probit posterior mean

In a recent arXiv report, Yuzo Maruyma shows that the posterior expectation of a probit parameter has an almost closed form (under a flat prior), namely

$\mathbb{E}[\beta|X,y] = (X^TX)^{-1} X^T\{2\text{diag}(y)-I_n\}\omega(X,y)$

where ω involves the integration of two quadratic forms over the n-dimensional unit sphere. Although this does not help directly with the MCMC derivation of the full posterior, this is an interesting lemma which shows a closed proximity with the standard least square estimate in linear regression.

This entry was posted on March 9, 2012 at 12:12 pm and is filed under Statistics, University life with tags Bayesian inference, generalised linear models, least squares, probit model. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.

One Response to “probit posterior mean”

Useful for referring–3-11-2012 « Honglang Wang's Blog Says:
March 12, 2012 at 3:45 am

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