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Title:

Modelling count data with overdispersion and spatial effects

Description:

Bayesian inference, Count data, Overdispersion, Spatial regression models, Zero inflated models

Bayesian inference, Count data, Overdispersion, Spatial regression models, Zero inflated models Minimize

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article

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Title:

Does a Gibbs sampler approach to spatial Poisson regression models outperform a single site MH sampler?

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In this paper we present and evaluate a Gibbs sampler for a Poisson regression model including spatial e#ects. The approach is based on Fruhwirth-Schnatter and Wagner (2004b) who show that by data augmentation using the introduction of two sequences of latent variables a Poisson regression model can be transformed into an approximate normal line...

In this paper we present and evaluate a Gibbs sampler for a Poisson regression model including spatial e#ects. The approach is based on Fruhwirth-Schnatter and Wagner (2004b) who show that by data augmentation using the introduction of two sequences of latent variables a Poisson regression model can be transformed into an approximate normal linear model. We show how this methodology can be extended to spatial Poisson regression models and give details of the resulting Gibbs sampler. In particular, the influence of model parameterisation and di#erent update strategies on the mixing of the MCMC chains is discussed. Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2009-04-19

Source:

http://www-m4.ma.tum.de/Papers/Czado/gibbsaugmentationrevised.ps

http://www-m4.ma.tum.de/Papers/Czado/gibbsaugmentationrevised.ps Minimize

Document Type:

text

Language:

en

Subjects:

Key words ; block updates ; collapsing ; data augmentation ; Gibbs sampler ; model parameterisa

Key words ; block updates ; collapsing ; data augmentation ; Gibbs sampler ; model parameterisa Minimize

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Metadata may be used without restrictions as long as the oai identifier remains attached to it.

Metadata may be used without restrictions as long as the oai identifier remains attached to it. Minimize

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Title:

Does a Gibbs sampler approach to spatial Poisson regression models outperform a single site MH sampler?

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2012-04-17

Source:

http://www-m4.mathematik.tu-muenchen.de/m4/Papers/Czado/gschloessl-czado-gibbssampler.pdf

http://www-m4.mathematik.tu-muenchen.de/m4/Papers/Czado/gschloessl-czado-gibbssampler.pdf Minimize

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text

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en

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Metadata may be used without restrictions as long as the oai identifier remains attached to it.

Metadata may be used without restrictions as long as the oai identifier remains attached to it. Minimize

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Title:

Spatial modelling of claim frequency and claim size in non-life insurance

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2012-04-17

Source:

http://www-m4.mathematik.tu-muenchen.de/m4/Papers/Czado/gschloesslSAJ_final.pdf

http://www-m4.mathematik.tu-muenchen.de/m4/Papers/Czado/gschloesslSAJ_final.pdf Minimize

Document Type:

text

Language:

en

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Metadata may be used without restrictions as long as the oai identifier remains attached to it.

Metadata may be used without restrictions as long as the oai identifier remains attached to it. Minimize

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Title:

Modelling count data with overdispersion and spatial effects

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2012-04-17

Source:

http://www-m4.ma.tum.de/Papers/Czado/paper08shortrevisedplain.pdf

http://www-m4.ma.tum.de/Papers/Czado/paper08shortrevisedplain.pdf Minimize

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text

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en

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Title:

Modelling count data with overdispersion and spatial effects

Description:

In this paper we consider regression models for count data allowing for overdispersion in a Bayesian framework. We account for unobserved heterogeneity in the data in two ways. On the one hand, we consider more flexible models than a common Poisson model allowing for overdispersion in different ways. In particular, the negative binomial and the ...

