate the relevance of the proposed approach. Key words: robust optimization; ∅-divergences; goodness-of-fit statistics History: Received April 20, 2011; accepted December 16, 2011, by Gerard P. Cachon, optimization. Published online in Articles in Advance November 9, 2012., 1. Introduction Several papers in the late 1990s (Kouvelis and Yu 1997; Ben-Tal and Nemirovski 1997, 1998; El Ghaoui and Lebret 1997; El Ghaoui et al. 1998) started a revival [...]

We provide an explicit gradient formula for linear chance constraints under a (possibly singular) multivariate Gaussian distribution. This formula allows one to reduce the calculus of gradients to the calculus [...]

We present upper and lower bounds for the tail distribution of the stationary waiting time D in the stable GI/GI/s first-come first-served (FCFS) queue. These bounds depend on the value [...]

I. Introduction One of the most interesting, if overlooked, observations made by the great mathematician I.J. Good is that we lose nothing from a purely mathematical point of view if [...]

Byline: Antoni Bosch-Domenech (1), Jose G. Montalvo (1), Rosemarie Nagel (1), Albert Satorra (1) Keywords: Beauty-contest experiments; Decision theory; Reasoning hierarchy; Finite mixture distribution; Beta distribution; EM algorithm; C14; C16; C72; C91; D03 Abstract: This paper introduces a mixture model based on the beta distribution, without pre-established means and variances, to analyze a large set of Beauty-Contest data obtained from diverse groups of experiments (Bosch-Domenech et al. 2002). This model gives a better fit of the experimental data, and more precision to the hypothesis that a large proportion of individuals follow a common pattern of reasoning, described as Iterated Best Reply (degenerate), than mixture models based on the normal distribution. The analysis shows that the means of the distributions across the groups of experiments are pretty stable, while the proportions of choices at different levels of reasoning vary across groups. Author Affiliation: (1) Department of Economics and Business, Universitat Pompeu Fabra, Ramon Trias Fargas 25-27, 08005, Barcelona, Spain Article History: Registration Date: 07/07/2010 Received Date: 14/07/2008 Accepted Date: 07/07/2010 Online Date: 28/07/2010 Article note: We thank the editor and two referees for insightful comments that helped improve the manuscript. Thanks are also due to the Spanish Ministerio de Educacion y Ciencia for financial help under research projects SEJ2005-03891/ECON (AB-D), SEJ2006-135 and SEJ2007-64340, and by the Barcelona GSE research network and the Fellowship Icrea Academia, Generalitat de Catalunya.

We consider large-scale studies in which there are hundreds or thousands of correlated cases to investigate, each represented by its own normal variate, typically a z-value. A familiar example is provided by a microarray experiment comparing healthy with sick subjects' expression levels for thousands of genes. This paper concerns the accuracy of summary statistics for the collection of normal variates, such as their empirical cdf or a false discovery rate statistic. It seems like we must estimate an N by N correlation matrix, N the number of cases, but our main result shows that this is nut necessary: good accuracy approximations can be based on the root mean square correlation over all N * (N - 1)/2 pairs, a quantity often easily estimated. A second result shows that z-values closely follow normal distributions even under nonnull conditions, supporting application of the main theorem. Practical application of the theory is illustrated for a large leukemia microarray study. KEY WORDS: Acceleration; Correlation penalty; Empirical process; Mehler's identity; Nonnull z-values; Rms correlation.

The favorite--long shot bias describes the long-standing empirical regularity that betting odds provide biased estimates of the probability of a horse winning: long shots are overbet whereas favorites are underbet. Neoclassical explanations of this phenomenon focus on rational gamblers who overbet long shots because of risk-love. The competing behavioral explanations emphasize the role of misperceptions of probabilities. We provide novel empirical tests that can discriminate between these competing theories by assessing whether the models that explain gamblers' choices in one part of their choice set (betting to win) can also rationalize decisions over a wider choice set, including compound bets in the exacta, quinella, or trifecta pools. Using a new, large-scale data set ideally suited to implement these tests, we find evidence in favor of the view that misperceptions of probability drive the favorite-long shot bias, as suggested by prospect theory.

Testing a proposed explanation of a statistical phenomenon is conceptually difficult. This class segment is intended to spotlight the issues. This article has supplementary material online. KEY WORDS: Benford's law; Fuzzy CLT; Normal distribution for data; Teaching.

This article explicates and defends Peirce's views on the relation of inductive inference to the concept of probability and to the concept of what Peirce calls 'verisimilitude' or 'likelihood.' In particular it discusses the difference between probability and verisimilitude, and it expands upon Peirce's claim that induction does not have a probability but rather has a verisimilitude. The article shows that Peirce rejected as absurd the dominant Bayesianism of his day, as famously utilized by his predecessor Pierre Simon Laplace and by his almost-contemporaries Augustus De Morgan and Adolphe Quetelet. The article argues that in this rejection of Bayesianism, and in Peirce's own account of verisimilitude as the crucial notion to be used in assessing the strength of an inductive argument, Peirce by 1878 had anticipated several standard ideas of twentieth-century statistics in connection with sampling theory and hypothesis-testing, ideas often associated with, for example, R. A. Fisher and Jerzy Neyman. Keywords: Probability, Induction, Bayes's Theorem, Rule of Succession, Hypothesis Testing, Likelihood, Verisimilitude, Peirce., Introduction In 1910, only four years before his death, Peirce began an adumbration of a life's worth of major results concerning nondeductive logic--results that he had reached after more than [...]

As noted by Persi Diaconis, the apparently simple problem of calculating the face probabilities of a shaved die defies exact mathematical analysis. However, this problem can be used to provide amusing and instructive examples of sufficiency, efficiency, information, ancillarity, and the value of statistical design. KEY WORDS: Ancillarity; Design; Efficiency; Estimation; Face probability; Fisher information; Multinomial distribution; Shaved die; Sufficiency.

Information consisting of probabilities of some (but possibly not all) events induces an integral with respect to a probability specified on a subalgebra. A decision maker evaluates the alternatives using [...]

This paper considers buffer overflow probabilities for stable queueing systems with one server and different classes of arrivals. The service priority is given to the class of customers whose current [...]

A long tradition of psychological research has lamented the systematic errors and biases in people's perception of the characteristics of sequences generated by a random mechanism such as a coin toss. It is proposed that once the likely nature of people's actual experience of such processes is taken into account, these 'errors' and 'biases' actually emerge as apt reflections of the probabilistic characteristics of sequences of random events. Specifically, seeming biases reflect the subjective experience of a finite data stream for an agent with a limited short-term memory capacity. Consequently, these biases seem testimony not to the limitations of people's intuitive statistics but rather to the extent to which the human cognitive system is finely attuned to the statistics of the environment. Keywords: randomness, intuitive statistics, representativeness, gambler's fallacy, probability

A comprehensive analysis on shielding against lightning is presented. For an air terminal, the design of its protection zone and collection volume is introduced on the basis of simple working relationships which take into account, besides lightning parameters and air terminal height, the interception probability and use as a reference the striking distance to earth surface. The analysis, based on lightning scale-model experimental results, includes a comparison with previously reported models and field data; a satisfactory agreement is found. Lightning incidence calculations have been performed on the basis of lightning interception probability; a close conformity between the actual and calculated number of lightning strikes exists. Both striking distance and interception radius and their statistical nature should be considered for an accurate description of lightning interception. Index Terms--Air gaps, attractive radius, electric breakdown, interception probability, lightning protection, striking distance.