Under-reported data analysis with INAR-hidden Markov chains

Abstract

In this work, we deal with correlated under-reported data through INAR(1)-hidden Markov chain models. These models are very flexible and can be identified through its autocorrelation function, which has a very simple form. A naïve method of parameter estimation is proposed, jointly with the maximum likelihood method based on a revised version of the forward algorithm. The most-probable unobserved time series is reconstructed by means of the Viterbi algorithm. Several examples of application in the field of public health are discussed illustrating the utility of the models. Copyright © 2016 John Wiley & Sons, Ltd.

Comment on “Under‐reported data analysis with INAR‐hidden Markov chains”

“…Each of them features a different combination of reporting probability q Y and decay factor γ Y for the autoregressive parameters. In Fernández‐Fontelo et al, identifiability is ensured by the assumption that the latent process is indeed INAR(1), ie γ X = 0. Unless there is substantial prior knowledge on the parameter γ X , however, the reporting probability q X cannot be estimated.…”

“…For illustration of the argument, we revisit the analysis of reported human papillomavirus (HPV) cases in Girona, Spain (2010‐2014) from Fernández‐Fontelo et al The authors assume the latent model with reporting process , but as with a confidence interval from 0.78 to 1.07, they suggest that the simpler version could be used as well. For simplicity, we will thus pretend that their parameter estimates come from such a model (even though it then cannot accommodate overdispersion; this could be addressed via a different immigration distribution).…”

“…For simplicity, we will thus pretend that their parameter estimates come from such a model (even though it then cannot accommodate overdispersion; this could be addressed via a different immigration distribution). The estimated data generating process (equation (22)‐(23) in the aforementioned work) is then …”

“…We read with great interest the article by Fernández‐Fontelo et al who discuss underreporting in count time series models, a problem which is encountered in many real‐world settings. In case studies, reporting probabilities for several diseases are estimated under the assumption of a hidden first‐order integer‐valued autoregressive (INAR(1)) process.…”

“…The thinning operations are assumed to be independent of each other and of { W t }; further, the thinning operations at each t and W t are assumed to be independent of X t − 1 , X t − 2 ,…. Fernández‐Fontelo et al introduce an underreported version of this model. However, they assume that counts are only subject to underreporting with a certain probability ω ; otherwise, reporting is assumed to be complete.…”