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Approximate Methods for Calculating Marginals and Likelihoods
Published in Marloes Maathuis, Mathias Drton, Steffen Lauritzen, Martin Wainwright, Handbook of Graphical Models, 2018
Like the log-likelihood, the log-pseudolikelihood is a concave function of the parameter vector θ $ \theta $ , but the log-pseudolikelihood has the notable advantage that the log-partition function is not required to compute the pseudolikelihood. The pseudolikelihood is a consistent estimator for identifiable model: if the data was generated from a probability distribution of the form (1), then as the number of data points goes to infinity, the parameters that maximize the pseudolikelihood are equal to the true parameters with probability one. In a data limited setting or if the data was not generated from a model of the form (1), the pseudolikelihood may not yield a better estimate of the parameters than the one produced by maximizing the likelihood.
A penalized autologistic regression with application for modeling the microstructure of dual-phase high-strength steel
Published in Journal of Quality Technology, 2020
Mohammad Aminisharifabad, Qingyu Yang, Xin Wu
The first challenge in model parameter estimation is dealing with the intractable computation of the constant in Eq. [4]. Given a microstructure image, we have to enumerate all possible realizations of the image to calculate the normalization constant To overcome this challenge, we adopt the pseudolikelihood approximation, proposed by Besag (1974), in the autologistic regression framework and develop a penalized pseudo-log likelihood (PPLL) function as follows: where is a tuning parameter. Note that if then Eq. [5] converts to a traditional pseudo-log-likelihood function. To estimate the model parameters in Eq [5] needs to be maximized.