Results 1  10
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25
Updating Probabilities
, 2002
"... As examples such as the Monty Hall puzzle show, applying conditioning to update a probability distribution on a "naive space", which does not take into account the protocol used, can often lead to counterintuitive results. Here we examine why. A criterion known as CAR ("coarsening a ..."
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Cited by 53 (6 self)
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As examples such as the Monty Hall puzzle show, applying conditioning to update a probability distribution on a "naive space", which does not take into account the protocol used, can often lead to counterintuitive results. Here we examine why. A criterion known as CAR ("coarsening at random") in the statistical literature characterizes when "naive" conditioning in a naive space works. We show that the CAR condition holds rather infrequently, and we provide a procedural characterization of it, by giving a randomized algorithm that generates all and only distributions for which CAR holds. This substantially extends previous characterizations of CAR. We also consider more generalized notions of update such as Jeffrey conditioning and minimizing relative entropy (MRE). We give a generalization of the CAR condition that characterizes when Jeffrey conditioning leads to appropriate answers, and show that there exist some very simple settings in which MRE essentially never gives the right results. This generalizes and interconnects previous results obtained in the literature on CAR and MRE.
Asymmetric Rendezvous on the Plane
, 1997
"... We consider rendezvous problems in which two players move on the plane and wish to cooperate in order to minimise their first meeting time. We begin by considering the case when they know that they are a distance d apart, but they do not know the direction in which they should travel. We also cons ..."
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Cited by 18 (0 self)
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We consider rendezvous problems in which two players move on the plane and wish to cooperate in order to minimise their first meeting time. We begin by considering the case when they know that they are a distance d apart, but they do not know the direction in which they should travel. We also consider a situation in which player 1 knows the initial position of player 2, while player 2 is only given information on the initial distance of player 1. Finally we give some results for the case where one of the players is placed at an initial position chosen equiprobably from a finite set of points.
Dynamical bias in the coin toss
, 2004
"... We analyze the natural process of flipping a coin which is caught in the hand. We prove that vigorouslyflipped coins are biased to come up the same way they started. The amount of bias depends on a single parameter, the angle between the normal to the coin and the angular momentum vector. Measureme ..."
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Cited by 11 (1 self)
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We analyze the natural process of flipping a coin which is caught in the hand. We prove that vigorouslyflipped coins are biased to come up the same way they started. The amount of bias depends on a single parameter, the angle between the normal to the coin and the angular momentum vector. Measurements of this parameter based on highspeed photography are reported. For natural flips, the chance of coming up as started is about.51.
Searching for the Next Best Mate
 In
, 1997
"... . How do we humans go about choosing a mate? Do we shop for them, checking prices and values and selecting the best? Do we apply for them, wooing several and taking the best that accepts us in return? Or do we screen them, testing one after another in succession until the right one comes along? Econ ..."
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Cited by 9 (1 self)
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. How do we humans go about choosing a mate? Do we shop for them, checking prices and values and selecting the best? Do we apply for them, wooing several and taking the best that accepts us in return? Or do we screen them, testing one after another in succession until the right one comes along? Economists and other behavioral scientists have analyzed these matechoice approaches to find their optimal algorithmic solutions; but what people really do is often quite different from these optima. In this paper, we analyze the third approach of mate choice as applicant screening and show through simulation analyses that a traditional optimal solution to this problemthe 37% rulecan be beaten along several dimensions by a class of simple "satisficing" algorithms we call the Take the Next Best mate choice rules. Thus, human mate search behavior should not necessarily be compared to the lofty optimal ideal, but instead may be more usefully studied through the development and analysis of poss...
The Lure of Choice
"... The contributors have asserted their moral rights. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, without the prior permission in writing of the publisher, nor be circulated in any form of binding or cover ..."
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Cited by 6 (0 self)
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The contributors have asserted their moral rights. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, without the prior permission in writing of the publisher, nor be circulated in any form of binding or cover other than that in which it is published. Typeset, printed and bound by:
Interpolation of Random Hyperplanes
, 2006
"... Let {(Zi,Wi) : i = 1,...,n} be uniformly distributed in [0,1] d × G(k,d), where G(k,d) denotes the space of kdimensional linear subspaces of R d. For a differentiable function f: [0,1] k → [0,1] d, we say that f interpolates (z,w) ∈ [0,1] d × G(k,d) if there exists x ∈ [0,1] k such that f(x) = z ..."
