scholarly journals Fully Bayesian inference for α -stable distributions using a Poisson series representation

2015 ◽  
Vol 47 ◽  
pp. 96-115 ◽  
Author(s):  
Tatjana Lemke ◽  
Marina Riabiz ◽  
Simon J. Godsill
PLoS ONE ◽  
2013 ◽  
Vol 8 (7) ◽  
pp. e68196 ◽  
Author(s):  
Paul Schmidt ◽  
Volker J. Schmid ◽  
Christian Gaser ◽  
Dorothea Buck ◽  
Susanne Bührlen ◽  
...  

2017 ◽  
Author(s):  
Sebastian Duchene ◽  
David Duchene ◽  
Jemma Geoghegan ◽  
Zoe Anne Dyson ◽  
Jane Hawkey ◽  
...  

Background: Recent developments in sequencing technologies make it possible to obtain genome sequences from a large number of isolates in a very short time. Bayesian phylogenetic approaches can take advantage of these data by simultaneously inferring the phylogenetic tree, evolutionary timescale, and demographic parameters (such as population growth rates), while naturally integrating uncertainty in all parameters. Despite their desirable properties, Bayesian approaches can be computationally intensive, hindering their use for outbreak investigations involving genome data for a large numbers of pathogen isolates. An alternative to using full Bayesian inference is to use a hybrid approach, where the phylogenetic tree and evolutionary timescale are estimated first using maximum likelihood. Under this hybrid approach, demographic parameters are inferred from estimated trees instead of the sequence data, using maximum likelihood, Bayesian inference, or approximate Bayesian computation. This can vastly reduce the computational burden, but has the disadvantage of ignoring the uncertainty in the phylogenetic tree and evolutionary timescale. Results: We compared the performance of a fully Bayesian and a hybrid method by analysing six whole-genome SNP data sets from a range of bacteria and simulations. The estimates from the two methods were very similar, suggesting that the hybrid method is a valid alternative for very large datasets. However, we also found that congruence between these methods is contingent on the presence of strong temporal structure in the data (i.e. clocklike behaviour), which is typically verified using a date-randomisation test in a Bayesian framework. To reduce the computational burden of this Bayesian test we implemented a date-randomisation test using a rapid maximum likelihood method, which has similar performance to its Bayesian counterpart. Conclusions: Hybrid approaches can produce reliable inferences of evolutionary timescales and phylodynamic parameters in a fraction of the time required for fully Bayesian analyses. As such, they are a valuable alternative in outbreak studies involving a large number of isolates.


2011 ◽  
Author(s):  
Mona Shokripour ◽  
Vahid Nassiri ◽  
Adel Mohammadpour ◽  
Ali Mohammad-Djafari ◽  
Jean-François Bercher ◽  
...  

2011 ◽  
Vol 19 (1) ◽  
pp. 32-47 ◽  
Author(s):  
Justin Grimmer

Markov chain Monte Carlo (MCMC) methods have facilitated an explosion of interest in Bayesian methods. MCMC is an incredibly useful and important tool but can face difficulties when used to estimate complex posteriors or models applied to large data sets. In this paper, we show how a recently developed tool in computer science for fitting Bayesian models, variational approximations, can be used to facilitate the application of Bayesian models to political science data. Variational approximations are often much faster than MCMC for fully Bayesian inference and in some instances facilitate the estimation of models that would be otherwise impossible to estimate. As a deterministic posterior approximation method, variational approximations are guaranteed to converge and convergence is easily assessed. But variational approximations do have some limitations, which we detail below. Therefore, variational approximations are best suited to problems when fully Bayesian inference would otherwise be impossible. Through a series of examples, we demonstrate how variational approximations are useful for a variety of political science research. This includes models to describe legislative voting blocs and statistical models for political texts. The code that implements the models in this paper is available in the supplementary material.


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