Upcoming SlideShare
×

Probability And Stats Intro2

763 views

Published on

Published in: Technology, Education
0 Likes
Statistics
Notes
• Full Name
Comment goes here.

Are you sure you want to Yes No
• Be the first to comment

• Be the first to like this

Views
Total views
763
On SlideShare
0
From Embeds
0
Number of Embeds
16
Actions
Shares
0
19
0
Likes
0
Embeds 0
No embeds

No notes for slide

Probability And Stats Intro2

1. 1. Crash course in probability theory and statistics – part 2 Machine Learning, Wed Apr 16, 2008
2. 2. Motivation All models are wrong, but some are useful. This lecture introduces distributions that have proven useful in constructing models.
3. 3. Densities, statistics and estimators A probability (density) is any function X a p(X ) that satisfies the probability theory axioms. A statistic is any function of observed data x a f(x). An estimator is a statistic used for estimating a parameter of the probability density x a m.
4. 4. Estimators Assume D = {x1,x2,...,xN} are independent, identically distributed (i.i.d) outcomes of our experiments (observed data). Desirable properties of an estimator are: for N®¥ and (unbiased)