Approximate Bayesian estimation for multivariate count time series models.

*(English)*Zbl 1336.62098
Choudhary, Pankaj K. (ed.) et al., Ordered data analysis, modeling and health research methods. In honor of H. N. Nagaraja’s 60th birthday. Selected papers based on the presentations at the international conference, Austin, TX, USA, March 7–9, 2014. Cham: Springer (ISBN 978-3-319-25431-9/hbk; 978-3-319-25433-3/ebook). Springer Proceedings in Mathematics & Statistics 149, 155-167 (2015).

Summary: In many areas of application, there is increasing interest in modeling multivariate time series of counts on several subjects as a function of subject-specific and time-dependent covariates. We propose a level correlated model (LCM) to account for the association among the components of the response vector, as well as possible overdispersion. The flexible LCM framework allows us to combine different marginal count distributions and to build a hierarchical model for the vector time series of counts. We employ the Integrated Nested Laplace Approximation (INLA) for fast approximate Bayesian modeling using the R package INLA (r-inla.org). We illustrate it by modeling the monthly prescription counts by physicians of a focal drug from a multinational pharmaceutical firm along with monthly counts of other drugs with a sizable market share for the same therapeutic category.

For the entire collection see [Zbl 1337.92005].

For the entire collection see [Zbl 1337.92005].

##### MSC:

62F15 | Bayesian inference |

62M10 | Time series, auto-correlation, regression, etc. in statistics (GARCH) |

##### Keywords:

Bayesian framework; discrete-valued time series; INLA; marketing; multivariate Poisson; ZIP model
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\textit{V. Serhiyenko} et al., in: Ordered data analysis, modeling and health research methods. In honor of H. N. Nagaraja's 60th birthday. Selected papers based on the presentations at the international conference, Austin, TX, USA, March 7--9, 2014. Cham: Springer. 155--167 (2015; Zbl 1336.62098)

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