Paul Yip

Estimating the initial relative infection rate for a stochastic epidemic model.

Consider the problem of making inference about the initial relative infection rate of a stochastic epidemic model. A relatively complete analysis of infectious disease data is possible when it is assumed that the latent and infectious periods are non-random. Here two related martingale-based techniques are used to derive estimates and associated standard errors for the initial relative infection rate. The first technique requires complete information on the epidemic, the second only the total number of people who were infected and the population size. Explicit expressions for the estimates are obtained. The estimates of the parameter and its associated standard error are easily computed and compare well with results of other methods in an application to smallpox data. Asymptotic efficiency differences between the two martingale techniques are considered.

Estimating population size from a capture-recapture experiment with known removals

Abstract We use martingale theory and a method of moments technique to derive a class of estimators for the size of a closed population in a capture—recapture experiment with known removals in either discrete or continuous time. The capture probabilities may vary on each successive capture occasion. Some of the estimators and their associated standard errors have explicit expressions. Optimal estimators in the sense of giving tightest asymptotic confidence intervals for the population size in either cases are also found. Asymptotic results are readily obtained by an application of a martingale central limit theorem. In contrast to previously proposed estimation procedures the present approach requires only a modest amount of calculation and is based on less restrictive assumptions. An example and a small simulation study showed that the proposed estimators perform better than the existing ones.

Inference on a fatal disease

We consider the problem of inference on the initial relative infection rate of a fatal disease. The model used was considered by Saunders, Gani, Gleissner, and Watson. Here two related mertingale-based techniques are used to derive estimates, and associated standard errors, for the initial relative infection rate. The first technique requires complete information on the epidemic, the second only the total number of people who were infected at a time point and the population size. Explicit expressions for the estimates and the associated standard errors are obtained. They involve only simple calculation.

An inference procedure for conflict models

An inference procedure is proposed for a parameter related to the relative mortality rates of two forces in conflict. By constructing martingales and applying a martingale central limit theorem, explicit expressions are obtained for the estimates and associated standard errors which involve only simple computation. Only the information on the state of the two forces at the end of the conflict is required. Asymptotic results are given. A kernel type estimator for the mortality rates of the two forces is also given.

Nonparametric estimation of partially observed stochastic multicompartmental systems

Methods of nonparametric inference are proposed for an irreversible k-compartmental system. It is assumed that the time of transitions between the transient states is unobservable. Explicit expression for the estimator of the transition rate is provided. Asymptotic result is given. A comparsion is made with the maximum likelihood estimator which relies on observing the process continuously.

A note on estimation of the infection rate

Choi and Severo (1988) proposed an estimator as an approximation to the maximum likelihood estimator of the infection rate of the simple epidemic model. It is shown that this estimator can be regarded as an approximation to the martingale estimator which is optimal in the sense of Godambe (1985). This idea is readily extended to an epidemic model allowing removal to produce an estimator of the infection rate.

Estimating selective advantage and related parameters of a model for two populations competing in a bounded environment

We use martingale theory and a method of moments to derive a class of estimators for the selective advantage of two types of individuals competing in a bounded environment in continuous time. Explicit expressions are given for these estimators which involve only simple computations. Also, an optimal estimator in the sense of giving tightest asymptotic bounds is obtained. Asymptotic results are given and simulation was performed to assess the quality of the proposed estimators. Estimates for the cumulative mortality rate and mortality rate at a specific point in time are also given.