Robust Bayesian analysis of loss reserving data using scale mixtures distributions

Choy, S. T. Boris; Chan, Jennifer; Makov, Udi

doi:10.1080/02664763.2015.1063115

Cited by 8 publications

(5 citation statements)

References 37 publications

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“…In these cases, a more flexible modeling framework, such as a mixture modelling framework, is to be preferred. The flexibility of finite mixtures in accommodating various shapes of insurance data is now widely recognized [9,17,18,54]. Among them, mixtures of gamma distributions were successfully considered in Dey et al…”

Section: Bodily Injury Claimsmentioning

confidence: 99%

“…Maximum a posteriori classification of incomes, as good or bad, is represented by ticks of different colors (gray for good incomes and black for bad incomes) on the x-axis. To be more precise, according to the decision rule in (17), incomes are classified as good if they lie in the interval delimited by 0.351 and 82.706 millions of lire; refer to formula (19).…”

Section: Income Of Italian Households In 1986mentioning

confidence: 99%

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A new look at the inverse Gaussian distribution with applications to insurance and economic data

Punzo

2018

Journal of Applied Statistics

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Insurance and economic data are often positive, and we need to take into account this peculiarity in choosing a statistical model for their distribution. An example is the inverse Gaussian (IG), which is one of the most famous and considered distributions with positive support. With the aim of increasing the use of the IG distribution on insurance and economic data, we propose a convenient mode-based parameterization yielding the reparametrized IG (rIG) distribution; it allows/simplifies the use of the IG distribution in various branches of statistics, and we give some examples. In nonparametric statistics, we define a smoother based on rIG kernels. By construction, the estimator is well-defined and does not allocate probability mass to unrealistic negative values. We adopt likelihood cross-validation to select the smoothing parameter. In robust statistics, we propose the contaminated IG distribution, a heavy-tailed generalization of the rIG distribution to accommodate mild outliers. Finally, for modelbased clustering and semiparametric density estimation, we present finite mixtures of rIG distributions. We use the EM algorithm to obtain maximum likelihood estimates of the parameters of the mixture and contaminated models. We use insurance data about bodily injury claims, and economic data about incomes of Italian households, to illustrate the models.

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Section: Bodily Injury Claimsmentioning

confidence: 99%

Section: Income Of Italian Households In 1986mentioning

confidence: 99%

A new look at the inverse Gaussian distribution with applications to insurance and economic data

Punzo

2018

Journal of Applied Statistics

View full text Add to dashboard Cite

show abstract

“…In these cases, a more flexible modelling framework, such as a mixture modelling framework, is to be preferred. The flexibility of finite mixtures in accommodating various shapes of insurance data is now widely recognized (Choy and Chan, 2003, Bernardi et al, 2012, Choy et al, 2016. Among them, mixtures of gamma distributions were successfully considered in Dey et al (1995), Wiper et al (2001), andVenturini et al (2008).…”

Section: Bodily Injury Claimsmentioning

confidence: 99%

A new look at the inverse Gaussian distribution

Punzo

2017

Preprint

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The inverse Gaussian (IG) is one of the most famous and considered distributions with positive support. We propose a convenient modebased parameterization yielding the reparametrized IG (rIG) distribution; it allows/simplifies the use of the IG distribution in various statistical fields, and we give some examples in nonparametric statistics, robust statistics, and model-based clustering. In nonparametric statistics, we define a smoother based on rIG kernels. By construction, the estimator is well-defined and free of boundary bias. We adopt likelihood cross-validation to select the smoothing parameter. In robust statistics, we propose the contaminated IG distribution, a heavy-tailed generalization of the rIG distribution to accommodate mild outliers; they can be automatically detected by the model via maximum a posteriori probabilities. To obtain maximum likelihood estimates of the parameters, we illustrate an expectation-maximization (EM) algorithm. Finally, for model-based clustering and semiparametric density estimation, we present finite mixtures of rIG distributions. We use the EM algorithm to obtain ML estimates of the parameters of the mixture model. Applications to economic and insurance data are finally illustrated to exemplify and enhance the use of the proposed models.

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“…Another example is Yang & Yuan (), who develop a method of drawing iid samples from an approximation to the posterior distribution. Salazar et al () and Ferreira & Salazar () develop default prior distributions for the specific case in which the errors are from the exponential power distribution (which corresponds to scaled positive stable mixing density), and Choy et al () perform a Bayesian analysis of insurance data.…”

Section: Introductionmentioning

confidence: 99%

Convergence Analysis of MCMC Algorithms for Bayesian Multivariate Linear Regression with Non‐Gaussian Errors

Hobert

Jung

Khare

et al. 2018

Scandinavian J Statistics

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When Gaussian errors are inappropriate in a multivariate linear regression setting, it is often assumed that the errors are iid from a distribution that is a scale mixture of multivariate normals. Combining this robust regression model with a default prior on the unknown parameters results in a highly intractable posterior density. Fortunately, there is a simple data augmentation (DA) algorithm and a corresponding Haar PX-DA algorithm that can be used to explore this posterior. This paper provides conditions (on the mixing density) for geometric ergodicity of the Markov chains underlying these Markov chain Monte Carlo algorithms. Letting d denote the dimension of the response, the main result shows that the DA and Haar PX-DA Markov chains are geometrically ergodic whenever the mixing density is generalized inverse Gaussian, log-normal, inverted Gamma (with shape parameter larger than d=2) or Fréchet (with shape parameter larger than d=2). The results also apply to certain subsets of the Gamma, F and Weibull families.We assume throughout the paper that .N1/ and .N 2/ hold. Under these two conditions, the Markov chain of interest is well-defined, and we can engage in a convergence rate analysis

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Robust Bayesian analysis of loss reserving data using scale mixtures distributions

Cited by 8 publications

References 37 publications

A new look at the inverse Gaussian distribution with applications to insurance and economic data

A new look at the inverse Gaussian distribution with applications to insurance and economic data

A new look at the inverse Gaussian distribution

Convergence Analysis of MCMC Algorithms for Bayesian Multivariate Linear Regression with Non‐Gaussian Errors

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