Results 1  10
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15
Game Theory, Maximum Entropy, Minimum Discrepancy And Robust Bayesian Decision Theory
 ANNALS OF STATISTICS
, 2004
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Competitive online statistics
 International Statistical Review
, 1999
"... A radically new approach to statistical modelling, which combines mathematical techniques of Bayesian statistics with the philosophy of the theory of competitive online algorithms, has arisen over the last decade in computer science (to a large degree, under the influence of Dawid’s prequential sta ..."
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Cited by 65 (10 self)
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A radically new approach to statistical modelling, which combines mathematical techniques of Bayesian statistics with the philosophy of the theory of competitive online algorithms, has arisen over the last decade in computer science (to a large degree, under the influence of Dawid’s prequential statistics). In this approach, which we call “competitive online statistics”, it is not assumed that data are generated by some stochastic mechanism; the bounds derived for the performance of competitive online statistical procedures are guaranteed to hold (and not just hold with high probability or on the average). This paper reviews some results in this area; the new material in it includes the proofs for the performance of the Aggregating Algorithm in the problem of linear regression with square loss. Keywords: Bayes’s rule, competitive online algorithms, linear regression, prequential statistics, worstcase analysis.
Mutual information, Fisher information and population coding
 Neural Computation
, 1998
"... In the context of parameter estimation and model selection, it is only quite recently that a direct link between the Fisher information and information theoretic quantities has been exhibited. We give an interpretation of this link within the standard framework of information theory. We show that in ..."
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Cited by 62 (3 self)
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In the context of parameter estimation and model selection, it is only quite recently that a direct link between the Fisher information and information theoretic quantities has been exhibited. We give an interpretation of this link within the standard framework of information theory. We show that in the context of population coding, the mutual information between the activity of a large array of neurons and a stimulus to which the neurons are tuned is naturally related to the Fisher information. In the light of this result we consider the optimization of the tuning curves parameters in the case of neurons responding to a stimulus represented by an angular variable. To appear in Neural Computation Vol. 10, Issue 7, published by the MIT press. 1 Laboratory associated with C.N.R.S. (U.R.A. 1306), ENS, and Universities Paris VI and Paris VII 1 Introduction A natural framework to study how neurons communicate, or transmit information, in the nervous system is information theory (see e...
An empirical study of minimum description length model selection with infinite parametric complexity
 JOURNAL OF MATHEMATICAL PSYCHOLOGY
, 2006
"... Parametric complexity is a central concept in Minimum Description Length (MDL) model selection. In practice it often turns out to be infinite, even for quite simple models such as the Poisson and Geometric families. In such cases, MDL model selection as based on NML and Bayesian inference based on J ..."
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Cited by 10 (1 self)
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Parametric complexity is a central concept in Minimum Description Length (MDL) model selection. In practice it often turns out to be infinite, even for quite simple models such as the Poisson and Geometric families. In such cases, MDL model selection as based on NML and Bayesian inference based on Jeffreys ’ prior can not be used. Several ways to resolve this problem have been proposed. We conduct experiments to compare and evaluate their behaviour on small sample sizes. We find interestingly poor behaviour for the plugin predictive code; a restricted NML model performs quite well but it is questionable if the results validate its theoretical motivation. A Bayesian marginal distribution with Jeffreys’ prior can still be used if one sacrifices the first observation to make a proper posterior; this approach turns out to be most dependable.
An empirical study of MDL model selection with infinite parametric complexity
 J. Mathematical Psychology
, 2006
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Universal and composite hypothesis testing via mismatched divergence
 IEEE Trans. Inf. Theory
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Online Prediction with Experts under a Logscoring Rule  Online Expert Prediction
"... F13.39> (x) = p(xj) is a stochastic process: This means that if we write X = X n = (X 1 ; :::; X n ) to mean the random variable with outcomes x = x n = (x 1 ; :::; x n ) then the density p(x n j) for n is the result of integrating p(x n+1 j) over x n+1 . Write J() to mean the Jereys p ..."
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Cited by 2 (1 self)
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F13.39> (x) = p(xj) is a stochastic process: This means that if we write X = X n = (X 1 ; :::; X n ) to mean the random variable with outcomes x = x n = (x 1 ; :::; x n ) then the density p(x n j) for n is the result of integrating p(x n+1 j) over x n+1 . Write J() to mean the Jereys prior on the parameter space, assuming it exists, and let w be another prior density on the parameter space. We use J() as a dominating measure for other priors unless stated otherwise. Denote by <F13
Heterogeneity, Selection and Wealth Dynamics
"... The market selection hypothesis states that, among expected utility maximizers, competitive markets select for agents with correct beliefs. In some economies this holds, while in others it fails. It holds in complete market economies with a common discount factor and bounded aggregate consumption. I ..."
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The market selection hypothesis states that, among expected utility maximizers, competitive markets select for agents with correct beliefs. In some economies this holds, while in others it fails. It holds in complete market economies with a common discount factor and bounded aggregate consumption. It can fail when markets are incomplete, when consumption grows too quickly, or when discount factors and beliefs are correlated. These insights have implication for the analysis of the heterogeneous agent stochastic dynamic general equilibrium models common in finance and macroeconomics. 1 “The trading floor is a jungle, ” he went on, “and the guy you end up working for is your jungle leader. Whether you succeed here or not depends on knowing how to survive in the jungle.” Lewis (1989, pp. 39–40.) 1