A Comparison of Bayesian and Sampling Theory Inferences in a Probit Model

HE PROBIT MODEL IS A POPULAR DEVICE for explaining binary choice decisions in econometrics. It has been used to describe choices such as labor force participation, travel mode, home ownership, and type of education. These and many more examples can be found in papers by Amemiya (1981) and Maddala (1983). Given the contribution of economics towards explaining such choices, and given the nature of data that are collected, prior information on the relationship between a choice probability and several explanatory variables frequently exists. Bayesian inference is a convenient vehicle for including such prior information. Given the increasing popularity of Bayesian inference it is useful to ask whether inferences from a probit model are sensitive to a choice between Bayesian and sampling theory techniques. Of interest is the sensitivity of inference on coefficients, probabilities, and elasticities. We consider these issues in a model designed to explain choice between fixed and variable interest rate mortgages. Two Bayesian priors are employed: a uniform prior on the coefficients, designed to be noninformative for the coefficients, and an inequality restricted prior on the signs of the coefficients. We often know, a priori, whether increasing the value of a particular explanatory variable will have a positive or negative effect on a choice probability. This knowledge can be captured by using a prior probability density function (pdf) that is truncated to be positive or negative. Thus, three sets of results are compared:those from maximum likelihood (ML) estimation, those from Bayesian estimation with an unrestricted uniform prior on the coefficients, and those from Bayesian estimation with a uniform prior truncated to accommodate inequality restrictions on the coefficients.

A Comparison of the Home Range Sizes of Mainland and Island Populations of Black-Faced Lion Tamarins (Leontopithecus caissara) Using Different Spatial Analysis

The critically endangered black-faced lion tamarin, Leontopithecus caissara, has a restricted geographical distribution consisting of small mainland and island populations, each with distinct habitats in coastal southeastern Brazil. Necessary conservation management actions require an assessment of whether differences in habitats are reflected in use of space by the species. We studied two tamarin groups on the mainland at Sao Paulo state between August 2005 and March 2007, and compared the results with data from Superagui Island. Three home range estimators were used: minimum convex polygon (MCP), Kernel, and the new technique presented dissolved monthly polygons (DMP). These resulted, respectively, in home ranges of 345, 297, and 282 ha for the 12-month duration of the study. Spatial overlap of mainland groups was extensive, whereas temporal overlap was not, a pattern that indicates resource partitioning is an important strategy to avoid intraspecific competition. L. caissara large home ranges seem to be dynamic, with constant incorporation of new areas and abandonment of others through time. The main difference between mainland and island groups is the amount and variety of sleeping sites. A better understanding of the home range sizes, day range lengths, and territorial behavior of this species will aid in developing better management strategies for its protection. Additionally, the presented DMP protocol is a useful improvement over the MCP method as it results in more realistic home range sizes for wildlife species. Am. J. Primatol. 73: 1114-1126, 2011. (C) 2011 Wiley Periodicals, Inc.