Bayesian inference for generalized extreme value distributions via Hamiltonian Monte Carlo

Hartmann, Marcelo; Ehlers, Ricardo S.

doi:10.1080/03610918.2016.1152365

Cited by 10 publications

(6 citation statements)

References 7 publications

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“…The gradient is obtained through automatic differentiation (Carpenter et al (2015)) in STAN. The HMC sampler has shown good performance in several other cases (Hajian (2007); Pakman and Paninski (2014); Hartmann and Ehlers (2017)). We provide a short introduction to HMC in Appendix B and refer to Neal et al (2011) or Betancourt (2017) for more details.…”

Section: Hamiltonian Monte Carlomentioning

confidence: 98%

A Bayesian Non-linear State Space Copula Model to Predict Air Pollution in Beijing

Kreuzer,

Valle,

Czado

2019

Preprint

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Air pollution is a serious issue that currently affects many industrial cities in the world and can cause severe illness to the population. In particular, it has been proven that extreme high levels of airborne contaminants have dangerous short-term effects on human health, in terms of increased hospital admissions for cardiovascular and respiratory diseases and increased mortality risk. For these reasons, accurate estimation and prediction of airborne pollutant concentration is crucial. In this paper, we propose a flexible novel approach to model hourly measurements of fine particulate matter and meteorological data collected in Beijing in 2014. We show that the standard state space model, based on Gaussian assumptions, does not correctly capture the time dynamics of the observations. Therefore, we propose a non-linear non-Gaussian state space model where both the observation and the state equations are defined by copula specifications, and we perform Bayesian inference using the Hamiltonian Monte Carlo method. The proposed copula state space approach is very flexible, since it allows us to separately model the marginals and to accommodate a wide variety of dependence structures in the data dynamics. We show that the proposed approach allows us not only to predict particulate matter measurements, but also to investigate the effects of user specified climate scenarios.

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Section: Hamiltonian Monte Carlomentioning

confidence: 98%

A Bayesian Non-linear State Space Copula Model to Predict Air Pollution in Beijing

Kreuzer,

Valle,

Czado

2019

Preprint

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“…To sample β, τ 2 , a, z in PGM, we use a block of HMC and Gibbs sampler. The HMC technique requires fewer iterations to explore the parameter space and converges rapidly to the target distribution (Hartmann and Ehlers, 2017). Therefore, we implement the HMC and Gibbs sampler with 5000 iterations and 1000 burn-in.…”

Section: Simulationsmentioning

confidence: 99%

Comparison of Bayesian Nonparametric Density Estimation Methods

Bedoui¹,

Rosen²

2020

Preprint

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In this paper, we propose a nonparametric Bayesian approach for Lindsey and penalized Gaussian mixtures methods. We compare these methods with the Dirichlet process mixture model. Our approach is a Bayesian nonparametric method not based solely on a parametric family of probability distributions. Thus, the fitted models are more robust to model misspecification. Also, with the Bayesian approach, we have the entire posterior distribution of our parameter of interest; it can be summarized through credible intervals, mean, median, standard deviation, quantiles, etc. The Lindsey, penalized Gaussian mixtures, and Dirichlet process mixture methods are reviewed. The estimations are performed via Markov chain Monte Carlo (MCMC) methods. The penalized Gaussian mixtures method is implemented via Hamiltonian Monte Carlo (HMC). We show that under certain regularity conditions, and as n increases, the posterior distribution of the weights converges to a Normal distribution. Simulation results and data analysis are reported.

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“…The GEV distribution comprises into a single form all three Extreme Value (EV) distributions: Gumbel (EV-I, ξ = 0), Fréchet (EV-II, ξ > 0), and Weibull (EV-III, ξ < 0). The density function g(z) and cumulative distribution function G(z) of the GEV distribution can be written as [23], [8]:…”

Section: The Gev Distributionmentioning

confidence: 99%

“…Besides the general algorithms of MCMC, namely the Gibbs [19], the Metropolis [20,21] and the Metropolis-Hastings [22], for the purpose of estimating the parameters in GEV distributions, Hamiltonian Monte Carlo (HMC) algorithms are more efficient. In addition, the HMC parameter estimation is relatively robust and much faster [23]. In extreme value analysis with GEV models, avoidance of random-walk behavior is one of the major advantages of HMC [24].…”

Section: Introductionmentioning

confidence: 99%

Bayesian Modeling of Flood Frequency Analysis in Bangladesh Using Hamiltonian Monte Carlo Techniques

Alam

Farnham

Emura

2018

Water

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In recent years, several Bayesian Markov chain Monte Carlo (MCMC) methods have been proposed in extreme value analysis (EVA) for assessing the flood risk in a certain location. In this study, the Hamiltonian Monte Carlo (HMC) method was employed to obtain the approximations to the posterior marginal distribution of the Generalized Extreme Value (GEV) model by using annual maximum discharges in two major river basins in Bangladesh. As a comparison, the well-known Metropolis-Hasting (MH) algorithm was also applied, but did not converge well and yielded skewness values opposite those of HMC and the statistical characteristic of the data sets. The discharge records of the Ganges and Brahmaputra rivers in Bangladesh for the past 42 years were analyzed. To estimate flood risk, a return level with 95% confidence intervals (CI) has also been calculated. Results show that the shape parameter of each station was greater than zero, which describes the heavy-tailed Fréchet cases of the GEV distributions. One station, Bahadurabad in the Brahmaputra river basin, estimated 141,387 m 3 ·s −1 with a 95% CI range of [112,636, 170,138] for the 100-year return level, and the 1000-year return level was 195,018 m 3 ·s −1 with a 95% CI of [122,493, 267,544]. The other station, Hardinge Bridge at the Ganges basin, estimated 124,134 m 3 ·s −1 with a 95% CI of [108,726, 139,543] for the 100-year return level, and the 1000-year return level was 170,537 m 3 ·s −1 with a 95% CI of [133,784, 207,289]. As Bangladesh is a flood-prone country, the approach of Bayesian with HMC in EVA can help policy-makers to plan initiatives that could result in preventing damage to both lives and assets.

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Bayesian inference for generalized extreme value distributions via Hamiltonian Monte Carlo

Cited by 10 publications

References 7 publications

A Bayesian Non-linear State Space Copula Model to Predict Air Pollution in Beijing

A Bayesian Non-linear State Space Copula Model to Predict Air Pollution in Beijing

Comparison of Bayesian Nonparametric Density Estimation Methods

Bayesian Modeling of Flood Frequency Analysis in Bangladesh Using Hamiltonian Monte Carlo Techniques

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