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- W1661524993 abstract "The number of points (x_1,...x_n) that lie in an integer cube C in R_n and satisfy the constraints S_i=sum_i[ h_{ij}(x_j) ] is approximated by an Edgeworth corrected gaussian approximation based on the maximum entropy density p on C, that satisfies ES = s . Under p, the variables X_1,...X_n are independent with densities of exponential form. Conditional on S = s, X is uniformly distributed over the integers in C that satisfy S = s . The number of points in C satisfying S=s is p{S=s} exp(I(p)) where I(p) is the entropy of the density p . We first estimate p{S=s}by P{Z=s} where Z is multivariate gaussian with the same first two moments as S ;and when d is large we use in addition an Edgeworth factor that requires the first four moments of S under p. The asymptotic validity of the Edgeworth corrected estimate is examined for counting contingency tables with given row sums and column sums, and for counting the number of graphs with a given degree sequence." @default.
- W1661524993 created "2016-06-24" @default.
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- W1661524993 date "2009-10-13" @default.
- W1661524993 modified "2023-09-27" @default.
- W1661524993 title "Maximum Entropy Edgeworth Estimates of Volumes of Polytopes" @default.
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