## probit posterior mean

**I**n 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

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.

March 12, 2012 at 3:45 am

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