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85
From Laplace To Supernova Sn 1987a: Bayesian Inference In Astrophysics
, 1990
"... . The Bayesian approach to probability theory is presented as an alternative to the currently used longrun relative frequency approach, which does not offer clear, compelling criteria for the design of statistical methods. Bayesian probability theory offers unique and demonstrably optimal solutions ..."
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Cited by 57 (2 self)
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. The Bayesian approach to probability theory is presented as an alternative to the currently used longrun relative frequency approach, which does not offer clear, compelling criteria for the design of statistical methods. Bayesian probability theory offers unique and demonstrably optimal solutions to wellposed statistical problems, and is historically the original approach to statistics. The reasons for earlier rejection of Bayesian methods are discussed, and it is noted that the work of Cox, Jaynes, and others answers earlier objections, giving Bayesian inference a firm logical and mathematical foundation as the correct mathematical language for quantifying uncertainty. The Bayesian approaches to parameter estimation and model comparison are outlined and illustrated by application to a simple problem based on the gaussian distribution. As further illustrations of the Bayesian paradigm, Bayesian solutions to two interesting astrophysical problems are outlined: the measurement of wea...
Provenance of correlations in psychological data
 PSYCHONOMIC BULLETIN & REVIEW
, 2005
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Maximum Entropy MIMO Wireless Channel Models with Limited Information
 in Proc. MATHMOD Conference on Mathematical Modeling
, 2006
"... In this contribution, models of wireless channels are derived from the maximum entropy principle, for several cases where only limited information about the propagation environment is available. First, analytical models are derived for the cases where certain parameters (channel energy, average ener ..."
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Cited by 9 (6 self)
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In this contribution, models of wireless channels are derived from the maximum entropy principle, for several cases where only limited information about the propagation environment is available. First, analytical models are derived for the cases where certain parameters (channel energy, average energy, spatial correlation matrix) are known deterministically. Frequently, these parameters are unknown (typically because the received energy or the spatial correlation varies with the user position), but still known to represent meaningful system characteristics. In these cases, analytical channel models are derived by assigning entropymaximizing distributions to these parameters, and marginalizing them out. For the MIMO case with spatial correlation, we show that the distribution of the covariance matrices is conveniently handled through its eigenvalues. The entropymaximizing distribution of the covariance matrix is shown to be a Wishart distribution. Furthermore, the corresponding probability density function of the channel matrix is shown to be described analytically by a function of the channel Frobenius norm. This technique can provide channel models incorporating the effect of shadow fading and spatial correlation between antennas without the need to assume explicit values for these parameters. The results are compared in terms of mutual information to the classical i.i.d. Gaussian model.
Partially adaptive estimation via the maximum entropy densities
 Econom. J. 2005
"... Adaptive estimation is frequently used when the error distribution is nonnormal. We propose a partially adaptive estimator based on the maximum entropy estimate of the error distribution. Under the conditions specified in McDonald and Newey (1988), the proposed estimator is asymptotically normal a ..."
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Cited by 6 (2 self)
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Adaptive estimation is frequently used when the error distribution is nonnormal. We propose a partially adaptive estimator based on the maximum entropy estimate of the error distribution. Under the conditions specified in McDonald and Newey (1988), the proposed estimator is asymptotically normal and efficient for the slope parameters. We investigate the finite sample performance of the proposed method and compare it with existing methods. We also apply the estimator to real world data.
An entropy measure of uncertainty in vote choice.” Electoral Studies 24(3):371–386
, 2005
"... We examine voters ’ uncertainty as they assess candidates ’ policy positions in the 1994 congressional election and test the hypothesis that the Contract with America reduced voter uncertainty about the issue positions of Republican House candidates. This is done with an aggregate evaluation of issu ..."
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We examine voters ’ uncertainty as they assess candidates ’ policy positions in the 1994 congressional election and test the hypothesis that the Contract with America reduced voter uncertainty about the issue positions of Republican House candidates. This is done with an aggregate evaluation of issue uncertainty and corresponding vote choice where the uncertainty parameterization is derived from an entropy calculation on a set of salient election issues. The primary advantage is that it requires very few assumptions about the nature of the data. The entropic model suggests that voters used the written and explicit Republican agenda as a means of reducing issue uncertainty without substantially increasing time spent evaluating candidate positions.
China’s Income Distribution: 19852001
 The Review of Economics and Statistics
, 2005
"... We employ a new method to estimate China’s income distributions using publicly available interval summary statistics. We examine rural, urban, and overall income distributions from 19852001. We show how the distributions change directly as well as examine trends in inequality. Using an intertempor ..."
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We employ a new method to estimate China’s income distributions using publicly available interval summary statistics. We examine rural, urban, and overall income distributions from 19852001. We show how the distributions change directly as well as examine trends in inequality. Using an intertemporal decomposition of aggregate inequality, we determine that increases in inequality within rural and urban sectors and the growing ruralurban income gap have been equally responsible for the growth in overall inequality over the last two decades. However, the ruralurban gap has played an increasingly important role in recent years. We also show that urban consumption inequality rose considerably. Using a new technique to estimate income distributions from grouped summary statistics, we show that Chinese income inequality rose substantially from 1985 to 2001 because of increases in inequality within urban and rural areas and the widening ruralurban income gap. We find that China’s dramatic economic growth—a fivefold increase in the economy and a
Approximate Inference for Robust Gaussian Process Regression
, 2005
"... Abstract. Gaussian process (GP) priors have been successfully used in nonparametric Bayesian regression and classification models. Inference can be performed analytically only for the regression model with Gaussian noise. For all other likelihood models inference is intractable and various approxim ..."
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Abstract. Gaussian process (GP) priors have been successfully used in nonparametric Bayesian regression and classification models. Inference can be performed analytically only for the regression model with Gaussian noise. For all other likelihood models inference is intractable and various approximation techniques have been proposed. In recent years expectationpropagation (EP) has been developed as a general method for approximate inference. This article provides a general summary of how expectationpropagation can be used for approximate inference in Gaussian process models. Furthermore we present a case study describing its implementation for a new robust variant of Gaussian process regression. To gain further insights into the quality of the EP approximation we present experiments in which we compare to results obtained by Markov chain Monte Carlo (MCMC) sampling. 1 Introduction – Robustness & Bayesian Regression To solve a realworld regression problem the analyst should carefully screen the data and use all prior information at hand in order to choose an appropriate regression model. The model is selected so as to approximate the beliefs about the data generating process. A mismatch seems unavoidable in practice. Robust regression methods can be understood as attempts to limit undesired distractions and distortions
A SmallSample Estimator for the SampleSelection Model by
, 2001
"... A semiparametric estimator for evaluating the parameters of data generated under a sample selection process is developed. This estimator is based on the generalized maximum entropy estimator and performs well for small and illposed samples. Theoretical and sampling comparisons with parametric and s ..."
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Cited by 4 (0 self)
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A semiparametric estimator for evaluating the parameters of data generated under a sample selection process is developed. This estimator is based on the generalized maximum entropy estimator and performs well for small and illposed samples. Theoretical and sampling comparisons with parametric and semiparametric estimators are given. This method and standard ones are applied to three smallsample empirical applications of the wageparticipation