Bayesian Outlier Detection in GPAR(1)

Campylobacter infections in Québec, Canada, from jan/1990 to oct/2000 and the posterior probability of outliers for each time insntant

Abstract

In this work implement the Bayesian Additive Integer Outlier Detection (BAIOD) method proposed by Silva, Pereira and McCabe [Journal of Time Series Analysis, 40(5), 2019] to the Generalized Poisson AR(1) model. Simple MCMC methods are applyed for inference instead of adaptative as in the original work. The method is applyed to both simulated and real data. Despite relatively complex, the model results are satisfactory and, once it is based on posterior probabilities, more easy to take conclusions.

Instructions

• baiod_gpar_mcmc.R: main file with the model and MCMC procudure. Some resulting plots are stored in the folder /plot, while others are just ploted in the RStudio.
• data_generation.R: file used to generate the simulated timeseries. CSV files and .RData objects are stored in the folder /data
• almeida-report: report (in portuguese).

References

• Silva, M. E., Pereira, I., and McCabe, B. (2019). Bayesian outlier detection in non-gaussian autoregressive time series. Journal of Time Series Analysis, 40(5):631–648