CiteULike: Tag probability

On the minimum hop count and connectivity in one-dimensional ad hoc wireless networks

Nelson Antunes — 2008-07-16T11:03:39-00:00

Telecommunication Systems

Abstract This paper investigates connectivity in one-dimensional ad hoc networks by means of the distribution of the minimum hop count between source and destination nodes. We derive the exact probability distribution of the minimum hop count from the location density of relay nodes in the multihop path selected with the Most Forward within Radius (MFR) scheme. The probability that the source and destination nodes are connected (provided by Ghasemi and Nader-Esfahani [IEEE Commun. Lett. 10(4):251–253, 2006]) can be obtained by summing the probability masses for each possible value of the minimum hop count, which provides new insights to the connectivity probability. Numerical results show the effect of the number of nodes and the transmission range on the minimum hop count.

Network heavy traffic modeling using α-stable self-similar processes

A Karasaridis — 2008-01-24T12:06:07-00:00

Communications, IEEE Transactions on, Vol. 49, No. 7. (2001), pp. 1203-1214.

We propose a new model for network heavy traffic approximation, based on α-stable self-similar processes, namely the skewed linear fractional stable noise. The model demonstrates more flexibility than existing models in fitting different levels of burstiness and correlation in the data. Nonetheless, it is parsimonious in the number of parameters, which have a direct physical meaning. An algorithmic procedure for the estimation of the model parameters is presented, and an asymptotic lower bound of the residual queueing distribution is derived. Extensive simulations are presented, where the new model is fitted to bursty Ethernet data collected at Bellcore (now Telcordia) Laboratories. Furthermore, new measurements of aggregate Web and Webcasting traffic are introduced along with traffic generated by the fitted new model. Queueing simulations of a G/D/1 system confirm our analytical results regarding the tail of the queue distribution

Neural correlates of decision processes: neural and mental chronometry.

JD Schall — 2005-02-08T00:36:59-00:00

Curr Opin Neurobiol, Vol. 13, No. 2. (April 2003), pp. 182-186.

Recent studies aim to explain the duration and variability of behavioral reaction time in terms of neural processes. The time taken to make choices is occupied by at least two processes. Neurons in sensorimotor structures accumulate evidence that leads to alternative categorizations, while other neurons within these structures prepare and initiate overt responses. These distinct stages of stimulus encoding and response preparation support variable but flexible behavior.

Neural computation of log likelihood in control of saccadic eye movements.

RH Carpenter — 2005-02-08T01:18:29-00:00

Nature, Vol. 377, No. 6544. (7 September 1995), pp. 59-62.

The latency between the appearance of a visual target and the start of the saccadic eye movement made to look at it varies from trial to trial to an extent that is inexplicable in terms of ordinary 'physiological' processes such as synaptic delays and conduction velocities. An alternative interpretation is that it represents the time needed to decide whether a target is in fact present: decision processes are necessarily stochastic, because they depend on extracting information from noisy sensory signals. In one such model, the presence of a target causes a signal in a decision unit to rise linearly at a rate r from its initial value s0 until it reaches a fixed threshold theta, when a saccade is initiated. One can regard this decision signal as a neural estimate of the log likelihood of the hypothesis that the target is present, the threshold being the significance criterion or likelihood level at which the target is presumed to be present. Experiments manipulating the prior probability of the target's appearing confirm this notion: the latency distribution then changes in the way expected if s0 simply reflects the prior log likelihood of the stimulus.

Diagrammatic Reasoning as the Basis for Developing Concepts: A Semiotic Analysis of Students' Learning about Statistical Distribution

Arthur Bakker — 2005-11-30T17:22:41-00:00

Educational Studies in Mathematics, Vol. 60, No. 3. (November 2005), pp. 333-358.

The Evolution with Age of Probabilistic, Intuitively Based Misconceptions

Efraim Fischbein — 2006-02-07T15:17:23-00:00

Journal for Research in Mathematics Education, Vol. 28, No. 1. (1997), pp. 96-105.

The purpose of this research was to investigate the evolution, with age, of probabilistic, intuitively based misconceptions. We hypothesized, on the basis of previous research with infinity concepts, that these misconceptions would stabilize during the emergence of the formal operation period. The responses to probability problems of students in Grades 5, 7, 9, and 11 and of prospective teachers indicated, contrary to our hypothesis, that some misconceptions grew stronger with age, whereas others grew weaker. Only one misconception investigated was stable across ages. An attempt was made to find a theoretical explanation for this rather strange and complex situation.

Informal Conceptions of Probability

Clifford Konold — 2006-02-07T15:16:07-00:00

A model of informal reasoning under conditions of uncertainty, the outcome approach, was developed to account for the nonnormative responses of a subset of 16 undergraduates who were interviewed. For individuals who reason according to the outcome approach, the goal in questions of uncertainty is to predict the outcome of an individual trial. Their predictions take the form of yes-no decisions on whether an outcome will occur on a particular trial. These predictions are then evaluated as having been either right or wrong. Their predictions are often based on a deterministic model of the situation. In follow-up interviews using a different set of problems, responses of outcome-oriented participants were predicted interpretations of probabiltity and with the "representativeness heuristic" (Kahneman & Tversky, 1972). Although the outcome approach is inconsistent with formal theories of probability, its components are logically consistent and reasonable in the context of everyday decision making.

