scholarly journals On the use of marginal posteriors in marginal likelihood estimation via importance sampling

2014 ◽  
Vol 77 ◽  
pp. 54-69 ◽  
Author(s):  
Konstantinos Perrakis ◽  
Ioannis Ntzoufras ◽  
Efthymios G. Tsionas
Keyword(s):  
Importance Sampling ◽  
Marginal Likelihood ◽  
Likelihood Estimation ◽  
Marginal Likelihood Estimation

scholarly journals Stochastic Gradient Annealed Importance Sampling for Efficient Online Marginal Likelihood Estimation

Entropy ◽  
2019 ◽  
Vol 21 (11) ◽  
pp. 1109
Author(s):  
Scott A. Cameron ◽  
Hans C. Eggers ◽  
Steve Kroon
Keyword(s):  
Importance Sampling ◽  
Marginal Likelihood ◽  
Likelihood Estimation ◽  
Stochastic Gradient ◽  
Model Combination ◽  
Monte Carlo Techniques ◽  
Important Benefit ◽  
Weighted Model ◽  
Traditional Approaches ◽  
Marginal Likelihood Estimation

We consider estimating the marginal likelihood in settings with independent and identically distributed (i.i.d.) data. We propose estimating the predictive distributions in a sequential factorization of the marginal likelihood in such settings by using stochastic gradient Markov Chain Monte Carlo techniques. This approach is far more efficient than traditional marginal likelihood estimation techniques such as nested sampling and annealed importance sampling due to its use of mini-batches to approximate the likelihood. Stability of the estimates is provided by an adaptive annealing schedule. The resulting stochastic gradient annealed importance sampling (SGAIS) technique, which is the key contribution of our paper, enables us to estimate the marginal likelihood of a number of models considerably faster than traditional approaches, with no noticeable loss of accuracy. An important benefit of our approach is that the marginal likelihood is calculated in an online fashion as data becomes available, allowing the estimates to be used for applications such as online weighted model combination.

scholarly journals Parallel power posterior analyses for fast computation of marginal likelihoods in phylogenetics

PeerJ ◽  
2021 ◽  
Vol 9 ◽  
pp. e12438
Author(s):  
Sebastian Höhna ◽  
Michael J. Landis ◽  
John P. Huelsenbeck
Keyword(s):  
Open Source Software ◽  
Marginal Likelihood ◽  
Substantial Reduction ◽  
Likelihood Estimation ◽  
Marginal Likelihoods ◽  
Parallelization Strategy ◽  
Sampling Algorithms ◽  
Primary Focus ◽  
Bayesian Phylogenetic Inference ◽  
Marginal Likelihood Estimation

In Bayesian phylogenetic inference, marginal likelihoods can be estimated using several different methods, including the path-sampling or stepping-stone-sampling algorithms. Both algorithms are computationally demanding because they require a series of power posterior Markov chain Monte Carlo (MCMC) simulations. Here we introduce a general parallelization strategy that distributes the power posterior MCMC simulations and the likelihood computations over available CPUs. Our parallelization strategy can easily be applied to any statistical model despite our primary focus on molecular substitution models in this study. Using two phylogenetic example datasets, we demonstrate that the runtime of the marginal likelihood estimation can be reduced significantly even if only two CPUs are available (an average performance increase of 1.96x). The performance increase is nearly linear with the number of available CPUs. We record a performance increase of 13.3x for cluster nodes with 16 CPUs, representing a substantial reduction to the runtime of marginal likelihood estimations. Hence, our parallelization strategy enables the estimation of marginal likelihoods to complete in a feasible amount of time which previously needed days, weeks or even months. The methods described here are implemented in our open-source software RevBayes which is available from http://www.RevBayes.com.

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