* Bayes Rule: "P(A,B) = P(A|B) P(B)" means "forall a,b . P(A=a, B=b) = P(A=a|B=b) P(B=b)". This is very standard.

* "variance of the estimator" means "variance of the sampling distribution of the estimator". AFAICT, this is unambiguous, and the only reasonable interpretation is for "estimator" to mean the random variable. To make this even more ( Read more... )

Bootstrap sampling is a procedure for estimating (properties of) the sampling distribution of a statistic when you can't sample directly from the population (i.e. the typical setting), but have a limited IID sample S ( Read more... )

Over lunch on Friday, Michael Littman told me the following idea: Suppose you have a procedure for making confidence intervals out of an IID sample from a population. If you run this sample/estimate cycle multiple times, the resulting confidence intervals should mostly overlap with each other. This is a coherence constraint, which I'll try to make ( Read more... )

Hypothesis: In exponential family distributions, the moments are sufficient statistics. Prove or refute.

Your answer could fill what seems to be a Google gap.

Regarding Google's ability to answer such queries: my previous post on the triangle equality for correlation distance (including en_ki's elegant solution) seems to have fallen off Google's map. ( Read more... )

Suppose you have points on the real line, from two classes, e.g. random samples from the sampling distribution of a certain statistic, under two experimental conditions, C1 and C2.


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Given a dataset with 3 variables A, B, C, you observe a value for the correlation between A and B, and another value for the correlation between B and C.

Question: what are the possible values of the correlation between A and C?

Answer (due to en_ki): if your dataset has n points, center it, and consider A, B and C as vectors in ℜn. The empirical ( Read more... )

Why do we care about finding MLE, MAP parameter-settings? The focus on the maximum reminds me of the mode, a statistic that one doesn't care about most of the time. (Instead, one tends to focus on the mean and median).

Take the graph below:


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