Inconsistencies in Students' Reasoning about Probability

Clifford Konold — 2006-02-07T15:15:13-00:00

Journal for Research in Mathematics Education, Vol. 24, No. 5. (1993), pp. 392-414.

Subjects were asked to select from among four possible sequences the "most likely" to result from flipping a coin five times. Contrary to the results of Kahneman and Tversky (1972), the majority of subjects (72%) correctly answered that the sequences are equally likely to occur. This result suggests, as does performance on similar NAEP items, that most secondary school and college-age students view successive outcomes of a random process as independent. However, in a follow-up question, subjects were also asked to select the "least likely" result. Only half the subjects who had answered correctly responded again that the sequences were equally likely; the others selected one of the sequences as least likely. This result was replicated in a second study in which 20 subjects were interviewed as they solved the same problems. One account of these logically inconsistent responses is that subjects reason about the two questions from different perspectives. When asked to select the most likely outcome, some believe they are being asked to predict what actually will happen, and give the answer "equally likely" to indicate that all of the sequences are possible. This reasoning has been described by Konold (1989) as an "outcome approach" to uncertainty. This prediction scheme does not fit questions worded in terms of the least likely result, and thus some subjects select an incompatible answer based on "representativeness" (Kahneman & Tversky, 1972). These results suggest that the percentage of secondary school students who understand the concept of independence is much lower than the latest NAEP results would lead us to believe and, more generally, point to the difficulty of assessing conceptual understanding with multiple-choice items.

Judgment of Coincidences: Mine versus Yours

Ruma Falk — 2006-02-07T15:13:36-00:00

The American Journal of Psychology, Vol. 102, No. 4. (1989), pp. 477-493.

Previous research indicated that subjects are not very surprised when reading coincidence stories, apparently because they regard the coincidence as one of many events that could have happened. This was true with respect to coincidences written by somebody else. However, there were indications that subjects found their own coincidences more surprising than those of others. The present study examines that egocentric bias and explores it further. In Experiment 1, a rotating design was employed in which the same story served, in turn, as self- and as other-coincidence, thereby controlling for the story's objective surprisingness. In Experiment 2, the coincidences occurred "spontaneously" in the course of the experiment, thus controlling for self-selection of subjectively surprising stories. Self-coincidences were judged more surprising than those of others in both experiments. The results suggest that the more personally meaningful the self-coincidence, the more surprising it is.

Design and sensitivity analysis using the probability-safety-factor method. An application to retaining walls

Enrique Castillo — 2008-07-29T16:05:29-00:00

Structural Safety, Vol. 26, No. 2. (April 2004), pp. 159-179.

This paper presents a new method for designing engineering works that makes the classical approach, based on safety factors, and the modern, probability-based, approach compatible, and includes a sensitivity analysis. The method consists of a sequence of classical designs, based on given safety factors, that (a) minimize cost or optimize an alternative objective function, (b) calculate the different failure mode probabilities or their upper bounds, and (c) update the safety factors to satisfy both the safety factors and the failure probability requirements. The process is repeated until convergence. As a result, an automatic design of the engineering work, the safety factors and the corresponding probabilities of failure for all failure modes are obtained. A double safety check is used and the correspondence between safety factors and probabilities of failure for the different modes are easily understood. An advantage of this approach is that the optimization procedure and the reliability calculations are decoupled. In addition, a sensitivity analysis is performed using a method that consists of transforming the data parameters into artificial variables and using the dual associated problem. The method is illustrated by its application to a retaining wall design.

Probability Theory : The Logic of Science

ET Jaynes — 2005-07-01T16:10:36-00:00

(10 April 2003)

Going beyond the conventional mathematics of probability theory, this study views the subject in a wider context. It discusses new results, along with applications of probability theory to a variety of problems. The book contains many exercises and is suitable for use as a textbook on graduate-level courses involving data analysis. Aimed at readers already familiar with applied mathematics at an advanced undergraduate level or higher, it is of interest to scientists concerned with inference from incomplete information.

Building probabilistic networks: where do the numbers come from

M Druzdzel — 2007-08-11T10:48:39-00:00

(1995)

This paper focuses on the task of obtaining the probabilities required, the most daunting task in building probabilistic networks; the paper basically is a guide to the relevant literature. In Section 2, we describe the various sources of probabilistic information that are typically available for the task. In Section 3, we address the question how accurate the numbers obtained should be to arrive at satisfactory behaviour of a probabilistic network. In Section 5, we review various methods and...

