scholarly journals Exact and efficient hybrid Monte Carlo algorithm for accelerated Bayesian inference of gene expression models from snapshots of single-cell transcripts

2019 ◽  
Vol 151 (2) ◽  
pp. 024106
Author(s):  
Yen Ting Lin ◽  
Nicolas E. Buchler
Keyword(s):  
Gene Expression ◽  
Monte Carlo ◽  
Bayesian Inference ◽  
Single Cell ◽  
Monte Carlo Algorithm ◽  
Hybrid Monte Carlo

scholarly journals Accelerated Bayesian inference of gene expression models from snapshots of single-cell transcripts

2018 ◽  
Author(s):  
Yen Ting Lin ◽  
Nicolas E. Buchler
Keyword(s):  
Gene Expression ◽  
Monte Carlo ◽  
Bayesian Inference ◽  
Model Selection ◽  
Single Cell ◽  
Kinetic Parameters ◽  
Information Criterion ◽  
Time Dependent ◽  
Data Sets ◽  
Bayesian Evidence

Understanding how stochastic gene expression is regulated in biological systems using snapshots of single-cell transcripts requires state-of-the-art methods of computational analysis and statistical inference. A Bayesian approach to statistical inference is the most complete method for model selection and uncertainty quantification of kinetic parameters from single-cell data. This approach is impractical because current numerical algorithms are too slow to handle typical models of gene expression. To solve this problem, we first show that time-dependent mRNA distributions of discrete-state models of gene expression are dynamic Poisson mixtures, whose mixing kernels are characterized by a piece-wise deterministic Markov process. We combined this analytical result with a kinetic Monte Carlo algorithm to create a hybrid numerical method that accelerates the calculation of time-dependent mRNA distributions by 1000-fold compared to current methods. We then integrated the hybrid algorithm into an existing Monte Carlo sampler to estimate the Bayesian posterior distribution of many different, competing models in a reasonable amount of time. We validated our method of accelerated Bayesian inference on several synthetic data sets. Our results show that kinetic parameters can be reasonably constrained for modestly sampled data sets, if the model is known a priori. If the model is unknown,the Bayesian evidence can be used to rigorously quantify the likelihood of a model relative to other models from the data. We demonstrate that Bayesian evidence selects the true model and outperforms approximate metrics, e.g., Bayesian Information Criterion (BIC) or Akaike Information Criterion (AIC), often used for model selection.

scholarly journals Testing a Fourier-accelerated hybrid Monte Carlo algorithm

2002 ◽  
Vol 528 (3-4) ◽  
pp. 301-305 ◽  
Author(s):  
Simon Catterall ◽  
Sergey Karamov
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Algorithm ◽  
Hybrid Monte Carlo

scholarly journals COMPARISON OF UPDATE ALGORITHMS FOR PURE GAUGE SU(3)

1988 ◽  
Vol 03 (14) ◽  
pp. 1367-1378 ◽  
Author(s):  
RAJAN GUPTA ◽  
GREGORY W. KILCUP ◽  
APOORVA PATEL ◽  
STEPHEN R. SHARPE ◽  
PHILIPPE DE FORCRAND
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Algorithm ◽  
Hybrid Monte Carlo ◽  
Pure Gauge

We show that the overrelaxed algorithm of Creutz and of Brown and Woch is the optimal local update algorithm for simulation of pure gauge SU(3). Our comparison criterion includes computer efficiency and decorrelation times. We also investigate the rate of decorrelation for the Hybrid Monte Carlo algorithm.

scholarly journals Measure of autocorrelation times of local hybrid Monte Carlo algorithm for lattice QCD

1993 ◽  
Vol 315 (1-2) ◽  
pp. 152-156 ◽  
Author(s):  
Paolo Marenzoni ◽  
Luigi Pugnetti ◽  
Pietro Rossi
Keyword(s):  
Monte Carlo ◽  
Lattice Qcd ◽  
Monte Carlo Algorithm ◽  
Hybrid Monte Carlo

scholarly journals Berezinskii-Kosterlitz-Thouless phase transition from lattice sine-Gordon model

2018 ◽  
Vol 175 ◽  
pp. 14003
Author(s):  
Joel Giedt ◽  
James Flamino
Keyword(s):  
Phase Transition ◽  
Monte Carlo ◽  
Critical Temperature ◽  
Finite Size ◽  
Monte Carlo Algorithm ◽  
Finite Size Scaling ◽  
Hybrid Monte Carlo ◽  
Lattice Field ◽  
Autocorrelation Time ◽  
Sine Gordon Model

We obtain nonperturbative results on the sine-Gordon model using the lattice field technique. In particular, we employ the Fourier accelerated hybrid Monte Carlo algorithm for our studies. We find the critical temperature of the theory based autocorrelation time, as well as the finite size scaling of the “thickness” observable used in an earlier lattice study by Hasenbusch et al.

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