Bayesian optimisation for fast approximate inference in state-space models with intractable likelihoods (2015-06-23T00:00:00.000000Z)

TL;DR

This work proposes a computationally efficient novel method based on the combination of Gaussian process optimisation and SMC-ABC to create a Laplace approximation of the intractable posterior of stochastic volatility models with both synthetic and real-world data.

Abstract

We consider the problem of approximate Bayesian parameter inference in non-linear state-space models with intractable likelihoods. Sequential Monte Carlo with approximate Bayesian computations (SMC-ABC) is one approach to approximate the likelihood in this type of models. However, such approximations can be noisy and computationally costly which hinders efficient implementations using standard methods based on optimisation and Monte Carlo methods. We propose a computationally efficient novel method based on the combination of Gaussian process optimisation and SMC-ABC to create a Laplace approximation of the intractable posterior. We exemplify the proposed algorithm for inference in stochastic volatility models with both synthetic and real-world data as well as for estimating the Value-at-Risk for two portfolios using a copula model. We document speed-ups of between one and two orders of magnitude compared to state-of-the-art algorithms for posterior inference.

Authors

T. Schon

2 papers

J. Dahlin

1 papers

M. Villani

1 papers

References30 items

Book review: quantitative risk management: concepts, techniques and tools, revised edition, by A.F. McNeil, R. Frey and P. Embrechts. Princeton University Press, 2015, ISBN 978-0-691-16627-8, xix + 700 pp.

Bayesian optimisation for fast approximate inference in state-space models with intractable likelihoods

TL;DR

Abstract

Authors

References30 items

Book review: quantitative risk management: concepts, techniques and tools, revised edition, by A.F. McNeil, R. Frey and P. Embrechts. Princeton University Press, 2015, ISBN 978-0-691-16627-8, xix + 700 pp.

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Bayesian Optimization for Likelihood-Free Inference of Simulator-Based Statistical Models

Recursive Gaussian process: On-line regression and learning

GPS-ABC: Gaussian Process Surrogate Approximate Bayesian Computation

Parameter Estimation in Hidden Markov Models With Intractable Likelihoods Using Sequential Monte Carlo

Particle Filter-Based Gaussian Process Optimisation for Parameter Inference

Finite Sample Bernstein -- von Mises Theorem for Semiparametric Problems

On Some Properties of Markov Chain Monte Carlo Simulation Methods Based on the Particle Filter

An adaptive sequential Monte Carlo method for approximate Bayesian computation

Asymptotic behaviour of approximate Bayesian estimators

Parameter Estimation for Hidden Markov Models with Intractable Likelihoods

Convergence Rates of Efficient Global Optimization Algorithms

Approximate Bayesian computational methods

A Tutorial on Bayesian Optimization of Expensive Cost Functions, with Application to Active User Modeling and Hierarchical Reinforcement Learning

Statistical inference for noisy nonlinear ecological dynamic systems

Particle Markov chain Monte Carlo methods

Filtering via approximate Bayesian computation

Stochastic models for risk estimation in volatile markets: a survey

Convergence properties of the expected improvement algorithm with fixed mean and covariance functions

Asymptotic efficiency of the two-stage estimation method for copula-based models

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Implementation of the simultaneous perturbation algorithm for stochastic optimization

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Getting started with particle Metropolis-Hastings for inference in nonlinear models

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The GPy authors. GPy: A Gaussian process framework in Python

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