A Resource Framework for Quantum Shannon Theory

I Devetak — 2006-01-20T01:37:09-00:00

(2 Dec 2005)

Quantum Shannon theory is loosely defined as a collection of coding theorems, such as classical and quantum source compression, noisy channel coding theorems, entanglement distillation, etc., which characterize asymptotic properties of quantum and classical channels and states. In this paper we advocate a unified approach to an important class of problems in quantum Shannon theory, consisting of those that are bipartite, unidirectional and memoryless. We formalize two principles that have long been tacitly understood. First, we describe how the Church of the larger Hilbert space allows us to move flexibly between states, channels, ensembles and their purifications. Second, we introduce finite and asymptotic (quantum) information processing resources as the basic objects of quantum Shannon theory and recast the protocols used in direct coding theorems as inequalities between resources. We develop the rules of a resource calculus which allows us to manipulate and combine resource inequalities. This framework simplifies many coding theorem proofs and provides structural insights into the logical dependencies among coding theorems. We review the above-mentioned basic coding results and show how a subset of them can be unified into a family of related resource inequalities. Finally, we use this family to find optimal trade-off curves for all protocols involving one noisy quantum resource and two noiseless ones.

What is Probability?

Simon Saunders — 2004-12-28T11:12:19-00:00

(24 December 2004)

Probabilities may be subjective or objective; we are concerned with both kinds of probability, and the relationship between them. The fundamental theory of objective probability is quantum mechanics: it is argued that neither Bohr's Copenhagen interpretation, nor the pilot-wave theory, nor stochastic state-reduction theories, give a satisfactory answer to the question of what objective probabilities are in quantum mechanics, or why they should satisfy the Born rule; nor do they give any reason why subjective probabilities should track objective ones. But it is shown that if probability only arises with decoherence, then they must be given by the Born rule. That further, on the Everett interpretation, we have a clear statement of what probabilities are, in terms of purely categorical physical properties; and finally, along lines recently laid out by Deutsch and Wallace, that there is a clear basis in the axioms of decision theory as to why subjective probabilities should track these objective ones. These results hinge critically on the absence of hidden-variables or any other mechanism (such as state-reduction) from the physical interpretation of the theory. The account of probability has traditionally been considered the principal weakness of the Everett interpretation; on the contrary it emerges as one of its principal strengths.

Facts, Values and Quanta

DM Appleby — 2005-09-28T04:57:59-00:00

(3 Feb 2004)

Quantum mechanics is a fundamentally probabilistic theory (at least so far as the empirical predictions are concerned). It follows that, if one wants to properly understand quantum mechanics, it is essential to clearly understand the meaning of probability statements. The interpretation of probability has excited nearly as much philosophical controversy as the interpretation of quantum mechanics. 20th century physicists have mostly adopted a frequentist conception. In this paper it is argued that we ought, instead, to adopt a logical or Bayesian conception. The paper includes a comparison of the orthodox and Bayesian theories of statistical inference. It concludes with a few remarks concerning the implications for the concept of physical reality.

Quantum Theory From Five Reasonable Axioms

Lucien Hardy — 2005-07-29T04:54:27-00:00

(25 Sep 2001)

The usual formulation of quantum theory is based on rather obscure axioms (employing complex Hilbert spaces, Hermitean operators, and the trace rule for calculating probabilities). In this paper it is shown that quantum theory can be derived from five very reasonable axioms. The first four of these are obviously consistent with both quantum theory and classical probability theory. Axiom 5 (which requires that there exists continuous reversible transformations between pure states) rules out classical probability theory. If Axiom 5 (or even just the word "continuous" from Axiom 5) is dropped then we obtain classical probability theory instead. This work provides some insight into the reasons quantum theory is the way it is. For example, it explains the need for complex numbers and where the trace formula comes from. We also gain insight into the relationship between quantum theory and classical probability theory.

A Philosophical Essay on Probabilities

Marquis de Laplace — 2007-01-18T10:58:10-00:00

(18 January 1996)

<div>Scientific classic introduces lay readers to the concepts and uses of probability theory, demonstrating, without the use of higher mathematics, the application of probability to games of chance, physics, reliability of witnesses, astronomy, insurance, democratic government and many other areas. Also demonstrates how a great scientist could express many complex ideas in simple terms. </div>

Fooled by Randomness: The Hidden Role of Chance in the Markets and in Life, First Edition

Nassim Taleb — 2005-07-17T21:05:08-00:00

(04 October 2001)

