The statistical objective in survey research and in a number of other applications is generally to estimate the parameters of a finite population rather than to estimate the parameters of a statistical model. As an example, the finite population for a survey conducted to estimate the unemployment rate might be all adults aged 18 or older living in a country at a given date. If valid estimates o...

We show that the model-calibration estimator for the finite population mean, which was proposed by Wu & Sitter (2001) through an intuitive argument, is optimal among a class of calibration estimators. We also present optimal calibration estimators for the finite population distribution function, the population variance, the variance of a linear estimator and other quadratic finite population fu...

We investigate the evolutionary dynamics of a finite population of sequences adapting to NK fitness landscapes. We find that, unlike in the case of an infinite population, the average fitness in a finite population is maximized at a small but finite, rather than vanishing, mutation rate. The highest local maxima in the landscape are visited for even larger mutation rates, close to a transition ...

We consider the initial invasion of an infectious disease in a finite, homogeneous population. Methodology for evaluating the basic reproduction number, R(0), and the probability mass function of secondary infections is presented. The impact of finite population size, and infectious period distribution (between exponential, two-phase gamma, and constant), is assessed. Implications for infectiou...

We present an efficient finite difference method for the computation of parameter sensitivities that is applicable to a wide class of continuous time Markov chain models. The estimator for the method is constructed by coupling the perturbed and nominal processes in a natural manner, and the analysis proceeds by utilizing a martingale representation for the coupled processes. The variance of the...

This paper presents a new method for designing vehicle structures for crashworthiness using surrogate models and a genetic algorithm. Inspired by the classifier ensemble approaches in pattern recognition, the method estimates the crash performance of a candidate design based on an ensemble of surrogate models constructed from the different sets of samples of finite element analyses. Multiple su...

We propose a method to approximate numerically the diffusion of an age-structured population in a spatial environment. We integrate separately the age and time variables by finite differences and we discretize the space variable by finite elements. The method is implicit in time and, inside each time step, implicit in age. We provide stability and convergence results and we illustrate our appro...

We consider the finite generation-time effect in virus evolution models, introducing differential equations with delay. The suggested approach more adequately describes the evolution in case of growing populations than the popular models of population genetics, especially for the viruses with large number of offspring during one life cycle. Now the mean fitness, as a coefficient for exponential...

This paper is concerned with a new class of mean-field games which involve finite number agents. Necessary and sufficient conditions are obtained for the existence decentralized open-loop Nash equilibrium in terms non-standard forward–backward stochastic differential equations (FBSDEs). By solving FBSDEs, we design set strategies by virtue two Riccati equations. Instead ɛ-Nash classical games, ...