The Time Machine: A Simulation Approach for Stochastic Trees

Details The Time Machine: A Simulation Approach for Stochastic Trees The Time Machine: A Simulation Approach for Stochastic Trees

2010-09-26

arxiv.org/abs/1009.5103v1

Statistics

Computation

22 Pages, 5 Figures

Scientific paper

In the following paper we consider a simulation technique for stochastic trees. One of the most important areas in computational genetics is the calculation and subsequent maximization of the likelihood function associated to such models. This typically consists of using importance sampling (IS) and sequential Monte Carlo (SMC) techniques. The approach proceeds by simulating the tree, backward in time from observed data, to a most recent common ancestor (MRCA). However, in many cases, the computational time and variance of estimators are often too high to make standard approaches useful. In this paper we propose to stop the simulation, subsequently yielding biased estimates of the likelihood surface. The bias is investigated from a theoretical point of view. Results from simulation studies are also given to investigate the balance between loss of accuracy, saving in computing time and variance reduction.

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