scholarly journals The Exact Inference of Beta Process and Beta Bernoulli Process From Finite Observations

2019 ◽  
Vol 121 (1) ◽  
pp. 49-82
Author(s):  
Yang Cheng ◽  
Dehua Li ◽  
Wenbin Jiang
2017 ◽  
Vol 14 (134) ◽  
pp. 20170340 ◽  
Author(s):  
Aidan C. Daly ◽  
Jonathan Cooper ◽  
David J. Gavaghan ◽  
Chris Holmes

Bayesian methods are advantageous for biological modelling studies due to their ability to quantify and characterize posterior variability in model parameters. When Bayesian methods cannot be applied, due either to non-determinism in the model or limitations on system observability, approximate Bayesian computation (ABC) methods can be used to similar effect, despite producing inflated estimates of the true posterior variance. Owing to generally differing application domains, there are few studies comparing Bayesian and ABC methods, and thus there is little understanding of the properties and magnitude of this uncertainty inflation. To address this problem, we present two popular strategies for ABC sampling that we have adapted to perform exact Bayesian inference, and compare them on several model problems. We find that one sampler was impractical for exact inference due to its sensitivity to a key normalizing constant, and additionally highlight sensitivities of both samplers to various algorithmic parameters and model conditions. We conclude with a study of the O'Hara–Rudy cardiac action potential model to quantify the uncertainty amplification resulting from employing ABC using a set of clinically relevant biomarkers. We hope that this work serves to guide the implementation and comparative assessment of Bayesian and ABC sampling techniques in biological models.


1997 ◽  
Vol 34 (4) ◽  
pp. 898-907 ◽  
Author(s):  
Aihua Xia

This note gives the rate for a Wasserstein distance between the distribution of a Bernoulli process on discrete time and that of a Poisson process, using Stein's method and Palm theory. The result here highlights the possibility that the logarithmic factor involved in the upper bounds established by Barbour and Brown (1992) and Barbour et al. (1995) may be superfluous in the true Wasserstein distance between the distributions of a point process and a Poisson process.


Biometrics ◽  
2019 ◽  
Vol 75 (2) ◽  
pp. 485-493
Author(s):  
Haben Michael ◽  
Suzanne Thornton ◽  
Minge Xie ◽  
Lu Tian

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