If the prescriptions for getting rich that are outlined in books such as The Millionaire Next Door and Rich Dad Poor Dad are successful enough to make the books bestsellers, then one must ask, Why aren't there more millionaires? In Fooled by Randomness, Nassim Nicholas Taleb, a professional trader and mathematics professor, examines what randomness means in business and in life and why human beings are so prone to mistake dumb luck for consummate skill. This eccentric and highly personal exploration of the nature of randomness meanders from the court of Croesus and trading rooms in New York and London to Russian roulette, Monte Carlo engines, and the philosophy of Karl Popper. Part of what makes this book so good is Taleb's ability to make seemingly arcane mathematical concepts (at least to this reviewer) entirely relevant in evaluating and understanding everything from the stock market to the success of those millionaires cited in the aforementioned bestsellers. Here's an articulate, wise, and humorous meditation on the nature of success and failure that anyone who wants a little more of the former would do well to consider. Highly recommended. --Harry C. Edwards This book is about luck -- or more precisely how we perceive and deal with luck in business and life. Set against the backdrop of the most conspicuous forum in which luck is mistaken for skill -- the world of trading -- Fooled by Randomness is a captivating insight into one of the least understood factors in all our lives. Writing in an entertaining and narrative style, the author succeeds in tackling and explaining three major intellectual issues: the problem of induction, the survivorship biases, and our genetic unfitness to the modern world. The book is populated with an array of characters, some of whom have grasped, in their own way, the significance of chance: Yogi Berra, the baseball legend; Karl Popper, the philosopher of knowledge; Solon, the Ancient World's wisest man; the modern financier George Soros; and the Greek voyager Ulysses. In addition we meet the fictional Nero, who seems to understand the role of randomness in his trading life, but who also falls victim to his own superstitious foolishness. But the most recognizable character of all remains unnamed -- the lucky fool in the right place at the right time. The embodiment of the "Survival of the Least Fit." Such individuals attract devoted followers who believe in their guru's insights and methods. But no one can replicate what is obtained through chance. A monkey banging on a keyboard may eventually produce the Iliad, but would you sign him to write the sequel? Are we capable of distinguishing the fortunate charlatan from the genuine visionary? Must we always try to uncover non-existent messages in random events? It may be impossible to guard ourselves against the vagaries of the Goddess Fortuna, but after reading Fooled by Randomness we can be a little better prepared.

A Probabilistic Approach to WLAN User Location Estimation

Teemu Roos — 2005-07-16T07:16:49-00:00

International Journal of Wireless Information Networks, Vol. 9, No. 3. (July 2002), pp. 155-164.

Sudden Infant Death or Murder? A Royal Confusion About Probabilities

Neven Sesardic — 2007-07-04T12:36:02-00:00

Br J Philos Sci, Vol. 58, No. 2. (1 June 2007), pp. 299-329.

In this article I criticize the recommendations of some prominent statisticians about how to estimate and compare probabilities of the repeated sudden infant death and repeated murder. The issue has drawn considerable public attention in connection with several recent court cases in the UK. I try to show that when the three components of the Bayesian inference are carefully analyzed in this context, the advice of the statisticians turns out to be problematic in each of the steps. 1 Introduction 2 Setting the Stage: Bayes's Theorem 3 Prior Probabilities of Single SIDS and Single Homicide 4 Prior Probabilities of the Recurrence of SIDS and Homicide 5 Likelihoods of Double SIDS and Double Homicide 6 Posterior Probabilities of Double SIDS and Double Homicide 7 Conclusion 10.1093/bjps/axm015

Reasoning about Uncertainty

Joseph Halpern — 2005-03-05T20:11:59-00:00

(01 October 2003)

Uncertainty is a fundamental and unavoidable feature of daily life; in order to deal with uncertaintly intelligently, we need to be able to represent it and reason about it. In this book, Joseph Halpern examines formal ways of representing uncertainty and considers various logics for reasoning about it. While the ideas presented are formalized in terms of definitions and theorems, the emphasis is on the philosophy of representing and reasoning about uncertainty; the material is accessible and relevant to researchers and students in many fields, including computer science, artificial intelligence, economics (particularly game theory), mathematics, philosophy, and statistics. Halpern begins by surveying possible formal systems for representing uncertainty, including probability measures, possibility measures, and plausibility measures. He considers the updating of beliefs based on changing information and the relation to Bayes' theorem; this leads to a discussion of qualitative, quantitative, and plausibilistic Bayesian networks. He considers not only the uncertainty of a single agent but also uncertainty in a multi-agent framework. Halpern then considers the formal logical systems for reasoning about uncertainty. He discusses knowledge and belief; default reasoning and the semantics of default; reasoning about counterfactuals, and combining probability and counterfactuals; belief revision; first-order modal logic; and statistics and beliefs. He includes a series of exercises at the end of each chapter.

Incremental Tradeoff Resolution in Qualitative Probabilistic Networks

Chao Liu — 2008-03-19T15:23:29-00:00

pp. 338-345.

ions, Decisions, and Uncertainty, Providence, RI, USA, July 1997 Incremental Tradeoff Resolution in Qualitative Probabilistic Networks Chao-Lin Liu and Michael P. Wellman University of Michigan AI Laboratory Ann Arbor, MI 48109-2110 fchaolin, wellmang@umich.edu Abstract Qualitative probabilistic reasoning in a Bayesian network often reveals tradeoffs: relationships that are ambiguous due to competing qualitative influences. We present two techniques that combine qualitative and numeric...

Stochastic Processes

Sheldon Ross — 2005-05-09T23:11:50-00:00

(03 August 1983)

Probabilistic score estimation with piecewise logistic regression

Jian Zhang — 2007-09-25T15:36:28-00:00

(2004)

Predicting Good Probabilities with Supervised Learning

Alexandru Mizil — 2007-02-28T08:27:18-00:00

We examine the relationship between the predictions made by different learning algorithms and true posterior probabilities. We show that maximum margin methods such as boosted trees and boosted stumps push probability mass away from 0 and 1 yielding a characteristic sigmoid shaped distortion in the predicted probabilities. Models such as Naive Bayes, which make unrealistic independence assumptions, push probabilities toward 0 and 1. Other models such as neural nets and bagged trees do ...

