D.V. Lindley. On the measure of information provided by an experiment. The Annals of Mathematical Statistics, 27(4):986--1005, 1956.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....experiments. 1 Introduction There are various measures of the information content of a statistical experiment E, among others the decision theoretic deficiency distance to the most informative experiment and the Shannon capacity (which was introduced in the statistical context by D.V. Lindley [9] and J.M. Bernardo [1] These numbers are not easily computed. Therefore it is desirable to describe at least their asymptotic behaviour when the experiments get more and more informative. To our knowledge the asymptotics of the Shannon capacity has not been studied for finite parameter ....

....f (E; is the value m E (f ) of the conical measure m E associated with the experiment E at the positively homogeneous function f : z 7 f( 1 z 1 ; n z n ) cf. 7] ch.3) So in this sense our paper deals with large deviations of conical measures . Extending the approach of D.V. Lindley [9] from entropy to general similarities one introduces the expected amount of information (measured in terms of the functional f) which one gains by passing from the prior to the posterior distribution. This corresponds to the transmission rate in Shannon theory. The maximal information gain ....

D.V. Lindley. On a measure of the information provided by an experiment. Ann. Math. Stat., 27:986--1005, 1956.

....rather than making the Kullback Leibler distance zero, as in the case of sucient statistics, MI statistics are found at local minima of the Kullback Liebler distance viewed as a functional of the statistic. This demonstrates how the approach of this paper generalizes that performed by Lindley [4]. 6 MI Statistics for the Gaussian distribution This section details the inference of the one dimensional MI statistic for the one dimensional Gaussian distribution. We take the position parameter of the Gaussian to be q, and the the goal is to nd R (x) so that (19) holds. From there note ....

D. V. Lindley. On a measure of the information provided by an experiment. Annals of Mathematical Statistics, 27:986-1005, 1961.

....problem with squared error loss. designing observation times for interval censored data 449 3. Information Theoretic Loss Information theory offers general measures of the amount of information gained about a parameter from experimentation. Information theoretic criteria have been introduced by Lindley (1956) and are widely used in experimental design. Lindley s approach is the method of choice for measuring the information contained in an experiment, when the purpose of the investigation is not tied to a specific decision Verdinelli (1992) Parmigiani and Berry (1994) Traditional information ....

Lindley, D. V. (1956), On a measure of the information provided by an experiment. Ann. Math. Statist., 27, 986--1005.

....from which the sample is drawn remains unknown. Hence it must be the case that H(p) H(p 0 ) and H(p) H(p 1 ) The excess of H(p) over 0 H(p 0 ) 1 H(p 1 ) is the average gain of information one can expect about the distribution itself. This quantity, called the mutual information [60, 61], J(p 0 ; p 1 ; 0 ; 1 ) H( 0 p 0 1 p 1 ) 0 H(p 0 ) 1 H(p 1 ) 2.101) is the natural candidate for distinguishability that we seek in this section. If the two distributions p 0 (b) and p 1 (b) are completely distinguishable, then all the information gained in a sampling ....

D. V. Lindley, \On a measure of the information provided by an experiment," The Annals of Mathematical Statistics, vol. 27, pp. 986-1005, 1956.

.... 1991) Therefore, we have established that Rn (w) I w ( Theta; X n ) 56) 39 The quantity I w measures the average amount of information contained in the data X n about the parameter Theta and has been used to measure information in a statistical context by Lindley as early as 1956 (cf. Lindley, 1956). Let R Gamma n denote the worst case minimal Bayes redundancy among all priors w: R Gamma n = sup w Rn (w) 57) This quantity also carries with it an information theoretic interpretation. Here, R Gamma n is referred to as the channel capacity, C ( Theta; X n ) Following Cover and ....

Lindley, D. V. (1956). On a measure of the information provided by an experiment. Ann. Math. Statist., 27, 986--1005.

....and Thomas, 1991#. Therefore, wehave established that Rn #w#=Iw ##; X n #: #56# 39 The quantity I w measures the average amount of information contained in the data X n about the parameter # and has been used to measure information in a statistical context by Lindley as early as 1956 #cf. Lindley, 1956#. Let R , n denote the worst case minimal Bayes redundancy among all priors w: R , n = sup w Rn #w#: #57# This quantity also carries with it an information theoretic interpretation. Here,R , n is referred to as the channel capacity,C##; X n #. Following Cover and Thomas #1991#, weenvision ....

Lindley, D. V. #1956#.On a measure of the information provided by an experiment. Ann. Math. Statist., 27, 986#1005.