In this paper we consider regression models for count data allowing for overdispersion in a Bayesian framework. We account for unobserved heterogeneity in the data in two ways. On the one hand, we consider more flexible models than a common Poisson model allowing for overdispersion in different ways. In particular, the negative binomial and the generalized Poisson distribution are addressed where overdispersion is modelled by an additional model parameter. Further, zero-inflated models in which overdispersion is assumed to be caused by an excessive number of zeros are discussed. On the other hand, extra spatial variability in the data is taken into account by adding spatial random effects to the models. This approach allows for an underlying spatial dependency structure which is modelled using a conditional autoregressive prior based on Pettitt et al. (2002). In an application the presented models are used to analyse the number of invasive meningococcal disease cases in Germany in the year 2004. Models are compared according to the deviance information criterion (DIC) suggested by Spiegelhalter et al. (2002) and using proper scoring rules, see for example Gneiting and Raftery (2004). We observe a rather high degree of overdispersion in the data which is captured best by the GP model when spatial effects are neglected. While the addition of spatial effects to the models allowing for overdispersion gives no or only little improvement, a spatial Poisson model is to be preferred over all other models according to the considered criteria. Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2012-04-17

Source:

http://www-m4.mathematik.tu-muenchen.de/m4/Papers/Czado/paper08shortrevisedplain.ps

http://www-m4.mathematik.tu-muenchen.de/m4/Papers/Czado/paper08shortrevisedplain.ps Minimize

Document Type:

text

Language:

en

DDC:

310 Collections of general statistics *(computed)*

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Title:

Does a Gibbs sampler approach to spatial Poisson regression models outperform a single site MH sampler?

Description:

In this paper we present and evaluate a Gibbs sampler for a Poisson regression model including spatial effects. The approach is based on Frühwirth-Schnatter and Wagner (2004b) who show that by data augmentation using the introduction of two sequences of latent variables a Poisson regression model can be transformed into an approximate normal lin...

In this paper we present and evaluate a Gibbs sampler for a Poisson regression model including spatial effects. The approach is based on Frühwirth-Schnatter and Wagner (2004b) who show that by data augmentation using the introduction of two sequences of latent variables a Poisson regression model can be transformed into an approximate normal linear model. We show how this methodology can be extended to spatial Poisson regression models and give details of the resulting Gibbs sampler. In particular, the influence of model parameterisation and different update strategies on the mixing of the MCMC chains is discussed. The developed Gibbs samplers are analysed in two simulation studies and applied to model the expected number of claims for policyholders of a German car insurance company. The mixing of the Gibbs samplers depends crucially on the model parameterisation and the update schemes. The best mixing is achieved when collapsed algorithms are used, reasonable low autocorrelations for the spatial effects are obtained in this case. For the regression effects however, autocorrelations are rather high, especially for data with very low heterogeneity. For comparison a single component Metropolis Hastings algorithms is applied which displays very good mixing for all components. Although the Metropolis Hastings sampler requires a higher computational effort, it outperforms the Gibbs samplers which would have to be run considerably longer in order to obtain the same precision of the parameters. Minimize

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2008-07-01

Source:

http://www-m4.ma.tum.de/Papers/Czado/gibbsaugmentationrevised.pdf

http://www-m4.ma.tum.de/Papers/Czado/gibbsaugmentationrevised.pdf Minimize

Document Type:

text

Language:

en

Subjects:

Key words ; block updates ; collapsing ; data augmentation ; Gibbs sampler ; model parameterisation

Key words ; block updates ; collapsing ; data augmentation ; Gibbs sampler ; model parameterisation Minimize

DDC:

310 Collections of general statistics *(computed)*

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Metadata may be used without restrictions as long as the oai identifier remains attached to it.

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Title:

Nonnested model comparison of GLM and GAM count regression models for life insurance data

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Pricing and product development of life insurance contracts require the determination of company specific risk factors and their resulting risk rates. The paper shows how to use generalized linear models (GLM) and generalized additive models (GAM) to quantify the effect of risk factors by allowing for non linear and interaction effects. Nonneste...

Pricing and product development of life insurance contracts require the determination of company specific risk factors and their resulting risk rates. The paper shows how to use generalized linear models (GLM) and generalized additive models (GAM) to quantify the effect of risk factors by allowing for non linear and interaction effects. Nonnested model comparison between GLM and GAM based specifications are facilitated using non-randomized probability integral transforms (see Czado, Gneiting, and Held (2009)) and proper scores (see Gneiting and Raftery (2007)) developed for count responses. These allow for the assessment of model fit and predictive capability of a model. For a life insurance portfolio it is shown that the computationally less demanding GLM specification performs similarly to a GAM specification. Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2010-03-31

