We maximize the log marginal likelihood functions for the models by scaled conjugate gradient method using the 'gptk' R package by Kalaitzis and Lawrence (2011).
Figure 10 The marginal spatial likelihood functions from real-data recording are presented.
The normalized marginal spatial likelihood functions are displayed in Figure 10.
However, it can effectively be attacked by alternating between optimizing the marginal likelihood as a function of p0 and the set of pattern locations, {x i,i = 1…M}, respectively.
Briefly, for each t, we first calculated the lower bound of the marginal log-likelihood function, log P (E, T | X t − 1, X I ), which can be obtained by integrating the joint probability with respect to X h (Supplementary Information S1.4): for distributions of X h, Q (X h ), log P (T, E | X t − 1, X I ) ≥ ∫ Q (X h ) log (P (X h, T, E | X t − 1, X I ) Q (X h ) ) d X h.
Gaussian processes allow marginalizing the latent function to obtain a marginal likelihood.
A useful transformation of the marginal likelihood is the so-called energy function, which is sometimes more convenient to deal with.
Similarly, when y i is known and x i is MAR, their contribution to the likelihood function (l6) is the marginal distribution function of y i.
It should be noted that any inference using the log-likelihood from the marginal method is potentially misleading, since the likelihood function assumes best and worst choices are made independently.
When x i is known and y i is MAR, their contribution to the likelihood function (l5) is simply the marginal distribution function of x i.
