A major open question, affecting the policy makers decisions, is the estimation of the true size of COVID-19 infections. Most of them are undetected, because of a large number of asymptomatic cases. We provide an efficient, easy to compute and robust lower bound estimator for the number of undetected cases. A "modified" version of the Chao estimator is proposed, based on the cumulative time-series distribution of cases and deaths.

The analysis of small area disease incidence has now developed to a degree where many methods have been proposed. However, there are few studies of the relative merits of the methods available. While many Bayesian models have been examined with respect to prior sensitivity, it is clear that wider comparisons of methods are largely missing from the literature. In this paper we present some preliminary results concerning the goodness-of-"t of a variety of disease mapping methods to simulated data for disease incidence derived from a range of models. These simulated models cover simple risk gradients to more complex true risk structures, including spatial correlation. The main general results presented here show that the gamma-Poisson exchangeable model and the Besag, York and Mollie (BYM) model are most robust across a range of diverse models. Mixture models are less robust. Non-parametric smoothing methods perform badly in general. Linear Bayes methods display behaviour similar to that of the gamma-Poisson methods.

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The daily average natural rainfall amounts in the five regions of Thailand can be estimated using the confidence intervals for the common mean of several delta-lognormal distributions based on the fiducial generalized confidence interval (FGCI), large sample (LS), method of variance estimates recovery (MOVER), parametric bootstrap (PB), and highest posterior density intervals based on Jeffreys' rule (HPD-JR) and normal-gammabeta (HPD-NGB) priors. Monte Carlo simulation was conducted to assess the performance in terms of the coverage probability and average length of the proposed methods. The numerical results indicate that MOVER and PB provided better performances than the other methods in a variety of situations, even when the sample case was large. The efficacies of the proposed methods were illustrated by applying them to real rainfall datasets from the five regions of Thailand.