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Probability: Theory and examples
 CAMBRIDGE U PRESS
, 2011
"... Some times the lights are shining on me. Other times I can barely see. Lately it occurs to me what a long strange trip its been. Grateful Dead In 1989 when the first edition of the book was completed, my sons David and Greg were 3 and 1, and the cover picture showed the Dow Jones at 2650. The last t ..."
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Cited by 1330 (16 self)
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Some times the lights are shining on me. Other times I can barely see. Lately it occurs to me what a long strange trip its been. Grateful Dead In 1989 when the first edition of the book was completed, my sons David and Greg were 3 and 1, and the cover picture showed the Dow Jones at 2650. The last twenty years have brought many changes but the song remains the same. The title of the book indicates that as we develop the theory, we will focus our attention on examples. Hoping that the book would be a useful reference for people who apply probability in their work, we have tried to emphasize the results that are important for applications, and illustrated their use with roughly 200 examples. Probability is not a spectator sport, so the book contains almost 450 exercises to challenge the reader and to deepen their understanding. The fourth edition has two major changes (in addition to a new publisher): (i) The book has been converted from TeX to LaTeX. The systematic use of labels should eventually eliminate problems with references to other points in the text. In
The weighted majority algorithm
, 1992
"... We study the construction of prediction algorithms in a situation in which a learner faces a sequence of trials, with a prediction to be made in each, and the goal of the learner is to make few mistakes. We are interested in the case that the learner has reason to believe that one of some pool of kn ..."
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Cited by 876 (42 self)
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We study the construction of prediction algorithms in a situation in which a learner faces a sequence of trials, with a prediction to be made in each, and the goal of the learner is to make few mistakes. We are interested in the case that the learner has reason to believe that one of some pool of known algorithms will perform well, but the learner does not know which one. A simple and effective method, based on weighted voting, is introduced for constructing a compound algorithm in such a circumstance. We call this method the Weighted Majority Algorithm. We show that this algorithm is robust in the presence of errors in the data. We discuss various versions of the Weighted Majority Algorithm and prove mistake bounds for them that are closely related to the mistake bounds of the best algorithms of the pool. For example, given a sequence of trials, if there is an algorithm in the pool A that makes at most m mistakes then the Weighted Majority Algorithm will
Using Daily Stock Returns: The Case of Event Studies
 Journal of Financial Economics
, 1985
"... This paper examines properties of daily stock returns and how the particular characteristics of these data affect event study methodologies. Daily data generally present few difficulties for event studies. Standard procedures are typically wellspecified even when special daily data characteristics ..."
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Cited by 800 (3 self)
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This paper examines properties of daily stock returns and how the particular characteristics of these data affect event study methodologies. Daily data generally present few difficulties for event studies. Standard procedures are typically wellspecified even when special daily data characteristics are ignored. However, recognition of autocorrelation in daily excess returns and changes in their variance conditional on an event can sometimes be advantageous. In addition, tests ignoring crosssectional dependence can be wellspecified and have higher power than tests which account for potential dependence. 1.
Design of capacityapproaching irregular lowdensity paritycheck codes
 IEEE TRANS. INFORM. THEORY
, 2001
"... We design lowdensity paritycheck (LDPC) codes that perform at rates extremely close to the Shannon capacity. The codes are built from highly irregular bipartite graphs with carefully chosen degree patterns on both sides. Our theoretical analysis of the codes is based on [1]. Assuming that the unde ..."
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Cited by 589 (6 self)
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We design lowdensity paritycheck (LDPC) codes that perform at rates extremely close to the Shannon capacity. The codes are built from highly irregular bipartite graphs with carefully chosen degree patterns on both sides. Our theoretical analysis of the codes is based on [1]. Assuming that the underlying communication channel is symmetric, we prove that the probability densities at the message nodes of the graph possess a certain symmetry. Using this symmetry property we then show that, under the assumption of no cycles, the message densities always converge as the number of iterations tends to infinity. Furthermore, we prove a stability condition which implies an upper bound on the fraction of errors that a beliefpropagation decoder can correct when applied to a code induced from a bipartite graph with a given degree distribution. Our codes are found by optimizing the degree structure of the underlying graphs. We develop several strategies to perform this optimization. We also present some simulation results for the codes found which show that the performance of the codes is very close to the asymptotic theoretical bounds.
Capacity of Fading Channels with Channel Side Information
, 1997
"... We obtain the Shannon capacity of a fading channel with channel side information at the transmitter and receiver, and at the receiver alone. The optimal power adaptation in the former case is "waterpouring" in time, analogous to waterpouring in frequency for timeinvariant frequencysele ..."
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Cited by 584 (20 self)
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We obtain the Shannon capacity of a fading channel with channel side information at the transmitter and receiver, and at the receiver alone. The optimal power adaptation in the former case is "waterpouring" in time, analogous to waterpouring in frequency for timeinvariant frequencyselective fading channels. Inverting the channel results in a large capacity penalty in severe fading.
Modeling and performance analysis of bittorrentlike peertopeer networks
 In SIGCOMM
, 2004
"... In this paper, we develop simple models to study the performance of BitTorrent, a second generation peertopeer (P2P) application. We first present a simple fluid model and study the scalability, performance and efficiency of such a filesharing mechanism. We then consider the builtin incentive mec ..."
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Cited by 574 (3 self)
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In this paper, we develop simple models to study the performance of BitTorrent, a second generation peertopeer (P2P) application. We first present a simple fluid model and study the scalability, performance and efficiency of such a filesharing mechanism. We then consider the builtin incentive mechanism of BitTorrent and study its effect on network performance. We also provide numerical results based on both simulations and real traces obtained from the Internet. 1
Bayesian inference in econometric models using monte carlo integration.
 Econometrica
, 1989
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MIXED MNL MODELS FOR DISCRETE RESPONSE
 JOURNAL OF APPLIED ECONOMETRICS J. APPL. ECON. 15: 447470 (2000)
, 2000
"... This paper considers mixed, or random coefficients, multinomial logit (MMNL) models for discrete response, and establishes the following results. Under mild regularity conditions, any discrete choice model derived from random utility maximization has choice probabilities that can be approximated as ..."
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Cited by 489 (15 self)
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This paper considers mixed, or random coefficients, multinomial logit (MMNL) models for discrete response, and establishes the following results. Under mild regularity conditions, any discrete choice model derived from random utility maximization has choice probabilities that can be approximated as closely as one pleases by a MMNL model. Practical estimation of a parametric mixing family can be carried out by Maximum Simulated Likelihood Estimation or Method of Simulated Moments, and easily computed instruments are provided that make the latter procedure fairly efficient. The adequacy of a mixing specification can be tested simply as an omitted variable test with appropriately defined artificial variables. An application to a problem of demand for alternative vehicles shows that MMNL provides a flexible and computationally practical approach to discrete response analysis.