Chapter 22
Graphical Causal Models
22.1
Causation and Counterfactuals
Take a piece of cotton, say an old rag. Apply ame to it; the cotton burns. We say
the re caused the cotton to burn. The ame is certainly correlated with the cotton
burning, but, as we a

Chapter 16
Simulation
You will recall from your previous statistics courses that quantifying uncertainty in
statistical inference requires us to get at the sampling distributions of things like
estimators. When the very strong simplifying assumptions of b

Chapter 23
Identifying Causal Effects from
Observations
There are two problems which are both known as causal inference:
1. Given the causal structure of a system, estimate the effects the variables have
on each other.
2. Given data about a system, nd its

Chapter 24
Estimating Causal Effects from
Observations
Chapter 23 gave us ways of identifying causal effects, that is, of knowing when quantities like Pr (Y = y|d o(X = x) are functions of the distribution of observable variables. Once we know that someth

Chapter 25
Discovering Causal Structure
from Observations
The last few chapters have, hopefully, convinced you that when you want to do causal
inference, knowing the causal graph is very helpful. We have looked at how it would
let us calculate the effects

Chapter 18
Principal Components Analysis
Principal components analysis (PCA) is one of a family of techniques for taking
high-dimensional data, and using the dependencies between the variables to represent
it in a more tractable, lower-dimensional form, w