Bayesian inference, Monte Carlo sampling and operational risk

2006 ◽  
Vol 1 (3) ◽  
pp. 27-50 ◽  
Author(s):  
G Peters ◽  
S Sisson
Keyword(s):  
Monte Carlo ◽  
Bayesian Inference ◽  
Operational Risk ◽  
Monte Carlo Sampling

scholarly journals An integrated inverse adaptive neural fuzzy system with Monte-Carlo sampling method for operational risk management

2018 ◽  
Vol 98 ◽  
pp. 11-26 ◽  
Author(s):  
Alejandro Peña ◽  
Isis Bonet ◽  
Christian Lochmuller ◽  
Francisco Chiclana ◽  
Mario Góngora
Keyword(s):  
Risk Management ◽  
Monte Carlo ◽  
Fuzzy System ◽  
Sampling Method ◽  
Operational Risk ◽  
Monte Carlo Sampling ◽  
Operational Risk Management ◽  
Neural Fuzzy

HMCtomo: A framework for Hamiltonian Monte Carlo sampling of Bayesian geophysical inverse problems

2020 ◽  
Author(s):  
Lars Gebraad ◽  
Andrea Zunino ◽  
Andreas Fichtner ◽  
Klaus Mosegaard
Keyword(s):  
Monte Carlo ◽  
Bayesian Inference ◽  
Inverse Problems ◽  
Large Scale ◽  
Monte Carlo Sampling ◽  
Hamiltonian Monte Carlo ◽  
Forward Models ◽  
Inference Problems ◽  
Wide Range ◽  
Gradient Based

<div>We present a framework to solve geophysical inverse problems using the Hamiltonian Monte Carlo (HMC) method, with a focus on Bayesian tomography. Recent work in the geophysical community has shown the potential for gradient-based Monte Carlo sampling for a wide range of inverse problems across several fields.</div><div> </div><div>Many high-dimensional (non-linear) problems in geophysics have readily accessible gradient information which is unused in classical probabilistic inversions. Using HMC is a way to help improve traditional Monte Carlo sampling while increasing the scalability of inference problems, allowing access to uncertainty quantification for problems with many free parameters (>10'000). The result of HMC sampling is a collection of models representing the posterior probability density function, from which not only "best" models can be inferred, but also uncertainties and potentially different plausible scenarios, all compatible with the observed data. However, the amount of tuning parameters required by HMC, as well as the complexity of existing statistical modeling software, has limited the geophysical community in widely adopting a specific tool for performing efficient large-scale Bayesian inference.</div><div> </div><div>This work attempts to make a step towards filling that gap by providing an HMC sampler tailored for geophysical inverse problems (by e.g. supplying relevant priors and visualizations) combined with a set of different forward models, ranging from elastic and acoustic wave propagation to magnetic anomaly modeling, traveltimes, etc.. The framework is coded in the didactic but performant languages Julia and Python, with the possibility for the user to combine their own forward models, which are linked to the sampler routines by proper interfaces. In this way, we hope to illustrate the usefulness and potential of HMC in Bayesian inference. Tutorials featuring an array of physical experiments are written with the aim of both showcasing Bayesian inference and successful HMC usage. It additionally includes examples on how to speed up HMC e.g. with automated tuning techniques and GPU computations.</div>

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