2 research outputs found
A Bayesian Joinpoint regression model with an unknown number of break-points
Joinpoint regression is used to determine the number of segments needed to
adequately explain the relationship between two variables. This methodology can
be widely applied to real problems, but we focus on epidemiological data, the
main goal being to uncover changes in the mortality time trend of a specific
disease under study. Traditionally, Joinpoint regression problems have paid
little or no attention to the quantification of uncertainty in the estimation
of the number of change-points. In this context, we found a satisfactory way to
handle the problem in the Bayesian methodology. Nevertheless, this novel
approach involves significant difficulties (both theoretical and practical)
since it implicitly entails a model selection (or testing) problem. In this
study we face these challenges through (i) a novel reparameterization of the
model, (ii) a conscientious definition of the prior distributions used and
(iii) an encompassing approach which allows the use of MCMC simulation-based
techniques to derive the results. The resulting methodology is flexible enough
to make it possible to consider mortality counts (for epidemiological
applications) as Poisson variables. The methodology is applied to the study of
annual breast cancer mortality during the period 1980--2007 in Castell\'{o}n, a
province in Spain.Comment: Published in at http://dx.doi.org/10.1214/11-AOAS471 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Efficient sampling schemes for Bayesian MARS models with many predictors
10.1007/s11222-005-6201-xStatistics and Computing15293-10