Events

Upcoming seminars, conferences, and workshops

Conflations of Probability Distributions

Ted Hill (Georgia Institute of Technology)

Wed, 24 Jun 2009, 15.15-16.00 hrs.
Venue: Tinbergen Institute, Roetersstraat 31, Amsterdam, room 4.08
For information: Henk Tijms.

The conflation of a finite number of probability distributions P_1,...,P_n is a consolidation of those distributions into a single probability distribution Q=Q(P_1,..., P_n), where intuitively Q is the conditional distribution of independent random variables X_1,..., X_n with distributions P_1,...,P_n, respectively, given that X_1= ... =X_n. Thus, in large classes of distributions the conflation is the distribution determined by the normalized product of the probability density or probability mass functions. Q is shown to be the unique probability distribution that minimizes the loss of Shannon Information in consolidating the combined information from P_1,..., P_n into a single distribution Q, and also to be the optimal consolidation of the distributions with respect to two minimax / likelihood-ratio criteria. When P_1,..., P_n are Gaussian, Q is Gaussian with mean the classical weighted-mean-squares reciprocal of variances. A version of the classical convolution theorem holds for conflations of a large class of a.c. measures.

[Econometrics] [Amsterdam Econometric Seminars and Workshop Series]