Bayesian estimation of intensity–duration–frequency curves and of the return period associated to a given rainfall event

Huard, David; Mailhot, Alain; Duchesne, Sophie

doi:10.1007/s00477-009-0323-1

Cited by 54 publications

(32 citation statements)

References 26 publications

(21 reference statements)

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“…Martins and Stedinger (2000) used a Beta(6, 9) pdf. This choice of prior restricts shape parameter to a plausible range (−0.5 ≤ ξ ≤ 0.5) consistent with rainfall and flood flows observed worldwide (Huard et al, 2010). The actual variance of the generalized extreme value (GEV) random variable is infinite when ξ > 0.5; in addition, the MLE of parameters is non-regular (asymptotic optimality is no more guaranteed) when ξ < −0.5.…”

Section: Introductionmentioning

confidence: 81%

A data-adaptive maximum penalized likelihood estimation for the generalized extreme value distribution

Lee

Shin

Park

2017

CSAM

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Maximum likelihood estimation (MLE) of the generalized extreme value distribution (GEVD) is known to sometimes over-estimate the positive value of the shape parameter for the small sample size. The maximum penalized likelihood estimation (MPLE) with Beta penalty function was proposed by some researchers to overcome this problem. But the determination of the hyperparameters (HP) in Beta penalty function is still an issue. This paper presents some data adaptive methods to select the HP of Beta penalty function in the MPLE framework. The idea is to let the data tell us what HP to use. For given data, the optimal HP is obtained from the minimum distance between the MLE and MPLE. A bootstrap-based method is also proposed. These methods are compared with existing approaches. The performance evaluation experiments for GEVD by Monte Carlo simulation show that the proposed methods work well for bias and mean squared error. The methods are applied to Blackstone river data and Korean heavy rainfall data to show better performance over MLE, the method of L-moments estimator, and existing MPLEs.

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Section: Introductionmentioning

confidence: 81%

A data-adaptive maximum penalized likelihood estimation for the generalized extreme value distribution

Lee

Shin

Park

2017

CSAM

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“…If large amounts of data are available, noninformative prior distribution can be useful. Many studies used the noninformative prior distribution [40][41][42]. As an informative prior distribution uses the analyst's beliefs regarding unknown parameters, it is contrary to the mathematical definition of the noninformative prior distribution.…”

Section: Elicitation Of Prior Distributionmentioning

confidence: 99%

Applicability of Zero-Inflated Models to Fit the Torrential Rainfall Count Data with Extra Zeros in South Korea

Lee¹,

Kim²

2017

Water

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Several natural disasters occur because of torrential rainfalls. The change in global climate most likely increases the occurrences of such downpours. Hence, it is necessary to investigate the characteristics of the torrential rainfall events in order to introduce effective measures for mitigating disasters such as urban floods and landslides. However, one of the major problems is evaluating the number of torrential rainfall events from a statistical viewpoint. If the number of torrential rainfall occurrences during a month is considered as count data, their frequency distribution could be identified using a probability distribution. Generally, the number of torrential rainfall occurrences has been analyzed using the Poisson distribution (POI) or the Generalized Poisson Distribution (GPD). However, it was reported that POI and GPD often overestimated or underestimated the observed count data when additional or fewer zeros were included. Hence, in this study, a zero-inflated model concept was applied to solve this problem existing in the conventional models. Zero-Inflated Poisson (ZIP) model, Zero-Inflated Generalized Poisson (ZIGP) model, and the Bayesian ZIGP model have often been applied to fit the count data having additional or fewer zeros. However, the applications of these models in water resource management have been very limited despite their efficiency and accuracy. The five models, namely, POI, GPD, ZIP, ZIGP, and Bayesian ZIGP, were applied to the torrential rainfall data having additional zeros obtained from two rain gauges in South Korea, and their applicability was examined in this study. In particular, the informative prior distributions evaluated via the empirical Bayes method using ten rain gauges were developed in the Bayesian ZIGP model. Finally, it was suggested to avoid using the POI and GPD models to fit the frequency of torrential rainfall data. In addition, it was concluded that the Bayesian ZIGP model used in this study provided the most accurate results for the count data having additional zeros. Moreover, it was recommended that the ZIP model could be an alternative from a practical viewpoint, as the Bayesian approach used in this study was considerably complex.

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“…The POT approach ensures that other extreme rainfall events apart from the annual maxima are included [3,4], but suffers from the subjective selection of a suitable threshold [5,6] and potential correlation between extreme events [7]. In contrast, the AM approach is simple, hence remaining popular in extreme rainfall studies [7].…”

Section: Literature Reviewmentioning

confidence: 99%

“…The GoF has been by used to determine the best-fitting probability distribution in studies where multiple distributions are considered [27,28]. GoF test results should however be treated with caution, as the results depends not only on the PD choice, but also the fitting procedures [4].…”

Section: Literature Reviewmentioning

confidence: 99%

Application of Linear Moments and Uncertainty Analysis to Extreme Rainfall Events in Sabah

2017

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Abstract. Linear moments (LM) has been applied in extreme rainfall study for several countries, including China, United States of America, and Peninsular Malaysia. In this study, the LM procedures were applied to extreme rainfall data corresponding to locations provided in Malaysia Urban Stromwater Manual (MSMA) to derive new design rainfalls. Different record lengths were considered to assess the changes in design rainfall, and Monte Carlo simulations were carried out to compute confidence interval of the derived design rainfalls. Based on the Goodnessof-Fit (GoF) test results, the Generalized Extreme Value (GEV) probability distribution was chosen to derive the design rainfalls. The updated design rainfalls at all four locations showed significant reduction at design rainfalls of 50-year ARI and above. The difference of the design rainfalls from shorter record lengths with respect to the full record length and the confidence intervals do not necessarily reduce with a longer record. In hypothetical cases where 100-yr ARI rainfall was added, the increase in design rainfalls did not exceed the upper bound of the confidence intervals. The derived confidence intervals hence allow for better risk assessment, and should be considered in the design of critical structures, i.e. dams.

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Bayesian estimation of intensity–duration–frequency curves and of the return period associated to a given rainfall event

Cited by 54 publications

References 26 publications

A data-adaptive maximum penalized likelihood estimation for the generalized extreme value distribution

A data-adaptive maximum penalized likelihood estimation for the generalized extreme value distribution

Applicability of Zero-Inflated Models to Fit the Torrential Rainfall Count Data with Extra Zeros in South Korea

Application of Linear Moments and Uncertainty Analysis to Extreme Rainfall Events in Sabah

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