Details

Autor(en) / Beteiligte

• Wang, Bo
• Titterington, D. M.
• Lawrence, Neil
• Winkler, Joab
• Niranjan, Mahesan

Titel

Variational Bayes Estimation of Mixing Coefficients

Ist Teil von

• Deterministic and Statistical Methods in Machine Learning, 2005, p.281-295

Ort / Verlag

Berlin, Heidelberg: Springer Berlin Heidelberg

Erscheinungsjahr

2005

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• We investigate theoretically some properties of variational Bayes approximations based on estimating the mixing coefficients of known densities. We show that, with probability 1 as the sample size n grows large, the iterative algorithm for the variational Bayes approximation converges locally to the maximum likelihood estimator at the rate of O(1/n). Moreover, the variational posterior distribution for the parameters is shown to be asymptotically normal with the same mean but a different covariance matrix compared with those for the maximum likelihood estimator. Furthermore we prove that the covariance matrix from the variational Bayes approximation is ‘too small’ compared with that for the MLE, so that resulting interval estimates for the parameters will be unrealistically narrow.