Cód. Trabalho: 2506 | Palavras-chave: counting time series, linear model in presence of change-points, non-homogeneous Poisson process, power law process, Bayesian approach, measles, education
Título: Bayesian estimation for change-points in counting time series: A unified approach using linear regression model and non-homogeneous Poisson processes
Autor(es): Ricardo Puziol de Oliveira, Charles Chen, Jorge Alberto Achcar
Resumo: In this study it is introduced a Bayesian approach to analyze counting time series data in presence of one or more change-points. This situation is very common in many areas of application, especially considering epidemiology counting time series. When the observed counting n(t) data are different of zero for each time t, t = 1,2,...,N (number of observed times), it is proposed a statistical model assuming normal distributions for the logarithm of the transformed data, that is, Y(t) = log(n(t)) in presence of one or more change-points. In situations in presence of counting data equals to zero at different times (that is, presence of zero counting) the statistical model based on the logarithm transformation for the counting data is not suitable in the data analysis. For this case, it is proposed the use of non-homogeneous Poisson processes (NHPP) assuming a PLP (power law process) modeling for its intensity function in presence of change-points. As first application, a dataset related to the time series for monthly counts of visitors to New Zealand from August 1989 to May 2012 where the visit purpose is education; and as second application, it is considered a dataset related to the incidences (notification cases) of measles disease in Brazil from January, 2012 to August, 2018 (follow-up of 80 months). Since measles is an epidemic almost eradicated but that in some times there is the notification of new cases, it is common to have time series with zero counting values which is a motivation for the use of NHPP.