Week 2

1. Bayes' Rule

1.1. Sensetivity

1.1.1. P(+|D)

1.2. Specificity

1.2.1. P(-|not D)

1.3. P(D^c) - это вероятность наступления не D события

1.4. Prelevance = вероятность наступления события D

1.5. P(D | +) - вероятность болезни D если тест на болезнь выдал позитивный результат

2. Common distributions

2.1. Bernoulli

2.1.1. Binary outcome

2.1.2. PMF = P(X = x) = p^x(1-p)^1-x

2.1.3. mean is p

2.1.4. variance = p(1-p)

2.1.5. (n) (x) - читается как (n choose x) и равно n! / (x!(n - x)!)

2.2. Normal (or Gaussian)

2.2.1. density is (2pimuy^2)^(-1/2)e^(-(x-muy)^2/2sigma^2)

2.3. Poisson

2.3.1. P(X = x; lambda) = lambda^2 e^-lambda / x!

2.3.2. Used for

2.3.2.1. modling event/time data

2.3.2.2. modeling survival data

2.3.2.3. contigency tables

3. Asymptopia

3.1. Term means: sample size limits to infinity or some other relevant number

3.2. Incredibly useful for simple statistical references

3.3. Limit of random variable

3.4. Law of Large numbers

3.4.1. If X1 ... Xn are iid from population with mean muy and variance sigma^2 then Xn converges in probability to myu

4. Central limit theorem

4.1. most important theorem in statistics

5. T Confidence intervals

5.1. ((n-1)S^2) / sigma^2 ~ Chi^2[n-1]

5.2. t distrubution

5.2.1. Invented by William Gosset

5.2.2. Looks like a normal, but squashed down