Monte Carlo integration of dissipative quantum systems

1995 ◽  
Vol 33 (2) ◽  
pp. 79-88 ◽  
Author(s):  
M. Naraschewski ◽  
A. Schenzle
Keyword(s):  
Monte Carlo ◽  
Quantum Systems ◽  
Monte Carlo Integration ◽  
Dissipative Quantum Systems

scholarly journals Control variate selection for Monte Carlo integration

2021 ◽  
Vol 31 (4) ◽  
Author(s):  
Rémi Leluc ◽  
François Portier ◽  
Johan Segers
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Integration ◽  
Control Variate ◽  
Selection For

scholarly journals Estimating effective population size from samples of sequences: a bootstrap Monte Carlo integration method

1992 ◽  
Vol 60 (3) ◽  
pp. 209-220 ◽  
Author(s):  
Joseph Felsenstein
Keyword(s):  
Monte Carlo ◽  
Maximum Likelihood ◽  
Population Size ◽  
Effective Population Size ◽  
Random Mating ◽  
Computational Effort ◽  
Monte Carlo Integration ◽  
Bootstrap Sampling ◽  
Effective Population ◽  
Full Data

SummaryWe would like to use maximum likelihood to estimate parameters such as the effective population size Ne, or, if we do not know mutation rates, the product 4Neμof mutation rate per site and effective population size. To compute the likelihood for a sample of unrecombined nucleotide sequences taken from a random-mating population it is necessary to sum over all genealogies that could have led to the sequences, computing for each one the probability that it would have yielded the sequences, and weighting each one by its prior probability. The genealogies vary in tree topology and in branch lengths. Although the likelihood and the prior are straightforward to compute, the summation over all genealogies seems at first sight hopelessly difficult. This paper reports that it is possible to carry out a Monte Carlo integration to evaluate the likelihoods pproximately. The method uses bootstrap sampling of sites to create data sets for each of which a maximum likelihood tree is estimated. The resulting trees are assumed to be sampled from a distribution whose height is proportional to the likelihood surface for the full data. That it will be so is dependent on a theorem which is not proven, but seems likely to be true if the sequences are not short. One can use the resulting estimated likelihood curve to make a maximum likelihood estimate of the parameter of interest, Ne or of 4Neμ. The method requires at least 100 times the computational effort required for estimation of a phylogeny by maximum likelihood, but is practical on today's work stations. The method does not at present have any way of dealing with recombination.

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