Probabilistic Forecasting and Bayesian Data Assimilation (Cambridge Texts in Applied Mathematics) by Sebastian Reich & Colin Cotter

Author:Sebastian Reich & Colin Cotter [Reich, Sebastian]
Language: eng
Format: epub
Publisher: Cambridge University Press
Published: 2015-05-13T23:00:00+00:00

with weights

(5.25)

This estimator is consistent (recall from Chapter 3 that an estimator is called consistent if the root mean square error between the estimator and the exact expectation value ga = E[g(Xa)] vanishes as M → ∞).

Example 5.16We return to the Bayesian inference problem of Example 5.9. Instead of the Brownian dynamics sampling approach considered in Example 5.14 we now consider importance sampling by drawing M samples xi from the Gaussian prior N(−2, 1/2) with posterior weights

The relative errors (as defined in Example 5.14) in the posterior mean and variance,

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