The Normal Distribution is the most important (but by no means the only) distribution for continuous values. Probability density:
2
1 1 |x - mu|
f(x) = ---------------- exp( - - |------| )
sqrt(2 pi) sigma 2 |sigma |
- loge f(x) :
2
1 |x - mu|
-ln f(x) = ln(sqrt(2 pi) sigma) + - |------|
2 |sigma |
This document is online at http://www.csse.monash.edu.au/~lloyd/Archive/2005-05-Normal/index.shtml and contains hyper-links to other resources.
| muML | = | (x1 + x2 + . . . + xn) / n |
| vML | = | SUMi=1..n (xi - muML)2/n |
and sigma = sqrt(v).
Consider n=1, and n=2.
with prior h(mu,v) ~ 1/v
| muMML | = | (x1 + x2 + . . . + xn) / n | = | muML |
| vMML | = | SUMi=1..n (xi - mu)2/(n-1) |
and sigma = sqrt(v).
Consider n=1, and n=2.