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Semiparametric Bayesian Count Data Models
Count data models have a large number of pratical applications.
However there can be several problems which prevent the use of
the standard Poisson regression. We may detect
individual unobserved heterogeneity, caused by missing covariates,
and/or excess of zero observations in our data. Both distributional issues
results in deviations of the response distribution from the classical Poisson
assumption. We may in addition want to extend our predictor
to model temporal or spatial correlation and possibly nonlinear effects
of continuous covariates or time scales available in the data.
Here we study and develop semiparametric count data
models which can solve these problems. We have extended the Poisson
distribution to account for overdispersion and/or zero inflation.
Additionally we have incorporated corresponding components in structured additive
form into the predictor. The models are fully Bayesian and inference
is carried out by computationally efficient MCMC techniques. In
simulation studies, we investigate how well the different components
can be identified with the data at hand. Finally, the approaches are
applied to two data sets: to a patent data set and to a large data set
of claim frequencies from car insurance.
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By Ludwig-Maximilians-Universität München
5
11 ratings
Count data models have a large number of pratical applications.
However there can be several problems which prevent the use of
the standard Poisson regression. We may detect
individual unobserved heterogeneity, caused by missing covariates,
and/or excess of zero observations in our data. Both distributional issues
results in deviations of the response distribution from the classical Poisson
assumption. We may in addition want to extend our predictor
to model temporal or spatial correlation and possibly nonlinear effects
of continuous covariates or time scales available in the data.
Here we study and develop semiparametric count data
models which can solve these problems. We have extended the Poisson
distribution to account for overdispersion and/or zero inflation.
Additionally we have incorporated corresponding components in structured additive
form into the predictor. The models are fully Bayesian and inference
is carried out by computationally efficient MCMC techniques. In
simulation studies, we investigate how well the different components
can be identified with the data at hand. Finally, the approaches are
applied to two data sets: to a patent data set and to a large data set
of claim frequencies from car insurance.
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