Testing Alternative Models To Estimate Population Size

Estimating population occurs in many fields of study and professions. In order to accurately receive the closest estimate, it is important to know what model is the most accurate to use. After using the removal sampling method to test population size of the red flour beetle, we thought that a simple model can be used to estimate the population of beetles in a jar and that the best model would be the Moran-Zippin Model. “The principle of removal sampling is based upon the fact that a known number of animals are removed from a habitat with each sample, thus affecting subsequent catches” (Ballard). After conducting this research, we discovered that the Modified Moran-Zippin Model gave the most accurate estimate and had the lowest error rate compared to the regression and normal Moran-Zippin model. The results are important because the chosen model can be used to estimate population sizes for endangered animals and pest control

Population size bias in Diffusion Monte Carlo

The size of the population of random walkers required to obtain converged estimates in DMC increases dramatically with system size. We illustrate this by comparing ground state energies of small clusters of parahydrogen (up to 48 molecules) computed by Diffusion Monte Carlo (DMC) and Path Integral Ground State (PIGS) techniques. We contend that the bias associated to a finite population of walkers is the most likely cause of quantitative numerical discrepancies between PIGS and DMC energy estimates reported in the literature, for this few-body Bose system. We discuss the viability of DMC as a general-purpose ground state technique, and argue that PIGS, and even finite temperature methods, enjoy more favorable scaling, and are therefore a superior option for systems of large size.Comment: Seven pages, four figure

Estimating the Division Kernel of a Size-Structured Population

We consider a size-structured population describing the cell divisions. The cell population is described by an empirical measure and we observe the divisions in the continuous time interval [0, T ]. We address here the problem of estimating the division kernel h (or fragmentation kernel) in case of complete data. An adaptive estimator of h is constructed based on a kernel function K with a fully data-driven bandwidth selection method. We obtain an oracle inequality and an exponential convergence rate, for which optimality is considered