A Bayesian semi-parametric mixture model for bivariate extreme value analysis with application to precipitation forecasting

Tian, Y.; Reich, Brian J.

doi:10.5705/ss.202018.0420

STAT SINICA

2021

DOI: 10.5705/ss.202018.0420

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A Bayesian semi-parametric mixture model for bivariate extreme value analysis with application to precipitation forecasting

Y. Tian¹,

Brian J. Reich²

Abstract: We propose a novel mixture Generalized Pareto (MIXGP) model to calibrate extreme precipitation forecasts. This model is able to describe the marginal distribution of observed precipitation and capture the dependence between climate forecasts and the observed precipitation under suitable conditions.In addition, the full range distribution of precipitation conditional on grid forecast ensembles can also be estimated. Unlike the classical Generalized Pareto distribution that can only model points over a hard thre… Show more

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2023

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Cited by 2 publications

References 37 publications

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A Restricted Four-Parameter IRT Model: The Dyad Four-Parameter Normal Ogive (Dyad-4PNO) Model

Kern

Culpepper

2020

Psychometrika

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Recently, there has been a renewed interest in the four-parameter item response theory model as a way to capture guessing and slipping behaviors in responses. Research has shown, however, that the nested three-parameter model suffers from issues of unidentifiability (San Martín et al. in Psychometrika 80:450–467, 2015), which places concern on the identifiability of the four-parameter model. Borrowing from recent advances in the identification of cognitive diagnostic models, in particular, the DINA model (Gu and Xu in Stat Sin https://doi.org/10.5705/ss.202018.0420, 2019), a new model is proposed with restrictions inspired by this new literature to help with the identification issue. Specifically, we show conditions under which the four-parameter model is strictly and generically identified. These conditions inform the presentation of a new exploratory model, which we call the dyad four-parameter normal ogive (Dyad-4PNO) model. This model is developed by placing a hierarchical structure on the DINA model and imposing equality constraints on a priori unknown dyads of items. We present a Bayesian formulation of this model, and show that model parameters can be accurately recovered. Finally, we apply the model to a real dataset.

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A Restricted Four-Parameter IRT Model: The Dyad Four-Parameter Normal Ogive (Dyad-4PNO) Model

Kern

Culpepper

2020

Psychometrika

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Extending an Identified Four-Parameter IRT Model: The Confirmatory Set-4PNO Model

Kern

2023

Journal of Educational and Behavioral Statistics

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Given the frequent presence of slipping and guessing in item responses, models for the inclusion of their effects are highly important. Unfortunately, the most common model for their inclusion, the four-parameter item response theory model, potentially has severe deficiencies related to its possible unidentifiability. With this issue in mind, the dyad-four-parameter normal ogive (4PNO) model was developed. This model allows for slipping and guessing effects by including binary augmented variables—each indicated by two items whose probabilities are determined by slipping and guessing parameters—which are subsequently related to a continuous latent trait through a two-parameter model. Furthermore, the dyad-4PNO assumes uncertainty as to which items are paired on each augmented variable. In this way, the model is inherently exploratory. In the current article, the new model, called the set-4PNO model, is an extension of the dyad-4PNO in two ways. First, the new model allows for more than two items per augmented variable. Second, these item sets are assumed to be fixed, that is, the model is confirmatory. This article discusses this extension and introduces a Gibbs sampling algorithm to estimate the model. A Monte Carlo simulation study shows the efficacy of the algorithm at estimating the model parameters. A real data example shows that this extension may be viable in practice, with the data fitting a more general set-4PNO model (i.e., more than two items per augmented variable) better than the dyad-4PNO, 2PNO, 3PNO, and 4PNO models.

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A Bayesian semi-parametric mixture model for bivariate extreme value analysis with application to precipitation forecasting

Cited by 2 publications

References 37 publications

A Restricted Four-Parameter IRT Model: The Dyad Four-Parameter Normal Ogive (Dyad-4PNO) Model

A Restricted Four-Parameter IRT Model: The Dyad Four-Parameter Normal Ogive (Dyad-4PNO) Model

Extending an Identified Four-Parameter IRT Model: The Confirmatory Set-4PNO Model

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