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Cited by 2 (0 self)
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Let {(Zi,Wi) : i = 1,...,n} be uniformly distributed in [0,1] d × G(k,d), where G(k,d) denotes the space of kdimensional linear subspaces of R d. For a differentiable function f: [0,1] k → [0,1] d, we say that f interpolates (z,w) ∈ [0,1] d × G(k,d) if there exists x ∈ [0,1] k such that f(x) = z and ⃗ f(x) = w, where ⃗ f(x) denotes the tangent space at x defined by f. For a smoothness class F of Hölder type, we obtain probability bounds on the maximum number of points a function f ∈ F interpolates. 1
Techniques for maintaining connectivity in wireless adhoc networks under energy constraints
 ACM Transaction on Embedded Computing Systems
, 2007
"... Distributed wireless systems (DWSs) are emerging as the enabler for nextgeneration wireless applications. There is a consensus that DWSbased applications, such as pervasive computing, sensor networks, wireless information networks, and speech and data communication networks, will form the backbone ..."
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Cited by 2 (2 self)
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Distributed wireless systems (DWSs) are emerging as the enabler for nextgeneration wireless applications. There is a consensus that DWSbased applications, such as pervasive computing, sensor networks, wireless information networks, and speech and data communication networks, will form the backbone of the next technological revolution. Simultaneously, with great economic, industrial, consumer, and scientific potential, DWSs pose numerous technical challenges. Among them, two are widely considered as crucial: autonomous localized operation and minimization of energy consumption. We address the fundamental problem of how to maximize the lifetime of the network using only local information, while preserving network connectivity. We start by introducing the carefree sleep (CS) Theorem that provides provably optimal conditions for a node to go into sleep mode while ensuring that global connectivity is not affected. The CS theorem is the basis for an efficient localized algorithm that decides which nodes will go to into sleep mode and for how long. We have also developed mechanisms for collecting neighborhood information and for the coordination of distributed energy minimization protocols. The effectiveness of the approach is demonstrated using a comprehensive study of the performance of the algorithm over a wide range of network parameters. Another important highlight is the first mathematical and Monte Carlo analysis that establishes the importance of considering nodes within a small number of hops in order to preserve energy.
Making Decisions Using Sets of Probabilities: Updating, Time Consistency, and Calibration
"... We consider how an agent should update her beliefs when her beliefs are represented by a set P of probability distributions, given that the agent makes decisions using the minimax criterion, perhaps the beststudied and most commonlyused criterion in the literature. We adopt a gametheoretic framew ..."
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Cited by 2 (1 self)
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We consider how an agent should update her beliefs when her beliefs are represented by a set P of probability distributions, given that the agent makes decisions using the minimax criterion, perhaps the beststudied and most commonlyused criterion in the literature. We adopt a gametheoretic framework, where the agent plays against a bookie, who chooses some distribution from P. We consider two reasonable games that differ in what the bookie knows when he makes his choice. Anomalies that have been observed before, like time inconsistency, can be understood as arising because different games are being played, against bookies with different information. We characterize the important special cases in which the optimal decision rules according to the minimax criterion amount to either conditioning or simply ignoring the information. Finally, we consider the relationship between updating and calibration when uncertainty is described by sets of probabilities. Our results emphasize the key role of the rectangularity condition of Epstein and Schneider. 1.
A Combinatorial Identity And The World Series
, 1993
"... In this note the author gives a simple probabilistic proof of a combinatorial identity by calculating the winning probability in the World Series. The winning probabilities and the expected length of the championship series are given by the applications of the identity and its generalization. ..."
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Cited by 2 (0 self)
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In this note the author gives a simple probabilistic proof of a combinatorial identity by calculating the winning probability in the World Series. The winning probabilities and the expected length of the championship series are given by the applications of the identity and its generalization.
The Monty Hall Problem is not a Probability Puzzle ∗ (It’s a challenge in mathematical modelling)
, 2010
"... Suppose you’re on a game show, and you’re given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what’s behind the doors, opens another door, say No. 3, which has a goat. He then says to you, “Do you want to pick door ..."
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Cited by 2 (1 self)
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Suppose you’re on a game show, and you’re given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what’s behind the doors, opens another door, say No. 3, which has a goat. He then says to you, “Do you want to pick door No. 2? ” Is it to your advantage to switch your choice? The answer is “yes ” but the literature offers many reasons why this is the correct answer. The present paper argues that the most common reasoning found in introductory statistics texts, depending on making a number of “obvious ” or “natural ” assumptions and then computing a conditional probability, is a classical example of solution driven science. The best reason to switch is to be found in von Neumann’s minimax theorem from game theory, rather than in Bayes’ theorem. 1