Markov chain Monte Carlo estimation of hazard model parameters in paleodemography

Abstract

Introduction In the early 1990s Konigsberg and Frankenberg wrote “A future direction that we expect to see in anthropological demography and paleodemography is the incorporation of uncertainty of age estimates into reduced parameterizations of life table functions. For example, hazards analysis, which reduces the mortality parameters to a small set, has recently been used in a number of anthropological demography studies” (Konigsberg and Frankenberg 1992:252). At the time we were writing we lacked the appropriate reference sample data for such an endeavor, as well as a number of the requisite statistical/computational tools. Today, neither of these issues is particularly problematical. Consequently, in this chapter we present some newer methods exploiting available reference sample data. The structure of this chapter is as follows. First, we discuss methods for modeling the dependence of an ordinal categorical variable on age. We then discuss the modeling of survivorship for archaeological human remains, and show how hazard model parameters can be estimated from an ordinal categorical variable using traditional maximization of the loglikelihood. We follow this presentation of methods with a brief example of estimating the parameters in a Gompertz–Makeham model using pubic symphyseal data and the method of maximum likelihood. We then turn to using a specific Markov chain Monte Carlo (MCMC) method known as the Gibbs Sampler to show how more general problems in hazard model and age estimation can be attacked.

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