Unknown Number Of Components Research Articles

Corrigendum: On Bayesian Analysis of Mixtures With An Unknown Number of Components

We regret to report that there is an error in equation (12) on p. 740, concerning the birth± death move for empty components. The correct expression is A ˆ p k‡ 1† p k† 1 B k , † w y1 j* 1y wj*† yk k‡ 1† dk‡1 k0 ‡ 1†bk 1 g1,k wj*† 1y wj*†: In the paper as printed, the power of 1y wj* in the ®nal factor, the Jacobian term, was given as k instead of ky 1. The source of the error was neglect of the condition j wj ˆ 1 in computing the partial derivatives of wj with respect to wj. Note that expression (11) for the split±combine move acceptance ratio is correct as printed. Having made the correction, we repeated the calculations leading to all the numerical results reported in the paper. As might be expected, the e€ects of the error are noticeable but small. The maximum changes to any of the posterior probabilities p kjy† presented in Tables 1 and 2 and Fig. 6 are 0.015, 0.011 and 0.020 respectively; in each case the maximum discrepancy occurs near the mode of the distributions, and so has little impact. The error in Fig. 2 is within plotting accuracy. In none of the ®gures is the visual impression altered, and none of our qualitative conclusions are a€ected. We are grateful to Tobias Ryden of Lund University for discovering this error, and we apologize for any confusion that it has caused.

On Bayesian Analysis of Mixtures with an Unknown Number of Components (with discussion)

Summary New methodology for fully Bayesian mixture analysis is developed, making use of reversible jump Markov chain Monte Carlo methods that are capable of jumping between the parameter subspaces corresponding to different numbers of components in the mixture. A sample from the full joint distribution of all unknown variables is thereby generated, and this can be used as a basis for a thorough presentation of many aspects of the posterior distribution. The methodology is applied here to the analysis of univariate normal mixtures, using a hierarchical prior model that offers an approach to dealing with weak prior information while avoiding the mathematical pitfalls of using improper priors in the mixture context.

Mixture Estimation and the Neurophysiological Quantal Hypothesis

Quantal release models provide a mechanistic description of the process by which neurotransmitter is released from the nerve cell. The usual such model assumes that the quantity of transmitter released after nerve depolarization follows a finite mixture distribution with an unknown number of components, and with constraints on component means and variances. General procedures for estimating the dimension of a finite mixture model are discussed, and applied to the analysis of a quantal release data set.