The Time Machine: A Simulation Approach for Stochastic Trees

TL;DR

This paper introduces a simulation method for stochastic trees in computational genetics that balances computational efficiency and accuracy by intentionally stopping simulations, resulting in biased likelihood estimates.

Contribution

It proposes a novel stopping technique for stochastic tree simulations, analyzing its bias and efficiency benefits compared to traditional importance sampling methods.

Findings

Biased estimates reduce computational time.

Bias-variance trade-off is characterized theoretically.

Simulation results show improved efficiency with acceptable bias.

Abstract

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.