Source:

http://www-m4.ma.tum.de/Papers/Czado/final_GS.pdf

http://www-m4.ma.tum.de/Papers/Czado/final_GS.pdf Minimize

Document Type:

text

Language:

en

Subjects:

Count regression ; GLM ; GAM ; prediction ; probability integral transform ; proper

Count regression ; GLM ; GAM ; prediction ; probability integral transform ; proper Minimize

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Title:

Calculation of LTC Premiums based on direct estimates of transition probabilities

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In this paper we model the life-history of LTC patients using a Markovian multi-state model in order to calculate premiums for a given LTC-plan. Instead of estimating the transition intensities in this model we use the approach suggested by Andersen et al. (2003) for a direct estimation of the transition probabilities. Based on the Aalen-Johanse...

In this paper we model the life-history of LTC patients using a Markovian multi-state model in order to calculate premiums for a given LTC-plan. Instead of estimating the transition intensities in this model we use the approach suggested by Andersen et al. (2003) for a direct estimation of the transition probabilities. Based on the Aalen-Johansen estimator, an almost unbiased estimator for the transition matrix of a Markovian multi-state model, we calculate so-called pseudo-values, known from Jackknife methods. Further, we assume that the relationship between these pseudo-values and the covariates of our data are given by a GLM with the logit as link-function. Since the GLMs do not allow for correlation between successive observations we use instead the ”Generalized Estimating Equations ” (GEEs) to estimate the parameters of our regression model. The approach is illustrated using a representative sample from a German LTC portfolio. Minimize

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2008-07-01

Source:

http://www-m4.mathematik.tu-muenchen.de/m4/Papers/Czado/paper393.pdf

http://www-m4.mathematik.tu-muenchen.de/m4/Papers/Czado/paper393.pdf Minimize

Document Type:

text

Language:

en

Subjects:

Markovian Multi-State Model ; Transition Probabilities ; Aalen-Johansen Estimator ; Pseudo-Values ; GLM ; GEE ; LTC ; Premium

Markovian Multi-State Model ; Transition Probabilities ; Aalen-Johansen Estimator ; Pseudo-Values ; GLM ; GEE ; LTC ; Premium Minimize

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310 Collections of general statistics *(computed)*

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Title:

Introducing and evaluating a Gibbs sampler for spatial Poisson regression models

Description:

In this paper we present a Gibbs sampler for a Poisson model including spatial effects. Frühwirth-Schnatter and Wagner (2004b) show that by data augmentation via the introduction of two sequences of latent variables a Poisson regression model can be transformed into a normal linear model. We show how this methodology can be extended to spatial P...

In this paper we present a Gibbs sampler for a Poisson model including spatial effects. Frühwirth-Schnatter and Wagner (2004b) show that by data augmentation via the introduction of two sequences of latent variables a Poisson regression model can be transformed into a normal linear model. We show how this methodology can be extended to spatial Poisson regression models and give details of the resulting Gibbs sampler. In particular, the influence of model parameterisation and different update strategies on the mixing of the MCMC chains are discussed. The developed Gibbs samplers are analysed in two simulation studies and applied to model the expected number of claims for policyholders of a German car insurance data set. In general, both large and small simulated spatial effects are estimated accurately by the Gibbs samplers and reasonable low autocorrelations are obtained when the data variability is rather large. However, for data with very low heterogeneity, the autocorrelations resulting from the Gibbs samplers are very high, withdrawing the computational advantage over a Metropolis Hastings independence sampler which exhibits very low autocorrelations in all settings. Minimize

Publisher:

Techn. Univ.; Sonderforschungsbereich 386, Statistische Analyse Diskreter Strukturen München

Year of Publication:

2005

Document Type:

doc-type:workingPaper

Language:

eng

Subjects:

ddc:310 ; spatial Poisson count data ; Gibbs sampler ; data augmentation ; model parameterisation ; block updates ; collapsing

ddc:310 ; spatial Poisson count data ; Gibbs sampler ; data augmentation ; model parameterisation ; block updates ; collapsing Minimize

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http://www.econstor.eu/dspace/Nutzungsbedingungen

http://www.econstor.eu/dspace/Nutzungsbedingungen Minimize

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Discussion paper // Sonderforschungsbereich 386 der Ludwig-Maximilians-Universität München 434

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