Analysis of Incomplete Multivariate Data by J.L. Schafer

By J.L. Schafer

Offers a unified, Bayesian method of the research of incomplete multivariate facts, protecting datasets within which the variables are non-stop, express or either. comprises actual info examples and sensible suggestion.

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Extra info for Analysis of Incomplete Multivariate Data

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In the above example, a particular factorization of the observed data likelihood enabled us to express the posterior in a tractable form. This will not always be the case. One cannot always factor the observed-data likelihood into complete-data likelihoods whose parameters are distinct. The techniques of Markov chain Monte Carlo to be introduced in Chapter 3 will free us from many of the constraints of mathematical tractability, allowing us to create random draws from the observed-data posterior whether or not it can be written in a tractable form.

2) where l(θ | Y ) = logP (Y|θ) denotes the complete-data loglikelihood, l(θ|Yo b s ) = log P ( Y|θ) the observed-data loglikelihood, and c an arbitrary constant. The term P(Ymis|Yobs , θ), which we shall call the predictive distribution of the missing data given θ, plays a central role in EM because it captures the interdependence between Ymis , and θ . When viewed as a probability distribution it summarizes knowledge about Ymis, for any assumed value of θ, and when viewed as a function of θ it conveys the evidence about θ contained in Ymis beyond that already provided by Yobs.

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