航海仿真课件NavSim03-3.ppt

Simulation Technology John Shi Chaojian Monte Carlo Simulation (Resampling ) Resampling refers to the use of the observed data or of a data generating mechanism (such as a die) to produce new hypothetical samples, the results of which can then be analyzed. Beneath the logic of a statistical inference there necessarily lies a physical process. The resampling methods allow us to work directly with the underlying physical model by simulating it, rather than describing it with formulae. Question If a family has two children and one of them is a boy, what is the probability that the other will also be a boy? D’Alembert’s Misery D’Alembert asked: What is the chance of throwing at least one head in two tosses of a coin? He reasoned that there are three cases: tail on both tosses, tail then head, head on the first toss (no second toss necessary). Of these three cases, two are successes, and therefore the probability sought is 2/3, he concluded D’Alembert (1717-1783; story in Schuh, Fred, The Master Book of Mathematical Recreations, 1968, p. 165). The treasure fleet recovered A Spanish treasure fleet of three ships was sunk at sea off Mexico. One ship had a trunk of gold forward and another aft, another ship had a trunk of gold forward and a trunk of silver aft, while a third ship had a trunk of silver forward and another trunk of silver aft. Divers just found one of the ships and a trunk of silver in it. They are now taking bets about whether the other trunk found on the same ship will contain silver or gold. What are fair odds? The treasure fleet recovered The treasure fleet recovered Simulation: Construct three urns containing the numbers “7,7,” “7,8,” and “8,8” respectively. Choose an urn at random, and shuffle the numbers in it. Choose the first element in the chosen urn’s vector (a vector is an array or list of numbers). If “8,” stop trial and make no further record. If “7,” continue. Record the second element in the chosen urn’s vector on the scoreboard. Repeat s