Fill out the pre-assessment survey Goal: measure difference in - - PowerPoint PPT Presentation

Fill out the pre-assessment survey

Goal: measure difference in knowledge from early in class to end of class Link is on Campuswire Answer if you know, but guess if you don't Completion = 100 on one homework (not substitutable)

Feb 13: Data generating processes, likelihood comparisons

n Choose k

Connection between sequences and counts. How many binary sequences of length n have k ones (and n-k zeros)? How many ways can you divide n things into two groups, where one group is of size k?

n! (n-k)!k! (a+b)! a!b! comb(n, k)

Three distributions (so far)

• Binomial

○ Out of n trials, x successes with probability p ○ 0 to n

• Geometric

○ x successes before first failure with probability p ○ no upper bound, always decreasing

• Poisson

○ x events with rate λ within an interval ○ no upper bound

Variations of a distribution

• Geometric

○ x successes before first failure with probability p

• or-

○ x trials including first failure with probability p

Which distribution?

• Length of a team's winning or losing streak
• Number of hits in a baseball game
• Number of wins in a team's season

Reversing Data Generating Process: Prediction

Source: Wikipedia, Flickr

1 2 3 4

Reversing Data Generating Processes: inference

[4, 4, 3, 2, 3]

Source: Wikipedia, Flickr

Thinking about log probability

Multiplying probabilities causes the

• verall probability to get very small

very fast. The probability of 44 streak lengths is 0.0000000000000000000000000000000000000014694 Dealing with log probabilities is much easier, but we have to remember that multiplication always becomes addition.

probability log probability 1.0 log(x)

Thinking about log probability

All probabilities are between 0 and 1 (x-axis), so all log probabilities are negative, and between -infinity and 0 (y-axis). Log is monotonic, meaning that if P(X) > P(Y), it is also true that log(P(X)) > log(P(Y)). As probability increases, log probability also increases.

probability log probability 1.0 log(x)