Finite mixture distributions, sequential likelihood and the EM algorithm

A popular way to account for unobserved heterogeneity is to assume that the data are drawn from a finite mixture distribution. A barrier to using finite mixture models is that parameters that could previously be estimated in stages must now be estimated jointly: using mixture distributions destroys any additive separability of the log-likelihood function. We show, however, that an extension of the EM algorithm reintroduces additive separability, thus allowing one to estimate parameters sequentially during each maximization step. In establishing this result, we develop a broad class of estimators for mixture models. Returning to the likelihood problem, we show that, relative to full information maximum likelihood, our sequential estimator can generate large computational savings with little loss of efficiency.

Finite size effects in the presence of a chemical potential: A study in the classical nonlinear O(2) sigma model

In the presence of a chemical potential, the physics of level crossings leads to singularities at zero temperature, even when the spatial volume is finite. These singularities are smoothed out at a finite temperature but leave behind nontrivial finite size effects which must be understood in order to extract thermodynamic quantities using Monte Carlo methods, particularly close to critical points. We illustrate some of these issues using the classical nonlinear O(2) sigma model with a coupling β and chemical potential μ on a 2+1-dimensional Euclidean lattice. In the conventional formulation this model suffers from a sign problem at nonzero chemical potential and hence cannot be studied with the Wolff cluster algorithm. However, when formulated in terms of the worldline of particles, the sign problem is absent, and the model can be studied efficiently with the "worm algorithm." Using this method we study the finite size effects that arise due to the chemical potential and develop an effective quantum mechanical approach to capture the effects. As a side result we obtain energy levels of up to four particles as a function of the box size and uncover a part of the phase diagram in the (β,μ) plane. © 2010 The American Physical Society.

Stable isotope ratios indicate diet and habitat use in New World monkeys.

This paper demonstrates the use of stable isotope ratios of carbon and nitrogen in animal tissue for indicating aspects of species behavioral strategy. We analyzed hair from individuals representing four species of New World monkeys (Alouatta palliata, the mantled howler; Ateles geoffroyi, the spider monkey; Cebus capucinus, the capuchin; and Brachyteles arachnoides, the woolly-spider monkey or muriqui) for delta 13C and delta 15N using previously developed methods. There are no significant differences in either carbon or nitrogen ratios between sexes, sampling year, or year of analysis. Seasonal differences in delta 13C reached a low level of significance but do not affect general patterns. Variation within species was similar to that recorded previously within single individuals. The omega 13C data show a bimodal distribution with significant difference between the means. The two monkey populations living in an evergreen forest were similar to each other and different from the other two monkey populations that inhabited dry, deciduous forests. This bimodal distribution is independent of any particular species' diet and reflects the level of leaf cover in the two types of forest. The delta 15N data display three significantly different modes. The omnivorous capuchins were most positive reflecting a trophic level offset. The spider monkeys and the muriquis were similar to one another and significantly more positive than the howlers. This distribution among totally herbivorous species correlates with the ingestion of legumes by the howler monkey population. In combination, these data indicate that museum-curated primate material can be analyzed to yield information on forest cover and diet in populations and species lacking behavioral data.