Unifying the error-correcting and output-code AdaBoost within the margin framework

Yijun Sun — 2005-12-09T02:00:42-00:00

(2005), pp. 872-879.

Hierarchical testing designs for pattern recognition

G Blanchard — 2007-06-07T09:24:00-00:00

ArXiv Mathematics e-prints (July 2005)

We explore the theoretical foundations of a “twenty questions” approach to pattern recognition. The object of the analysis is the computational process itself rather than probability distributions (Bayesian inference) or decision boundaries (statistical learning). Our formulation is motivated by applications to scene interpretation in which there are a great many possible explanations for the data, one (“background”) is statistically dominant, and it is imperative to restrict intensive computation to genuinely ambiguous regions. The focus here is then on pattern filtering: Given a large set Y of possible patterns or explanations, narrow down the true one Y to a small (random) subset Y⊂Y of “detected” patterns to be subjected to further, more intense, processing. To this end, we consider a family of hypothesis tests for Y∈ A versus the nonspecific alternatives Y∈ A^c. Each test has null type I error and the candidate sets A⊂Y are arranged in a hierarchy of nested partitions. These tests are then characterized by scope (|A|), power (or type II error) and algorithmic cost. We consider sequential testing strategies in which decisions are made iteratively, based on past outcomes, about which test to perform next and when to stop testing. The set Y is then taken to be the set of patterns that have not been ruled out by the tests performed. The total cost of a strategy is the sum of the “testing cost” and the “postprocessing cost” (proportional to | Y|) and the corresponding optimization problem is analyzed.

Mafia: A theoretical study of players and coalitions in a partial information environment

Mark Braverman — 2008-07-01T21:06:32-00:00

(16 Jun 2008)

In this paper, we study a game called “Mafia,” in which different players have different types of information, communication and functionality. The players communicate and function in a way that resembles some real-life situations. We consider two types of operations. First, there are operations that follow an open democratic discussion. Second, some subgroups of players who may have different interests make decisions based on their own group interest. A key ingredient here is that the identity of each subgroup is known only to the members of that group. In this paper, we are interested in the best strategies for the different groups in such scenarios and in evaluating their relative power. The main focus of the paper is the question: How large and strong should a subgroup be in order to dominate the game? The concrete model studied here is based on the popular game “Mafia.” In this game, there are three groups of players: Mafia, detectives and ordinary citizens. Initially, each player is given only his/her own identity, except the mafia, who are given the identities of all mafia members. At each “open” round, a vote is made to determine which player to eliminate. Additionally, there are collective decisions made by the mafia where they decide to eliminate a citizen. Finally, each detective accumulates data on the mafia/citizen status of players. The citizens win if they eliminate all mafia members. Otherwise, the mafia wins. We first find a randomized strategy that is optimal in the absence of detectives. This leads to a stochastic asymptotic analysis where it is shown that the two groups have comparable probabilities of winning exactly when the total population size is $R$ and the mafia size is of order $\sqrtR$. We then show that even a single detective changes the qualitative behavior of the game dramatically. Here, the mafia and citizens have comparable winning probabilities only for a mafia size linear in $R$. Finally, we provide a summary of simulations complementing the theoretical results obtained in the paper.

Measure, Integral and Probability

Marek Capinski — 2005-02-27T09:46:23-00:00

(30 August 2004)

Measure, Integral and Probability is a gentle introduction that makes measure and integration theory accessible to the average third-year undergraduate student. The ideas are developed at an easy pace in a form that is suitable for self-study, with an emphasis on clear explanations and concrete examples rather than abstract theory. For this second edition, the text has been thoroughly revised and expanded. New features include: · a substantial new chapter, featuring a constructive proof of the Radon-Nikodym theorem, an analysis of the structure of Lebesgue-Stieltjes measures, the Hahn-Jordan decomposition, and a brief introduction to martingales · key aspects of financial modelling, including the Black-Scholes formula, discussed briefly from a measure-theoretical perspective to help the reader understand the underlying mathematical framework. In addition, further exercises and examples are provided to encourage the reader to become directly involved with the material.

Probability

AN Shiryaev — 2005-02-27T09:43:55-00:00

(01 January 1996)

This book contains a systematic treatment of probability from the ground up, starting with intuitive ideas and gradually developing more sophisticated subjects, such as random walks, martingales, Markov chains, ergodic theory, weak convergence of probability measures, stationary stochastic processes, and the Kalman-Bucy filter. Many examples are discussed in detail, and there are a large number of exercises. The book is accessible to advanced undergraduates and can be used as a text for self-study. This new edition contains substantial revision and updated references. The reader will find a deeper study of topics such as the distance between probability measures, metrization of weak convergence, and contiguity of probability measures. Proofs for a number of some important results which were merely stated in the first edition have been added. The author has included new material on the probability of large deviations, on the central limit theorem for sums of dependent random variables, and on a discrete version of Ito's formula.

Equipossibility Theories of Probability

Ian Hacking — 2005-03-22T14:50:39-00:00

The British Journal for the Philosophy of Science, Vol. 22, No. 4. (1971), pp. 339-355.

