How deeply does Causal Inference for Data Science cover conditional distribution?

Defines subgroup selection, distributional comparison, and conditional expectation, but does not develop estimation methods.

Conditional distribution

As explained in Causal Inference for Data Science

A conditional distribution is the probability distribution of a variable after conditioning on specified information.

A conditional distribution describes how a variable is distributed after selecting cases with specified information. For Y|X = a, keep observations where X equals a, then examine their Y values. This differs from the unconditional distribution, which combines all observed cases. section 1.5.2

Selecting a subgroup

Suppose the selected cases have X = a and Y values 7.01 and 10.89. Their conditional distribution gives each observed value weight 1/2, so E[Y|X = a] = 8.95. Adding Z = B narrows the selection to Y = 10.89. section 1.5.2

Table 1.3 Simulated data conditioned on X = a

X	Y	Z
a	7.01	A
a	10.89	B

Inspect the rows remaining after conditioning the simulated data on X = a. section 1.5.2

For binary Y, the conditional expectation E[Y|X] equals the conditional probability P(Y|X). In general, E[Y|X = x] means calculating the average Y among cases with the chosen value x. section 1.5.2

How Causal Inference for Data Science covers it

Cover of Causal Inference for Data Science

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Related concepts

conditioningproduced by · Conditioning is restricting or guiding a probabilistic or generative process using specified information, variables, values, or events.
softmaxproduced by · Softmax is a function that exponentiates a vector of scores and normalizes the results into nonnegative values that sum to one.
joint probability distributionproduced by · A joint probability distribution specifies probabilities or densities for combinations of values taken simultaneously by multiple random variables.
likelihoodproduced by · A likelihood is the probability of observed data under a specified probabilistic model, regarded as a function of candidate hypotheses or parameter values.

This explainer was generated by Manning's knowledge graph from the text of Causal Inference for Data Science. The section links point to the parts of the book it draws on.