Wolford, and two anonymous reviewers for very useful comments on earlier drafts of the manuscript. Correspondence may be addressed to

Given two distributions over an n element set, we wish to check whether these distributions are statistically close by only sampling. We give a sublinear algorithm which uses O(n 2/3 ɛ −4 log n) independent samples from each distribution, runs in time linear in the sample size, makes no assumptions about the structure of the distributions, and distinguishes the cases ɛ when the distance between the distributions is small (less than max ( 2 32 3 √ n, ɛ 4 √)) or large (more n than ɛ) in L1-distance. We also give an Ω(n 2/3 ɛ −2/3) lower bound. Our algorithm has applications to the problem of checking whether a given Markov process is rapidly mixing. We develop sublinear algorithms for this problem as well.

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Data mining is on the interface of Computer Science and Statistics, utilizing advances in both disciplines to make progress in extracting information from large databases. It is an emerging field that has attracted much attention in a very short period of time. This article highlights some statistical themes and lessons that are directly relevant to data mining and attempts to identify opportunities where close cooperation between the statistical and computational communities might reasonably provide synergy for further progress in data analysis.

This report investigates the "decision lanisio es" that characterize several forms of biometric decision makinn The issues discussed inIP/PF (i) Estimatin the degrees-of-freedom associated with different biometrics, as a way ofmeasurin theranFfl3#9N an complexity(an therefore the unWflWW#9Nfl of their templates. (ii) The conflflP#9NflY of combin/I more than on biometric test to arrive at a decision (iii) The requiremen ts for performin iden tification by large-scale exhaustive database search, as opposed to mere verification bycomparison againr a sin;I template. (iv)ScenWP3F for Biometric Key Cryptography (the use of biometrics forenPflW/#9N of messages). These issues are conFFYI#9 here in abstract form, but where appropriate, the particular example of iris recognflfl#9 is used asan illustration Aun;FflI# theme of all four sets of issues is the role of combinF3PY#9 complexity, an itsmeasuremen t,in determinFP the potential decisiveness of biometric decision making.

This paper discusses diagnosis problems in distributed systems within the context of a language-theoretic discrete event formalism. A distributed system is seen as a system with multiple spatially separated sites with each site having a diagnoser that observes some of the events generated by the system and diagnoses the faults associated with the site. We allow the diagnosers to share information by sending messages to each other. The existence and synthesis of diagnosers is investigated. The formulation and results are motivated by the diagnosis of failures in a wireless LAN. 1 Introduction We are interested in understanding the design of diagnostics for distributed systems. This theoretical work is motivated by our experience with the design of distributed diagnostics for coordinating vehicle systems [5, 10] and wireless local area networks [3, 6]. These systems are comprised of spatially separated sites (e.g., vehicles or radios) of semi-autonomous activity. Since these systems op...

Despite the widespread use of key concepts of the Neyman–Pearson (N–P) statistical paradigm—type I and II errors, significance levels, power, confidence levels—they have been the subject of philosophical controversy and debate for over 60 years. Both current and long-standing problems of N–P tests stem from unclarity and confusion, even among N–P adherents, as to how a test’s (pre-data) error probabilities are to be used for (post-data) inductive inference as opposed to inductive behavior. We argue that the relevance of error probabilities is to ensure that only statistical hypotheses that have passed severe or probative tests are inferred from the data. The severity criterion supplies a meta-statistical principle for evaluating proposed statistical inferences, avoiding classic fallacies from tests that are overly sensitive, as well as those not sensitive enough to particular errors and discrepancies.

We consider neurally-based models for decision-making in the presence of noisy incoming data. The two-alternative forced-choice task has been extensively studied, and in that case it is known that mutually-inhibited leaky integrators in which leakage and inhibition balance can closely approximate a drift-diffusion process that is the continuum limit of the optimal sequential probability ratio test (SPRT). Here we study the performance of neural integrators in n ≥ 2 alternative choice tasks and relate them to a multihypothesis sequential probability ratio test (MSPRT) that is asymptotically optimal in the limit of vanishing error rates. While a simple race model can implement this ‘max-vs-next ’ MSPRT, it requires an additional computational layer, while absolute threshold crossing tests do not require such a layer. Race models with absolute thresholds perform relatively poorly, but we show that a balanced leaky accumulator model with an absolute crossing criterion can approximate a ‘max-vs-ave ’ test that is intermediate in performance between the absolute and max-vs-next tests. We consider free and fixed time response protocols, and show that the resulting mean reaction times under the former and decision times for fixed accuracy under the latter obey versions of Hick’s law in the low error rate range, and we interpret this in terms of information gained. Specifically, we derive relationships of the forms log(n − 1), log(n), or log(n + 1) depending on error rates, signal-to-noise ratio, and the test itself. We focus on linearized models, but also consider nonlinear effects of neural activities (firing rates) that are bounded below and show how they modify Hick’s law. KEYWORDS: leaky accumulator, drift-diffusion model, neural network, Hick’s law, multihypothesis sequential test, sequential ratio test.

This supplement provides detailed information about the functionalities of the Potters-Wheel toolbox as described in the main text. For further information please use the

It is generally believed that by combining several diverse intrusion detectors (i.e., forming an IDS ensemble), we may achieve better performance. However, there has been very little work on analyzing the effectiveness of an IDS ensemble. In this paper, we study the following problem: how to make a good fusion decision on the alerts from multiple detectors in order to improve the final performance. We propose a decision-theoretic alert fusion technique based on the likelihood ratio test (LRT). We report our experience from empirical studies, and formally analyze its practical interpretation based on ROC curve analysis. Through theoretical reasoning and experiments using multiple IDSs on several data sets, we show that our technique is more flexible and also outperforms other existing fusion techniques such as AND, OR, majority voting, and weighted voting.