Hierarchical mixture models: a probabilistic analysis

Mark Sandler — 2007-09-03T17:23:14-00:00

(2007), pp. 580-589.

Stimulus-response probability and inhibition of return.

J Ivanoff — 2005-09-07T02:33:50-00:00

Psychon Bull Rev, Vol. 11, No. 3. (June 2004), pp. 542-550.

Inhibition of return (IOR) refers to slowed responding to targets at a location previously occupied by an irrelevant cue. Here we explore the interaction between stimulus-response (S-R) probability and IOR effects using go/no-go (Experiment 1) and two-choice discrimination tasks (Experiment 2). In both experiments, the IOR effect was larger for the likely S-R ensemble than for the unlikely one. In the first experiment, there were more false alarms for uncued targets than for cued targets, and this difference was larger for the unlikely S-R ensemble than for the likely one. In the second experiment, the same pattern was observed for incorrect keypress responses. As with voluntary orienting in response to predictive central cues, the results suggest that IOR affects late stages of processing by altering the criteria to respond to targets presented at the cued (previously attended) location.

Finding useful questions: on bayesian diagnosticity, probability, impact, and information gain.

JD Nelson — 2005-11-17T02:14:27-00:00

Psychol Rev, Vol. 112, No. 4. (October 2005), pp. 979-999.

Several norms for how people should assess a question's usefulness have been proposed, notably Bayesian diagnosticity, information gain (mutual information), Kullback-Liebler distance, probability gain (error minimization), and impact (absolute change). Several probabilistic models of previous experiments on categorization, covariation assessment, medical diagnosis, and the selection task are shown to not discriminate among these norms as descriptive models of human intuitions and behavior. Computational optimization found situations in which information gain, probability gain, and impact strongly contradict Bayesian diagnosticity. In these situations, diagnosticity's claims are normatively inferior. Results of a new experiment strongly contradict the predictions of Bayesian diagnosticity. Normative theoretical concerns also argue against use of diagnosticity. It is concluded that Bayesian diagnosticity is normatively flawed and empirically unjustified. ((c) 2005 APA, all rights reserved).

Probability as a psychological distance: Construal and preferences

Alexander Todorov — 2006-07-24T10:49:03-00:00

Journal of Experimental Social Psychology, Vol. In Press, Corrected Proof

We argue that probability, like space and time, instantiates psychological distance. Unlikely outcomes may seem more remote than likely outcomes and may therefore be construed at a relatively high level. Specifically, when the probability of an outcome is low, ends-related primary features should be more salient than means-related secondary features, but as the probability of the outcome increases, means-related features may become no less and even more salient than ends-related features. Thus, increases in probability should increase the weight of means-related features relative to the weight of ends-related features in decisions, thereby decreasing (or even reversing) the preference for a more desirable/less feasible outcome over a less desirable/more feasible outcome. We observed this pattern in two experiments. Analyses of judgments, monetary decisions, and self-reported reasons for decisions showed that the weight of means-related features was more sensitive to changes in probability than the weight of ends-related features in decisions.

Differences between probability and frequency judgments: The role of individual differences in working memory capacity

Amber Sprenger — 2005-09-26T10:58:48-00:00

Organizational Behavior and Human Decision Processes, Vol. In Press, Corrected Proof

Most theories of probability judgment assume that judgments are made by comparing the strength of a focal hypothesis relative to the strength of alternative hypotheses. In contrast, research suggests that frequency judgments are assessed using a non-comparative process; the strength of the focal hypothesis is assessed without comparing it to the strength of alternative hypotheses. We tested this distinction between probability and frequency judgments using the alternative outcomes paradigm (Windschitl, Young, & Jenson, 2002). Assuming that judgments of probability (but not judgments of frequency) entail comparing the focal hypothesis with alternative hypotheses, we hypothesized that probability judgments would be sensitive to the distribution of the alternative hypotheses and would be negatively correlated with individual differences in working memory (WM) capacity. In contrast, frequency judgments should be unrelated to the distribution of the alternatives and uncorrelated with WM-capacity. Results supported the hypotheses.

Decision by sampling

Neil Stewart — 2006-03-03T14:05:41-00:00

Cognitive Psychology, Vol. In Press, Corrected Proof

We present a theory of decision by sampling (DbS) in which, in contrast with traditional models, there are no underlying psychoeconomic scales. Instead, we assume that an attribute's subjective value is constructed from a series of binary, ordinal comparisons to a sample of attribute values drawn from memory and is its rank within the sample. We assume that the sample reflects both the immediate distribution of attribute values from the current decision's context and also the background, real-world distribution of attribute values. DbS accounts for concave utility functions; losses looming larger than gains; hyperbolic temporal discounting; and the overestimation of small probabilities and the underestimation of large probabilities.

Bayesian models of human sentence processing

N Srini — 2006-11-28T00:35:40-00:00

(1998)

Human language processing relies on many kinds of linguistic knowledge, and is sensitive to their frequency, including lexical frequencies (Tyler, 1984; Salasoo & Pisoni, 1985; MarslenWilson, 1990; Zwitserlood, 1989; Simpson & Burgess, 1985), idiom frequencies (d'Arcais, 1993), phonological neighborhood frequencies (Luce, Pisoni, & Goldfinger, 1990), subcategorization frequencies (Trueswell, Tanenhaus, & Kello, 1993), and thematic role frequencies (Trueswell, Tanenhaus, & Garnsey, 1994;...

