>In sci.stat.edu Radford Neal <[EMAIL PROTECTED]> wrote: > >: You don't know what you are talking about. There are many, many >: situations in which data is analysed when there are more variables >: than observations.
In article <[EMAIL PROTECTED]>, Elliot Cramer <[EMAIL PROTECTED]> wrote: >but if you know anything about statistics, you don't analyze them as >variables but condense them based on your knowledge to many fewer >variables than observations If you knew as much about statistics as you think you do, you would know that there are many ways of analysing such data that don't involve first "condensing" the variables (based on prior knowledge alone, apparently, if you're not allowed to analyse the data before doing the condensing). For example, you can fit a model in which the data is regarded as a mixture of some number of multivariate Gaussian distributions, each of which has a diagonal covariance matrix. This works fine, even if the number of variables is much greater than the number of observations. Or you can fit a factor analysis model. In general, you can use any model that you would have wanted to use if you had more observations than variables, provided you do it right. Here, "doing it right" probably involves being Bayesian. The correct model and prior don't depend on how big your grant is, even if the number of observations you were able to collect does. >: PCA isn't necessarily the best way of analysing such data, but it >: isn't senseless. > >It's senseless That's a strange comment, considering that PCA is one way of doing the "condensing" that you advocate. Radford Neal ---------------------------------------------------------------------------- Radford M. Neal [EMAIL PROTECTED] Dept. of Statistics and Dept. of Computer Science [EMAIL PROTECTED] University of Toronto http://www.cs.utoronto.ca/~radford ---------------------------------------------------------------------------- . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
