Contents
How do you interpret causal risk ratio?
The causal risk ratio is defined as Pr[Ya = 1 = 1]/Pr[Ya = 0 = 1], where Ya is the counterfactual outcome variable Y that would have been observed under exposure level a (one of the possible values of A). Consider two mutually exclusive study designs that might have produced the data in table 1.
What do you mean by interchangeability?
(of two things) capable of being put or used in the place of each other: interchangeable symbols. (of one thing) capable of replacing or changing places with something else: an interchangeable part.
What are the properties of exchangeable random variables?
Exchangeable sequences have some basic covariance and correlation properties which mean that they are generally positively correlated. For infinite sequences of exchangeable random variables, the covariance between the random variables is equal to the variance of the mean of the underlying distribution function.
How to create an exchangeable random vector x?
A simple and rather general way to build an exchangeable random vector X = ( X k) 1 ⩽ k ⩽ n is to start from an i.i.d. sequence ( Y k) 1 ⩽ k ⩽ n and to define, for every k, X k = Φ ( U, Y k), where U is a random variable independent on ( Y k) 1 ⩽ k ⩽ n and Φ a measurable function.
What can we say about just identically distributed X J?
Consider a d -dimensional random vector X = ( X j). X is called exchangeable if ( X 1, …, X d) = d ( X j 1, …, X j d) for any permutation j 1, …, j d. If X j are iid, X is exchangeable. The converse is false (correct me if I’m wrong). What can we say about just identically distributed X j?
Which is stronger exchangeability or identical distribution?
Exchangeability is stronger than identical distribution. Note that X 1 = d X j 1, so these two are identically distributed, and j 1 could be any index. A couple of important examples of exchangeability: