This chapter describes several methods for estimating the parameter theta from observed data. Section 6.1 and 6.2 focus on this problem under the assumption that theta is fixed but unknown and section 6.3 views theta as a random variable with an associated probability distribution.

The first section describes a common approach for estimation parameters, maximizing the log likelihood of the data. Unfortunately, doing this can be computationally difficult, so two different solutions are provided. The first is a closed form function for triangulated graphs only and the second is an iterative method for arbitrary graphs based on coordinate ascent.

The next section describes a different setting, where the data is only partially observed (noisy). The EM algorithm is commonly used in this setting to calculate the maximum likelihood estimate of theta. This section first presents the exact form of EM for exponential families and then presents ‘variational’ EM for use when the mean parameters are not known exactly.

The last section focuses Variational Bayes, which is a method for estimating theta where theta is thought of as a random variable with a probability distribution.

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