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Please use this identifier to cite or link to this item: http://hdl.handle.net/11299/109730

Title: Supporting Theory and Data Analysis for "Long Range Search for Maximum Likelihood in Exponential Families"
Authors: Okabayashi, Saisuke
Geyer, Charles J.
Keywords: exponential family
maximum likelihood
social network model
Ising
Markov chain Monte Carlo
Issue Date: 23-Jul-2011
Series/Report no.: Technical Report
686
Abstract: Exponential families are often used to model data sets with complex dependence. Maximum likelihood estimators (MLE) can be difficult to estimate when the likelihood is expensive to compute. Markov chain Monte Carlo (MCMC) methods based on the MCMC-MLE algorithm in Geyer and Thompson (1992) are guaranteed to converge in theory under certain conditions when starting from any value, but in practice such an algorithm may labor to converge when given a poor starting value. We present a simple line search algorithm to find the MLE of a regular exponential family when the MLE exists and is unique. The algorithm can be started from any initial value and avoids the trial and error experimentation associated with calibrating algorithms like stochastic approximation. Unlike many optimization algorithms, this approach utilizes first derivative information only, evaluating neither the likelihood function itself nor derivatives of higher order than first. We show convergence of the algorithm for the case where the gradient can be calculated exactly. When it cannot, it has a particularly convenient form that is easily estimable with MCMC, making the algorithm still useful to a practitioner.
URI: http://purl.umn.edu/109730
Appears in Collections:Graduate Student Research

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