文档介绍：408 Resampling: The New Statistics
CHAPTER
Bayesian Analysis
25 by Simulation
Simple Decision Problems
Fundamental Problems In Statistical Practice
Problems Based On Normal And Other Distributions
Conclusion
Bayesian analysis is a way of thinking about problems in
probability and statistics that can help one reach
otherwise-difficult decisions. It also can sometimes be used in
science. The range of its mended uses is controversial,
but this chapter deals only with those uses of Bayesian analy-
sis that are uncontroversial.
Better than defining Bayesian analysis in formal terms is to
demonstrate its use. Therefore, to make clear the nature of
“Bayes’ rule,” we shall start with the simplest sort of prob-
lem, and proceed gradually from there.
Simple decision problems
Assessing the Likelihood That a Used Car Will Be Sound
Consider a problem in estimating the soundness of a used car
one considers purchasing (after Wonnacott and Wonnacott,
1990, p. 93). Seventy percent of the cars are known to be OK
on average, and 30 percent are faulty. Of the cars that are re-
ally OK, a mechanic correctly identifies 80 percent as “OK”
but says that 20 percent are “faulty”; of those that are faulty,
the mechanic correctly identifies 90 percent as faulty and says
(incorrectly) that 10 percent are OK.
We wish to know the probability that if the mechanic says a
car is “OK,” it really is faulty.
One can get the desired probabilities directly by simulation
without knowing Bayes’ Law, as we shall see. But one must
be able to model the physical problem correctly in order to
proceed with the simulation; this requirement of a clearly-vi-
Chapter 25—Bayesian Analysis by Simulation 409
sualized model is a strong point in favor of simulation.
The following steps determine the probability that a car said
to be “OK” will turn out to be really faulty:
1. Model in percentages the universe of all cars as an urn of
100 balls. Workin