Correcting delayed reporting of COVID-19 using the generalized-Dirichlet-multinomial method.

The COVID-19 pandemic has highlighted delayed reporting as a significant impediment to effective disease surveillance and decision-making. In the absence of timely data, statistical models which account for delays can be adopted to nowcast and forecast cases or deaths. We discuss the four key sources of systematic and random variability in available data for COVID-19 and other diseases, and critically evaluate current state-of-the-art methods with respect to appropriately separating and capturing this variability. We propose a general hierarchical approach to correcting delayed reporting of COVID-19 and apply this to daily English hospital deaths, resulting in a flexible prediction tool which could be used to better inform pandemic decision-making. We compare this approach to competing models with respect to theoretical flexibility and quantitative metrics from a 15-month rolling prediction experiment imitating a realistic operational scenario. Based on consistent leads in predictive accuracy, bias, and precision, we argue that this approach is an attractive option for correcting delayed reporting of COVID-19 and future epidemics.

Multivariate hierarchical frameworks for modeling delayed reporting in count data.

In many fields and applications, count data can be subject to delayed reporting. This is where the total count, such as the number of disease cases contracted in a given week, may not be immediately available, instead arriving in parts over time. For short-term decision making, the statistical challenge lies in predicting the total count based on any observed partial counts, along with a robust quantification of uncertainty. We discuss previous approaches to modeling delayed reporting and present a multivariate hierarchical framework where the count generating process and delay mechanism are modeled simultaneously in a flexible way. This framework can also be easily adapted to allow for the presence of underreporting in the final observed count. To illustrate our approach and to compare it with existing frameworks, we present a case study of reported dengue fever cases in Rio de Janeiro. Based on both within-sample and out-of-sample posterior predictive model checking and arguments of interpretability, adaptability, and computational efficiency, we discuss the relative merits of different approaches.

On species sampling sequences induced by residual allocation models.

We discuss fully Bayesian inference in a class of species sampling models that are induced by residual allocation (sometimes called stick-breaking) priors on almost surely discrete random measures. This class provides a generalization of the well-known Ewens sampling formula that allows for additional flexibility while retaining computational tractability. In particular, the procedure is used to derive the exchangeable predictive probability functions associated with the generalized Dirichlet process of Hjort (2000) and the probit stick-breaking prior of Chung and Dunson (2009) and Rodriguez and Dunson (2011). The procedure is illustrated with applications to genetics and nonparametric mixture modeling.

Regression Models For Multivariate Count Data.

Data with multivariate count responses frequently occur in modern applications. The commonly used multinomial-logit model is limiting due to its restrictive mean-variance structure. For instance, analyzing count data from the recent RNA-seq technology by the multinomial-logit model leads to serious errors in hypothesis testing. The ubiquity of over-dispersion and complicated correlation structures among multivariate counts calls for more flexible regression models. In this article, we study some generalized linear models that incorporate various correlation structures among the counts. Current literature lacks a treatment of these models, partly due to the fact that they do not belong to the natural exponential family. We study the estimation, testing, and variable selection for these models in a unifying framework. The regression models are compared on both synthetic and real RNA-seq data.