scholarly journals Tractable nonparametric Bayesian inference in Poisson processes with Gaussian process intensities

2009 ◽  
Author(s):  
Ryan Prescott Adams ◽  
Iain Murray ◽  
David J. C. MacKay
Keyword(s):  
Bayesian Inference ◽  
Gaussian Process ◽  
Poisson Processes ◽  
Nonparametric Bayesian

scholarly journals Adaptive Gaussian Process Approximation for Bayesian Inference with Expensive Likelihood Functions

2018 ◽  
Vol 30 (11) ◽  
pp. 3072-3094 ◽  
Author(s):  
Hongqiao Wang ◽  
Jinglai Li
Keyword(s):  
Bayesian Inference ◽  
Gaussian Process ◽  
Adaptive Algorithm ◽  
Posterior Density ◽  
Unknown Parameters ◽  
Likelihood Functions ◽  
Inference Problems ◽  
Active Learning Method ◽  
Computationally Intensive ◽  
Process Approximation

We consider Bayesian inference problems with computationally intensive likelihood functions. We propose a Gaussian process (GP)–based method to approximate the joint distribution of the unknown parameters and the data, built on recent work (Kandasamy, Schneider, & Póczos, 2015 ). In particular, we write the joint density approximately as a product of an approximate posterior density and an exponentiated GP surrogate. We then provide an adaptive algorithm to construct such an approximation, where an active learning method is used to choose the design points. With numerical examples, we illustrate that the proposed method has competitive performance against existing approaches for Bayesian computation.

scholarly journals Nonparametric Bayesian inference for Gamma-type Lévy subordinators

2019 ◽  
Vol 17 (3) ◽  
pp. 781-816 ◽  
Author(s):  
Denis Belomestny ◽  
Shota Gugushvili ◽  
Moritz Schauer ◽  
Peter Spreij
Keyword(s):  
Bayesian Inference ◽  
Nonparametric Bayesian ◽  
Lévy Subordinators
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