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The time machine: a simulation approach for stochastic trees

Jasra, A; De Iorio, M; Chadeau-Hyam, M; (2011) The time machine: a simulation approach for stochastic trees. P ROY SOC A-MATH PHY , 467 (2132) 2350 - 2368. 10.1098/rspa.2010.0497.

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Abstract

In this 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 with such models. This typically consists of using importance sampling and sequential Monte Carlo techniques. The approach proceeds by simulating the tree, backward in time from observed data, to a most recent common ancestor. 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.

Type:Article
Title:The time machine: a simulation approach for stochastic trees
DOI:10.1098/rspa.2010.0497
Keywords:stochastic trees, sequential Monte Carlo, coalescent, MONTE-CARLO METHODS, STATE-SPACE MODELS, MAXIMUM-LIKELIHOOD, ASYMPTOTIC PROPERTIES, COALESCENT HISTORIES, POPULATION-GENETICS, NEUTRAL ALLELES, SAMPLING THEORY, SEQUENCE DATA, ESTIMATORS
UCL classification:UCL > School of BEAMS > Faculty of Maths and Physical Sciences > Statistical Science

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