ECL 290 Statistical Models in Ecology using R（发射极耦合逻辑使用R 290统计模型在生态学）.pdfVIP

ECL 290 Statistical Models in Ecology using R Problem set for Week 6 Monte Carlo simulation, power analysis, bootstrapping 1. Monte Carlo simulations - Central Limit Theorem example To start getting a handle on Monte Carlo simulations, we will test the accuracy of the Central Limit Theorem. Lets hope it works, otherwise we all have to stop using ANOVAs. The logic behind Monte Carlo is very appealing to frequentists. Most frequentist stats are based on the idea that we are estimating the probability that a certain thing would happen if we repeated the same experiment very many times. Usually we never actually repeat the experiment because the grant has run out and we have to publish the manuscript. However, we can use Monte Carlo techniques to simulate repeating the experiment (assuming the data are described by a particular statistical distribution) and thus obtain a frequentist estimate of a particular event happening. To see how this works, we will perform Monte Carlo simulations and compare the results to a theoretical expectation, the Central Limit Theorem (CLT). The CLT says that when one takes random samples from any distribution with true mean µ and standard deviation σ, the distribution of the sample means will follow a normal distribution with mean µ and standard deviation σ/n0.5 (the standard devation of the disribution of means is usually called the standard error). The CLT is the reason that we calculate the standard error of our sample data and use the SE to construct 95% confidence intervals around our mean. If the 95% CIs dont overlap zero, then the mean is significantly different from zero. Anyway, the CLT is asymptotically true - it is guaranteed to be correct for large sample sizes n, but not so much for smaller n. It is always a good idea to calibrate our intuition about how large n must be before we start assuming that the CLT holds. This is where Monte Carlo comes in. First we will estab