TY - JOUR

T1 - Bayesian analysis of extreme values by mixture modeling

AU - Consonni, Guido

AU - 27494,

AU - statistiche, Area 13 - Scienze economiche e

AU - Bottolo, Leonardo

AU - FACOLTA', DI ECONOMIA

AU - statistiche, MILANO - Dipartimento di Scienze

AU - FACOLTA', DI ECONOMIA

AU - Dellaportas, Petros

AU - FACOLTA', DI ECONOMIA

AU - Lijoi, Antonio

PY - 2003

Y1 - 2003

N2 - Modeling of extreme values in the presence of heterogeneity is still a relatively unexplored area. We consider losses pertaining to several related categories. For each category, we view exceedances over a given threshold as generated by a Poisson process whose intensity is regulated by a specific location, shape and scale parameter. Using a Bayesian approach, we develop a hierarchical mixture prior, with an unknown number of components, for each of the above parameters. Computations are performed using Reversible Jump MCMC. Our model accounts for possible grouping effects and takes advantage of the similarity across categories, both for estimation and prediction purposes. Some guidance on the specification of the prior distribution is provided, together with an assessment of inferential robustness. The method is illustrated throughout using a data set on large claims against a well-known insurance company over a 15-year period.

AB - Modeling of extreme values in the presence of heterogeneity is still a relatively unexplored area. We consider losses pertaining to several related categories. For each category, we view exceedances over a given threshold as generated by a Poisson process whose intensity is regulated by a specific location, shape and scale parameter. Using a Bayesian approach, we develop a hierarchical mixture prior, with an unknown number of components, for each of the above parameters. Computations are performed using Reversible Jump MCMC. Our model accounts for possible grouping effects and takes advantage of the similarity across categories, both for estimation and prediction purposes. Some guidance on the specification of the prior distribution is provided, together with an assessment of inferential robustness. The method is illustrated throughout using a data set on large claims against a well-known insurance company over a 15-year period.

KW - Extreme value

KW - Mixture model

KW - Extreme value

KW - Mixture model

UR - http://hdl.handle.net/10807/12348

M3 - Article

VL - 6

SP - 25

EP - 47

JO - Extremes

JF - Extremes

SN - 1386-1999

ER -