MARKOV CHAIN MONTE CARLO: NEW TOOLS FOR BAYESIAN MODELING IN PALEONTOLOGY

Paleontologists often need to model complex systems with many variables and complex relationships. In such models, information is often characterized by high-dimensional statistical distributions that are difficult to analyze mathematically. In this poster, we describe the use of Markov Chain Monte Carlo (MCMC) in generating an approximate sample from any desired distribution. In so doing, the sample provides important insights into the nature of the distribution at hand. MCMC describes an iterative approach towards simulating a sample, creating a sequence of values (or vector of values) whose distribution more closely approximates the desired distribution the longer the chain is allowed to run. More specifically, we present the Metropolis-Hastings Algorithm, a particular implementation of MCMC, which easily adapts to high-dimensional problems.

In this poster, we use MCMC to gain insight into the primary causes of the Permian mass extinction. We use a computer model to simulate secondary extinctions in a Late Permian food web. Then, using MCMC methods and Bayesian modeling, we infer the level of primary production loss needed to cause observed levels of secondary extinction in Late Permian Karoo basin fauna.