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Perfect Simulation from Nonneutral Population Genetic Models: Variable Population Size and Population subdivision
"... Summary: We show how the idea of monotone coupling from the past can produce simple algorithms for simulating samples at a nonneutral locus under a range of demographic models. We specifically consider a biallelic locus, and either a general variable population size mode, or a general migration mo ..."
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Summary: We show how the idea of monotone coupling from the past can produce simple algorithms for simulating samples at a nonneutral locus under a range of demographic models. We specifically consider a biallelic locus, and either a general variable population size mode, or a general migration model for population subdivision. We investigate the effect of demography on the efficacy of selection, and the effect of selection on genetic divergence between populations.
Perfect Simulation of M/G/c Queues
, 2014
"... In this paper we describe a perfect simulation algorithm for the stableM/G/c queue. Sigman (2011: Exact Simulation of the Stationary Distribution of the FIFO M/G/c Queue. Journal of Applied Probability, 48A, 209213) showed how to build a dominated CFTP algorithm for perfect simulation of the supers ..."
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In this paper we describe a perfect simulation algorithm for the stableM/G/c queue. Sigman (2011: Exact Simulation of the Stationary Distribution of the FIFO M/G/c Queue. Journal of Applied Probability, 48A, 209213) showed how to build a dominated CFTP algorithm for perfect simulation of the superstable M/G/c queue operating under First Come First Served discipline, with dominating process provided by the corresponding M/G/1 queue (using Wolff's sample path monotonicity, which applies when service durations are coupled in order of initiation of service), and exploiting the fact that the workload process for theM/G/1 queue remains the same under different queueing disciplines, in particular under the Processor Sharing discipline, for which a dynamic reversibility property holds. We generalize Sigman's construction to the stable case by comparing the M/G/c queue to a copy run under Random Assignment. This allows us to produce a naïve perfect simulation algorithm based on running the dominating process back to the time it first empties. We also construct a more efficient algorithm that uses sandwiching by lower and upper processes constructed as coupledM/G/c queues started respectively from the empty state and the state of the M/G/c queue under
Perfect Sampling of Jackson Queueing
, 2013
"... HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte p ..."
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HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et a ̀ la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
MarkovChain Monte Carlo Methods for Simulations of Biomolecules
, 709
"... The computer revolution has been driven by a sustained increase of computational speed of approximately one order of magnitude (a factor of ten) every five years since about 1950. In natural sciences this has led to a continuous increase of the importance of computer simulations. Major enabling tech ..."
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The computer revolution has been driven by a sustained increase of computational speed of approximately one order of magnitude (a factor of ten) every five years since about 1950. In natural sciences this has led to a continuous increase of the importance of computer simulations. Major enabling techniques are Markov Chain Monte Carlo (MCMC) and Molecular Dynamics (MD) simulations. This article deals with the MCMC approach. First basic simulation techniques, as well as methods for their statistical analysis are reviewed. Afterwards the focus is on generalized ensembles and biased updating, two advanced techniques, which are of relevance for simulations of biomolecules, or are expected to become relevant with that respect. In particular we consider the multicanonical ensemble and the replica exchange method (also known as parallel tempering or method of multiple Markov chains). 1
ComputerIntensive Statistics
 APTS 2012–13 LECTURE MATERIAL
, 2012
"... ‘Computerintensive statistics’ is statistics that could only be done with ‘modern‘ computing resources, typically either • Statistical inference on small problems which needs a lot of computation to do at all, or to do well. Quite small datasets can need complex models to explain, and even simple m ..."
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‘Computerintensive statistics’ is statistics that could only be done with ‘modern‘ computing resources, typically either • Statistical inference on small problems which needs a lot of computation to do at all, or to do well. Quite small datasets can need complex models to explain, and even simple models can need a lot of computation for a realistic analysis (especially where dependence is involved). • Statistical inference on ‘huge ’ problems. All of these terms are relative and change quite rapidly—according to the most commonly quoted version of Moore’s Law (see section 6 and Ripley (2005)) computing power will quadruple during your doctoral studies. One very important idea for doing statistical inference ‘well ’ on analytically intractable statistical models (that is, most realworld ones) is to make use of simulation. So most of this module could be subtitled simulationbased inference, as in Geyer (1999)’s comments about MCMC for spatial point processes: If you can write down a model, I can do likelihood inference for it, not only maximum
Networks
"... Abstract: We consider open Jackson networks with losses with mixed finite and infinite queues and analyze the efficiency of sampling from their exact stationary distribution. We show that perfect sampling is possible, although the underlying Markov chain may have an infinite state space. The main id ..."
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Abstract: We consider open Jackson networks with losses with mixed finite and infinite queues and analyze the efficiency of sampling from their exact stationary distribution. We show that perfect sampling is possible, although the underlying Markov chain may have an infinite state space. The main idea is to use a Jackson network with infinite buffers (that has a product form stationary distribution) to bound the number of initial conditions to be considered in the coupling from the past scheme. We also provide bounds on the sampling time of this new perfect sampling algorithm for acyclic or hyperstable networks. These bounds show that the new algorithm is considerably more efficient than existing perfect samplers even in the case where all queues are finite. We illustrate this efficiency through numerical experiments. We also extend our approach to nonmonotone networks such as queueing networks with negative customers. Keywords: