An introduction to the Bootstrap method.ppt

An introduction to the An introduction to the Bootstrap method Bootstrap method Hugh Shanahan Hugh Shanahan University College London University College London November 2001 November 2001 I know that it will happen, Because I believe in the certainty of chance The edy Outline Outline ?? Origin of Statistics Origin of Statistics ?? Central Limit Theorem Central Limit Theorem ?? Difficulties in Difficulties in ““ Standard Statistics Standard Statistics ””?? Bootstrap - the basic idea Bootstrap - the basic idea ?? A simple example A simple example ?? Case Study I : ic Trees Case Study I : ic Trees ?? Case Study II : works Case Study II : works ?? Conclusions Conclusions Statistics 101 Statistics 101 ?? We want the We want the ‘‘ average average ’’ and and ‘‘ error error ’’ for some for some variable variable ?? Time between first and second division of frog Time between first and second division of frog embryo embryo ?? Half-life of a radioactive sample Half-life of a radioactive sample ?? How many days does Wimbledon get delayed How many days does Wimbledon get delayed by ( by ( grrr grrr …………..) ..) Strategy Strategy ?? Assuming only statistical variation Assuming only statistical variation ?? Carry out measurement Carry out measurement ““ many many ”” times times ?? Error decreases as number of measurements Error decreases as number of measurements increase increase In fact, there In fact, there ’’ s a huge amount of statistical s a huge amount of statistical machinery going on with this machinery going on with this …………. . Assume the Central Limit Theorem Assume the Central Limit Theorem ““ If random samples of n observations y If random samples of n observations y 1 1, y , y 2 2, , ……y y n n are are drawn from a population of finite mean drawn from a population of finite mean ?? and variance and variance ?? 2 2 , then when n is sufficiently large, the sampling , then when n is sufficiently large, the sampling distribution of t