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

Abstract

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.