Thanks. Just yesterday I came across this first paragraph in a paper I now see is by Jordan:
"Statistics has both optimistic and pessimistic faces, with the Bayesian perspective often associated with the former and the frequentist perspective with the latter, but with foundational thinkers such as Jim Berger reminding us that statistics is fundamentally a Janus-like creature with two faces." [Janus is a Roman god with two faces]
In my current project (stroke and [since the leap] gesture recognition), I'm using the covariance matrix of a training set and the difference a feature vector from the mean to calculate the mahalanobis distance of the input vector from the training set. I plan to use this same covariance matrix in the Gaussian density estimation formula to generate a probability distribution function (and then use the likelihood function instead of mahalanobis distance). Still trying to mentally connect this to the bigger-picture stuff though.
Berger's actually written a seminal book on the topic called "Statistical Decision Theory and Bayesian Analysis"[1]. If you're interested in that area, consider checking it out of your library.
I'm not quite as sharp in the area as I used to be, but feel free to hit me up over email if you have more questions, I can't guarantee that I'll know the answers, but I'm happy to give it a shot.
"Statistics has both optimistic and pessimistic faces, with the Bayesian perspective often associated with the former and the frequentist perspective with the latter, but with foundational thinkers such as Jim Berger reminding us that statistics is fundamentally a Janus-like creature with two faces." [Janus is a Roman god with two faces]
In my current project (stroke and [since the leap] gesture recognition), I'm using the covariance matrix of a training set and the difference a feature vector from the mean to calculate the mahalanobis distance of the input vector from the training set. I plan to use this same covariance matrix in the Gaussian density estimation formula to generate a probability distribution function (and then use the likelihood function instead of mahalanobis distance). Still trying to mentally connect this to the bigger-picture stuff though.
http://www.cs.berkeley.edu/~jordan/papers/berger-festschrift...