A short introduction to Bayesian statistics, part I
D. Joyce, Apr 2009
2nk
2nk + 2k
P (B|X) = 1 P (A|X)
2k
= nk
2
+ 2k
Ill try to make this introduction to Bayesian
statistics clear and short. First well look as a
specic example, then the general setting,
A short introduction to Bayesian statistics, part II
D. Joyce, Apr 2009
Bayes pool table example. The process we
just completed is what Thomas Bayes (17021761)
did. He illustrated the problem with balls on a
table. Ill paraphrase his illustration using th
A short introduction to Bayesian statistics, part III
D. Joyce, Apr 2009
5
The Poisson process
Gamma(, r). There are a couple dierent ways
that gamma distributions are parametrizedeither
in terms of and r as done here, or in terms of
and . The connection
A short introduction to Bayesian statistics, part IV
D. Joyce, Apr 2009
6
Normal distributions.
Thus, the family of all normal distributions is a
conjugate family for .
Example. Lets take an example. Suppose
were monitoring the production line of cans of
A short introduction to Bayesian statistics, part V
D. Joyce, Apr 2009
Normal distributions with unknown variances. Lets now consider normal distributions
with both unknown mean and unknown variance
2 . Well discover a way to nd a natural family of
conju
Common probability distributions
D. Joyce, Clark University
Aug 2006
1
Introduction.
I summarize here some of the more common distributions used in probability and statistics.
Some are more important than others, and not all of them are used in all elds.
Summary of basic probability theory, part 1
D. Joyce, Clark University
Math 218, Mathematical Statistics, Jan 2008
9. If event E is a subset of event F , then P (E)
P (F ).
10. Statement 7 above is called the principle of
inclusion and exclusion. It gene
Summary of basic probability theory, part 3
D. Joyce, Clark University
Math 218, Mathematical Statistics, Jan 2008
Joint distributions. When studing two related
real random variables X and Y , it is not enough
just to know the distributions of each. Rathe