....have been developed by di erent authors, rst Oehlert, then Nychka and Saltzman, and nally the approach developed in a series of papers by Sun, Le and Zidek. 6.1. A Bayesian formulation of optimal design An early discussion of the design of experiments from a Bayesian point of view was given by Lindley (1956). Lindley proposed a criterion which amounts to maximization of the expected Shannon information to be gained from an experiment, when the objective 501 is not to reach decisions but rather to gain knowledge about the world . Later Bernardo (1979) showed that this criterion can also be derived ....

....density of X will be denoted p X (x) R p(x j ) d . Since will not enter the following discussion except through , henceforth we write ( instead of ( The posterior density of given data X = x, evaluated at = will be ( j x) Bernardo (1979) following earlier work by Lindley (1956), proposed the following measure of the information contained in E when the prior density is ( IfE; g = Z p X (x) Z ( j x) log ( j x) d dx: 6:1) Given that the inner integral is essentially an information divergence between the prior and posterior densities, the expression ....

Lindley, D.V. (1956), On a measure of the information provided by an experiment.

.... 1991) Therefore, we have established that Rn (w) I w ( Theta; X n ) 59) The quantity I w measures the average amount of information contained in the data X n about the parameter Theta and has been used to measure information in a statistical context by Lindley as early as 1956 (cf. Lindley, 1956). Let R Gamma n denote the worst case minimal Bayes redundancy among all priors w: R Gamma n = sup w Rn (w) 60) This quantity also carries with it an information theoretic interpretation. Here, R Gamma n is referred to as the channel capacity, C ( Theta; X n ) Following Cover and ....

Lindley, D. V. (1956). On a measure of the information provided by an experiment. Ann. Math. Statist., 27, 986--1005.

....of Lindley Information Measure to the Design of Clinical Experiments Giovanni Parmigiani Donald A. Berry Institute of Statistics and Decision Sciences, Duke University Summary In a celebrated work, Lindley (1956) introduced a measure of the information provided by an experiment. In this paper we consider applications of Lindley information measure to the design of clinical experiments. We review the decision theoretic foundations underlying the use of Lindley information, and discuss its role in ....

....in utility can actually be used as a quantitative measure of the worth of an experiment in any given situation. This idea is about as old as Bayesian statistics (see Ramsey, 1990) and is discussed by Raiffa and Schlaifer (1961) and DeGroot (1984) The well known measure of information proposed by Lindley (1956) is the object of investigation in this paper. It can be seen as a very important special case of this general approach. Consider the decision problem of reporting a distribution regarding an unknown quantity Theta with values in Omega Gamma This is a Bayesian way of modelling a situation in ....

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Lindley, D.V. (1956) On the measure of information provided by an experiment, Annals of Statistics 27, pp. 986-1005.

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D.V. Lindley. On the measure of information provided by an experiment. The Annals of Mathematical Statistics, 27(4):986--1005, 1956.

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Lindley, D. V. (1956). On a measure of the information provided by an experiment. Ann. Math. Statist., 27, 986--1005.

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Lindley D.V. (1956). On the measure of information provided by an experiment. Ann. Math. Statist. Vol. 27, pp. 986--1005.

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Lindley, D. V. 1956 On the measure of information provided by an experiment. Ann. Math. Statist. 27, 986-1005.

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Lindley D.V. On the measure of information provided by an experiment. Ann. Math. Statist. Vol. 27, pp. 986--1005, 1956.

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Lindley, D. V. (1956), `On a measure of information provided by an experiment', Ann. Math. Stat., 29: 986-1005.

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D.V. Lindley. On a Measure of the Information provided by an Experiment. Ann. Math. Stat., 27:986--1005, 1956.

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D. V. Lindley. On the measure of information provided by an experiment. Ann. Stat., 27:986--1005, 1956.

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Lindley, D. V. (1956), \On a measure of information provided by an experiment", Ann. Math. Stat., 29, pp. 986-1005.

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Lindley, D. V. (1956), "On a measure of information provided by an experiment", Ann. Math. Stat., 29, pp. 986-1005.

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Lindley, D. V. (1956), `On a measure of information provided by an experiment', Ann. Math. Stat., 29: 986-1005.

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Lindley, D. V. (1956), "On a measure of information provided by an experiment", Ann. Math. Stat., 29, pp. 986-1005.

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Lindley, D. V. (1956), \On a measure of information provided by an experiment", Ann. Math. Stat., 29, pp. 986-1005.

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Lindley, D. (1956). On a Measure of Information provided by an experiment. Ann. Math. Stat. 27, 986-996.

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Lindley, D.V. (1956), On a measure of the information provided by an experiment.

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Dennis Lindley. On a measure of the information provided by an experiment. Annals of Mathematical Statistics, 27:986--1005, 1956.

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