Browsing by Author "Bhattacharjee, Debanjan"

Now showing 1 - 3 of 3
  • No Thumbnail Available
    Item
    Fixed-length interval estimation of population sizes : sequential adaptive Monte Carlo mark–recapture–mark sampling.
    (2023) Silva, Ivair Ramos; Bhattacharjee, Debanjan; Zhuang, Yan
    Mark–recapture sampling schemes are conventional approaches for population size (N) estimation. In this paper, we mainly focus on providing fixed-length confidence interval estimation methodologies for N under a mark–recapture–mark sampling scheme, where, during the resampling phase, non-marked items are marked before they are released back in the population. Using a Monte Carlo method, the interval estimates for N are obtained through a purely sequential procedure with an adaptive stopping rule. Such an adaptive deci- sion criterion enables the user to “learn” with the subsequent marked and newly tagged items. The method is then compared with a recently developed accelerated sequential procedure in terms of coverage probability and expected number of captured items during the resampling stage. To illustrate, we explain how the proposed procedure could be applied to estimate the number of infected COVID-19 individuals in a near-closed population. In addition, we present a numeric application inspired on the problem of estimating the population size of endangered monkeys of the Atlantic forest in Brazil.
  • No Thumbnail Available
    Item
    Numerical versus asymptotic sequential interval estimation of population sizes.
    (2021) Silva, Ivair Ramos; Bhattacharjee, Debanjan; Mukhopadhyay, Nitis
    The challenge of estimating a population size (N) is usually faced with the well-established mark-recapture sampling scheme. The basic idea is to tag t items of the population and then observe the number of tagged items appearing in a subsequent random sample. The frequencies of tagged versus non-tagged items are informative to estimate N. For construction of fixed-width and fixed-accuracy confidence intervals for N, this paper compares a numerical non-replacement-sampling sequential design against an asymptotic replacement-sampling sequential design. While the former has shown to perform better in terms of expected sample size, the latter was found superior in terms of robustness with respect to the magnitude of N.
  • No Thumbnail Available
    Item
    Regression model for the reported infected during emerging pandemics under the stochastic SEIR.
    (2023) Silva, Ivair Ramos; Zhuang, Yan; Bhattacharjee, Debanjan; Almeida, Igor Ribeiro de
    The COVID-19 pandemic revealed the necessity of measuring the statistical relationship between the transmission rate of epidemic diseases and the social/behavioral, logistical, and economic variables of the affected region. This paper introduces a regression model to estimate the impact of such covariates on the infectious rate of epidemiological agents. Hidden logistical predictor components, such as weekly seasonality of reported data, can also be accessed with the proposed methodology. For this, we assume that the dynamics of officially reported data of emerging pandemics, related to infected groups, follows a stochastic SEIR model. The main advantage of our method is that it is based on a new three- step algorithm that combines the classical likelihood principle, the minimization of the mean squared error, and a tri-section algorithm to estimate, simultaneously, the coefficients of the covariates and the parameters of the compartmental model. Simulation studies are provided to certify the accuracy of the proposed inference methodology. The model is further applied to analyze the official statistical reports of COVID-19 data in the state of São Paulo, Brazil.