Knowledge and Probability in Distributed Systems (Abstract)

Halpern — 2007-08-03T16:30:15-00:00

(1991)

: What should it mean for an agent to know or believe an assertion is true with probability :99? Different papers [FH94, FZ88a, HMT88] give different answers, choosing to use quite different probability spaces when computing the probability that an agent assigns to an event. We show that each choice can be understood in terms of a betting game. This betting game itself can be understood in terms of three types of adversaries influencing three different aspects of the game. The first selects the ...

Probabilistic knowledge and probabilistic common knowledge

Paul Krasucki — 2007-11-18T17:06:13-00:00

(1990), pp. 1-8.

Some Puzzles About Probability and Probabilistic Conditionals

Rohit Parikh — 2007-11-18T17:03:01-00:00

Logical Foundations of Computer Science (2007), pp. 449-456.

We examine some old and new paradoxes of probability, give a rough account of probabilistic conditionals, and prove a new result about non-monotonicity in probabilistic conditionals. It is well known that such conditionals are not monotonic – a conditional which is true can become false when additional hypotheses are added. We show that nonetheless, the conditionals are usually monotonic, or roughly speaking that we do not actually have to worry about non-monotonicity in practice.

The metric analogue of weak bisimulation for probabilistic processes

J Desharnais — 2007-11-28T20:47:26-00:00

(2002), pp. 413-422.

We observe that equivalence is not a robust concept in the presence of numerical information - such as probabilities - in the model. We develop a metric analogue of weak bisimulation in the spirit of our earlier work on metric analogues for strong bisimulation. We give a fixed point characterization of the metric. This makes available coinductive reasoning principles and allows us to prove metric analogues of the usual algebraic laws for process combinators. We also show that quantitative...

On weak convergence of filtrations

Fran\ccois Coquet — 2006-06-19T08:04:59-00:00

Vol. 1755 (2001), pp. 306-328.

A sequence of filtrations $≤ft(\scr F\sbt\spn\right)$ converges weakly to a filtration $≤ft(\scr F_t\right)\sbt≤ T$ if $∀ B∈\scr F\sbT$, the sequence of processes $≤ft(E≤ft(1\sbB|\scr F\sbt\spn\right)\right)\sbt≤ T$ converges in probability under the Skorokhod topology to the process $≤ft(E≤ft(1\sbB|\scr F\sbt\right)\right)\sbt≤ T$. Applications include results where convergence in probability of processes under the $J\sb1$ topology implies convergence of associated filtrations. One example concerns càdlàg processes with independent increments where $X\spn\buildrel Pover\rightarrowX$ under $J\sb1$ implies that $\scr F\spX\spn\buildrel wover\rightarrow\scr F\spX$. Another example treats the case of continuous pure local martingales such that $\langle M\rangle$ is strictly increasing. Then $M\spn\buildrel Pover\rightarrowM$ implies that $\scr F\spM\spn\rightarrow\scr F\spM$. Further results on stability and the notion of joint convergence of $≤ft(X\spn,\scr F\spX\spn\right)$ as developed by Aldous (unpublished work) are given. For the entire collection see <A HREF="/msnmain?fn=105&fmt=doc&r=1&pg1=CNO&s1=1837273&loc=fromrevtext">MR1837273 (2002a:60003)</A>.

Foundations of Modern Probability

Olav Kallenberg — 2006-04-12T13:51:20-00:00

(08 January 2002)

About the first edition: To sum it up, one can perhaps see a distinction among advanced probability books into those which are original and path-breaking in content, such as Levy's and Doob's well-known examples, and those which aim primarily to assimilate known material, such as Loeve's and more recently Rogers and Williams'. Seen in this light, Kallenberg's present book would have to qualify as the assimilation of probability par excellence. It is a great edifice of material, clearly and ingeniously presented, without any non-mathematical distractions. Readers wishing to venture into it may do so with confidence that they are in very capable hands. - Mathematical Reviews This new edition contains four new chapters as well as numerous improvements throughout the text. There are new chapters on measure Theory-key results, ergodic properties of Markov processes and large deviations.

Modelling Derivatives Pricing Mechanisms with Their Generating Functions

Shige Peng — 2006-05-26T23:30:38-00:00

(23 May 2006)

In this paper we study dynamic pricing mechanisms of financial derivatives. A typical model of such pricing mechanism is the so-called g--expectation defined by solutions of a backward stochastic differential equation with g as its generating function. Black-Scholes pricing model is a special linear case of this pricing mechanism. We are mainly concerned with two types of pricing mechanisms in an option market: the market pricing mechanism through which the market prices of options are produced, and the ask-bid pricing mechanism operated through the system of market makers. The later one is a typical nonlinear pricing mechanism. Data of prices produced by these two pricing mechanisms are usually quoted in an option market. We introduce a criteria, i.e., the domination condition (A5) in (2.5) to test if a dynamic pricing mechanism under investigation is a g--pricing mechanism. This domination condition was statistically tested using CME data documents. The result of test is significantly positive. We also provide some useful characterizations of a pricing mechanism by its generating function.

