Bayesian Prediction of Jumps in Large Panels of Time Series Data

Alexopoulos, Angelos; Δελλαπόρτας, Πέτρος; Papaspiliopoulos, Omiros

doi:10.1214/21-ba1268

Cited by 3 publications

(4 citation statements)

References 75 publications

(132 reference statements)

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“…To conduct Bayesian inference for the parameters m ∈ R, φ ∈ (−1, 1) and s 2 ∈ (0, ∞) we specify commonly used prior distributions (Kastner and Frühwirth-Schnatter 2014;Alexopoulos et al 2021): m ∼ N (0, 10), (φ + 1)/2 ∼ Beta(20, 1/5) and s 2 ∼ Gam(1/2, 1/2). The posterior of interest is…”

Section: Simulated Data: a Stochastic Volatility Modelmentioning

confidence: 99%

“…To assess the proposed variance reduction methods we simulated daily log-returns of a stock for d days by using values for the parameters of the model that have been previously estimated in real data applications (Kim et al 1998;Alexopoulos et al 2021) φ = 0.98, μ = −0.85 and s = 0.15. To draw samples from the d-dimensional, d = N + 3, target posterior in (24) we first transform the parameters φ and s 2 to real-valued parameters φ and s2 by taking the logit and logarithm transformations and we assign Gaussian prior distributions by matching the first two moments of the Gaussian distributions with the corresponding moments of the beta and gamma distributions used as priors for the parameters of the original formulation.…”

Section: Simulated Data: a Stochastic Volatility Modelmentioning

confidence: 99%

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Variance reduction for Metropolis–Hastings samplers

2022

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We introduce a general framework that constructs estimators with reduced variance for random walk Metropolis and Metropolis-adjusted Langevin algorithms. The resulting estimators require negligible computational cost and are derived in a post-process manner utilising all proposal values of the Metropolis algorithms. Variance reduction is achieved by producing control variates through the approximate solution of the Poisson equation associated with the target density of the Markov chain. The proposed method is based on approximating the target density with a Gaussian and then utilising accurate solutions of the Poisson equation for the Gaussian case. This leads to an estimator that uses two key elements: (1) a control variate from the Poisson equation that contains an intractable expectation under the proposal distribution, (2) a second control variate to reduce the variance of a Monte Carlo estimate of this latter intractable expectation. Simulated data examples are used to illustrate the impressive variance reduction achieved in the Gaussian target case and the corresponding effect when target Gaussianity assumption is violated. Real data examples on Bayesian logistic regression and stochastic volatility models verify that considerable variance reduction is achieved with negligible extra computational cost.

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Section: Simulated Data: a Stochastic Volatility Modelmentioning

confidence: 99%

Section: Simulated Data: a Stochastic Volatility Modelmentioning

confidence: 99%

Variance reduction for Metropolis–Hastings samplers

2022

View full text Add to dashboard Cite

show abstract

“…To conduct Bayesian inference for the parameters m ∈ R, φ ∈ (−1, 1) and s 2 ∈ (0, ∞) we specify commonly used prior distributions (Kastner and Frühwirth-Schnatter, 2014;Alexopoulos et al, 2021): m ∼ N (0, 10), (φ + 1)/2 ∼ Beta(20, 1/5) and…”

Section: Variance Reduction For Malamentioning

confidence: 99%

“…To assess the proposed variance reduction methods we simulated daily log-returns of a stock for d days by using values for the parameters of the model that have been previously estimated in real data applications (Kim et al, 1998;Alexopoulos et al, 2021) φ = 0.98, µ = −0.85 and s = 0.15. To draw samples from the d-dimensional, d = N + 3, target posterior in (24) we first transform the parameters φ and s 2 to real-valued parameters φ and s2 by taking the logit and logarithm transformations and we assign Gaussian prior distributions by matching the first two moments of the Gaussian distributions with the corresponding moments of the beta and gamma distributions used as priors for the parameters of the original formulation.…”

Section: Variance Reduction For Malamentioning

confidence: 99%

Variance Reduction for Metropolis-Hastings Samplers

Alexopoulos¹,

Δελλαπόρτας²,

Titsias³

2022

Preprint

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We introduce a general framework that constructs estimators with reduced variance for random walk Metropolis and Metropolis-adjusted Langevin algorithms. The resulting estimators require negligible computational cost and are derived in a post-process manner utilising all proposal values of the Metropolis algorithms. Variance reduction is achieved by producing control variates through the approximate solution of the Poisson equation associated with the target density of the Markov chain. The proposed method is based on approximating the target density with a Gaussian and then utilising accurate solutions of the Poisson equation for the Gaussian case. This leads to an estimator that uses two key elements: (i) a control variate from the Poisson equation that contains an intractable expectation under the proposal distribution, (ii) a second control variate to reduce the variance of a Monte Carlo estimate of this latter intractable expectation. Simulated data examples are used to illustrate the impressive variance reduction achieved in the Gaussian target case and the corresponding effect when target Gaussianity assumption is violated. Real data examples on Bayesian logistic regression and stochastic volatility models verify that considerable variance reduction is achieved with negligible extra computational cost.

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