Efficient Bayesian estimation for GARCH-type models via Sequential Monte Carlo

Li, Dan; Clements, Adam; Drovandi, Christopher

doi:10.1016/j.ecosta.2020.02.002

Cited by 8 publications

(4 citation statements)

References 57 publications

(85 reference statements)

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“…Note that the log-likelihood approximation we apply, based on the work of Bekaert et al (2015) is biased. Recently, Li et al (2020) proposed an unbiased likelihood estimator, for which there are SIMD opportunities also. For the purposes of this manuscript, we find the biased approximation of Bekaert et al (2015) lends itself more direct discourse.…”

Section: Discussionmentioning

confidence: 99%

Vector Operations for Accelerating Expensive Bayesian Computations – A Tutorial Guide

2021

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Many applications in Bayesian statistics are extremely computationally intensive. However, they are often inherently parallel, making them prime targets for modern massively parallel processors. Multi-core and distributed computing is widely applied in the Bayesian community, however, very little attention has been given to fine-grain parallelisation using single instruction multiple data (SIMD) operations that are available on most modern CPUs. In this work, we practically demonstrate, using standard programming libraries, the utility of the SIMD approach for several topical Bayesian applications. Using the C programming language, we show that SIMD can improve the single-core floating point arithmetic performance by up to a factor of 6× compared scalar C code and more than 25× compared with optimised R code. Such improvements are multiplicative to any gains achieved through multi-core processing. We illustrate the potential of SIMD for accelerating Bayesian computations and provide the reader with techniques for exploiting modern massively parallel processing environments.

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Section: Discussionmentioning

confidence: 99%

Vector Operations for Accelerating Expensive Bayesian Computations – A Tutorial Guide

2021

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“…There are many other variants to this classic approach, such as particle Gibbs sampling (Andrieu et al, 2010;Doucet et al, 2015), coupled Markov chains (Dodwell et al, 2015(Dodwell et al, , 2019, and more advanced particle filters (Doucet and Johanson, 2011) and proposal mechanisms (Botha et al, 2019;Cotter et al, 2013). It is also important to note that the pseudo-marginal approach is equally valid for Bayesian sampling strategies based on sequential Monte Carlo (Del Moral et al, 2006;Li et al, 2019;Sisson et al, 2007). Furthermore, advances in stochastic simulation (Schnoerr et al, 2017;Warne et al, 2019) can also improve the performance of the likelihood estimator, and the application of multilevel Monte Carlo to particle filters can further reduce estimator variance (Gregory et al, 2016;Jasra et al, 2017Jasra et al, , 2018.…”

Section: Discussionmentioning

confidence: 99%

A practical guide to pseudo-marginal methods for computational inference in systems biology

Warne

Baker

Simpson

2020

Journal of Theoretical Biology

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For many stochastic models of interest in systems biology, such as those describing biochemical reaction networks, exact quantification of parameter uncertainty through statistical inference is intractable. Likelihood-free computational inference techniques enable parameter inference when the likelihood function for the model is intractable but the generation of many sample paths is feasible through stochastic simulation of the forward problem. The most common likelihood-free method in systems biology is approximate Bayesian computation that accepts parameters that result in low discrepancy between stochastic simulations and measured data. However, it can be difficult to assess how the accuracy of the resulting inferences are affected by the choice of acceptance threshold and discrepancy function. The pseudo-marginal approach is an alternative likelihood-free inference method that utilises a Monte Carlo estimate of the likelihood function. This approach has several advantages, particularly in the context of noisy, partially observed, time-course data typical in biochemical reaction network studies. Specifically, the pseudo-marginal approach facilitates exact inference and uncertainty quantification, and may be efficiently combined with particle filters for low variance, high-accuracy likelihood estimation. In this review, we provide a practical introduction to the pseudo-marginal approach using inference for biochemical reaction networks as a series of case studies. Implementations of key algorithms and examples are provided using the Julia programming language; a high performance, open source programming language for scientific computing (https://github.com/davidwarne/Warne2019 GuideToPseudoMarginal).

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“…The SMC method is an attractive approach for Bayesian inference and forecasting in volatility modelling (Li et al, 2020). SMC can sample efficiently from non-standard posteriors, provides the marginal likelihood estimate as a by-product, and is a convenient way for computing onestep-ahead forecasts.…”

Section: Sequential Monte Carlo (Smc)mentioning

confidence: 99%

Recurrent Conditional Heteroskedasticity

Nguyen¹,

Tran²,

Kohn³

2020

Preprint

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We propose a new class of financial volatility models, which we call the REcurrent Conditional Heteroskedastic (RECH) models, to improve both the in-sample analysis and out-of-sample forecast performance of the traditional conditional heteroskedastic models. In particular, we incorporate auxiliary deterministic processes, governed by recurrent neural networks, into the conditional variance of the traditional conditional heteroskedastic models, e.g. the GARCH-type models, to flexibly capture the dynamics of the underlying volatility. The RECH models can detect interesting effects in financial volatility overlooked by the existing conditional heteroskedastic models such as the GARCH (Bollerslev, 1986), GJR (Glosten et al., 1993) and EGARCH (Nelson, 1991). The new models often have good out-of-sample forecasts while still explain well the stylized facts of financial volatility by retaining the well-established structures of the econometric GARCH-type models. These properties are illustrated through simulation studies and applications to four real stock index datasets. An user-friendly software package together with the examples reported in the paper are available at https://github.com/vbayeslab.

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Efficient Bayesian estimation for GARCH-type models via Sequential Monte Carlo

Cited by 8 publications

References 57 publications

Vector Operations for Accelerating Expensive Bayesian Computations – A Tutorial Guide

Vector Operations for Accelerating Expensive Bayesian Computations – A Tutorial Guide

A practical guide to pseudo-marginal methods for computational inference in systems biology

Recurrent Conditional Heteroskedasticity

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