Lucas Schiffer

January 20, 2016

Data Analysis for the Life Sciences

- Introduction
- Conditional Probability / Conditional Expectation
- Galton Height Data
- Regression as Machine Learning
- Conditional Expectation / Optimal Prediction
- Exercises

- Conditional probability and conditional expectation are slightly different
- Both are often useful as machine learning techniques
- Helpful in solving classification and prediction problems
- Generally useful for categorical and continuous outcomes

- Conditional probability
- What is the probability that the next marble is green given that the first was yellow?
- \[ f_{k}(x)=Pr(Y=k\ |\ X = x) \]
- Conditional Expectation
- Given that the first marble was yellow, what color is expected next?
- \[ E[(\hat{Y}-Y)^2|X=x] \]

- Francis Galton created a height dataset (1885)
- Useful for conditional expectation practice

- Suppose we want to predict a random son's height
- Suppose we want to predict a son's height who's father is 71 inches tall
- \[ E[(\hat{Y}-Y)^2|X=71] \]