Multivariate risks and depth-trimmed regions

Ignacio Cascos — 2006-06-25T18:48:49-00:00

(21 Jun 2006)

We describe a general framework for measuring risks, where the risk measure takes values in an abstract cone. It is shown that this approach naturally includes the classical risk measures and set-valued risk measures and yields a natural definition of vector-valued risk measures. Several main constructions of risk measures are described in this abstract axiomatic framework. It is shown that the concept of depth-trimmed (or central) regions from the multivariate statistics is closely related to the definition of risk measures. In particular, the halfspace trimming corresponds to the Value-at-Risk, while the zonoid trimming yields the expected shortfall. In the abstract framework, it is shown how to establish a both-ways correspondence between risk measures and depth-trimmed regions. It is also demonstrated how the lattice structure of the space of risk values influences this relationship.

Awareness of action: Inference and prediction

James Moore — 2008-03-22T05:45:19-00:00

Consciousness and Cognition, Vol. 17, No. 1. (March 2008), pp. 136-144.

This study investigates whether the conscious awareness of action is based on predictive motor control processes, or on inferential "sense-making" process that occur after the action itself. We investigated whether the temporal binding between perceptual estimates of operant actions and their effects depends on the occurrence of the effect (inferential processes) or on the prediction that the effect will occur (predictive processes). By varying the probability with which a simple manual action produced an auditory effect, we showed that both the actual and the predicted occurrence of the effect played a role. When predictability of the effect of action was low, temporal binding was found only on those trials where the auditory effect occurred. In contrast, when predictability of the effect of action was high, temporal binding occurred even on trials where the action produced no effect. Further analysis showed that the predictive process is modulated by recent experience of the action-effect relation. We conclude that the experience of action depends on a dynamic combination of predictive and inferential processes.

Saccadic probability influences motor preparation signals and time to saccadic initiation.

MC Dorris — 2005-02-20T19:52:17-00:00

J Neurosci, Vol. 18, No. 17. (1 September 1998), pp. 7015-7026.

One must be prudent when selecting potential saccadic targets because the eyes can only move to one location at a time, yet movements must occur quickly enough to permit interaction with a rapidly changing world. This process of efficiently acquiring relevant targets may be aided by advanced planning of a movement toward an upcoming target whose location is gathered via environmental cues or situational experience. We studied how saccadic reaction times (SRTs) and early pretarget neuronal activity covaried as a function of saccadic probability. Monkeys performed a saccadic task in which the probability of the required saccade being directed into the response field of a neuron varied systematically between blocks of trials. We recorded simultaneously the early pretarget activity of saccade-related neurons in the intermediate layers of the superior colliculus. We found that, as the likelihood of the saccade being generated into the response field of the neuron increased, the level of neuronal activity preceding target presentation also increased. Our data suggest that this early activity codes motor preparation because its activity was related to not only the metrics but also the timing of the saccade, with 94% (29/31) of the neurons tested having significant negative correlations between discharge rate and SRT. This view is supported by cases in which exceptionally high levels of pretarget activity were associated with anticipatory saccades into the response field of a neuron that occurred in advance of the target being presented. This study demonstrates how situational experience can expedite motor behavior via the advanced preparation of motor programs.

Stimulus probability directs spatial attention: an enhancement of sensitivity in humans and monkeys.

VM Ciaramitaro — 2005-02-22T21:48:25-00:00

Vision Res, Vol. 41, No. 1. (January 2001), pp. 57-75.

We examined whether improvements in sensory processing, defined as changes in sensitivity, could be elicited in a simple luminance discrimination task without eliciting concomitant changes in decision processing. To this end we developed a task, for use in both humans and monkeys, in which prior knowledge about where a discriminative stimulus was likely to appear (1) offered no decisional advantage in solving our task and (2) could be parametrically varied to yield a psychometric function. We found that if we parametrically varied the quality of prior knowledge, by increasing the probability, and thus the certainty, that a discriminative stimulus would appear at a particular location under these conditions, luminance discrimination improved for both human and monkey subjects. This improvement was correlated with an enhancement in sensory processing, but not with any systematic changes in decisional processing, as assessed by signal detection theory. These results suggest that (1) sensory processing and decision processing can be separated by task design and (2) systematic changes in prior knowledge about where a stimulus may appear can lead to systematic changes in sensitivity; providing a psychometric function for the influence of prior knowledge on perceptual sensitivity. Importantly, these results were obtained from both human and monkey subjects. Similar task designs could be used in physiological studies attempting to generate linking hypotheses between psychometric and neurometric functions, ultimately allowing changes in perceptual sensitivity to be linked to changes in an underlying neural substrate.

A Generalized Stochastic Method for Estimating the Characteristics of Potential Conflicts of a Controlled Air Traffic

V Kharchenko — 2005-10-06T09:07:18-00:00

Cybernetics and Systems Analysis, Vol. 41, No. 3. (May 2005), pp. 385-396.