Hi Digby The short answer to your least squares question is 'because Matheron was a least squares person' ;-)
There are three basic schools of statistics: (1) least squares (sometimes known as frequentist) which probably includes the majority of non-statisticians doing statistics. The least squares approach might be paraphrased as "closest to the real answer on average". It is based on the concept of approximately Normal 'errors' (2) maximum likelihood. This could be paraphrased as 'that solution from which the samples are most likely to have come'. This yields much more general but not always unbiassed answers. For example, the maximum likelihood estimator of the variance is divided by 'n' not 'n-1' as in least squares. Maximum likelihood demands a pretty fair knowledge of the underlying distribution of the samples, not the errors as such. (3) bayesian estimation. Based somewhat on a maximum likelihood method, you can build in your own prior knowledge about the situation to affect the final answers. (1) and (2) above rely solely on hard data. This is, of course, a massive over-simplification but serves, I think, to emphasise why there are many different answers to the same problem and why you have to define what you mean by "best" before you get the "best answer". I try to cover these concepts in non-rigorous terms in all my teaching. It is also true that the mathematics is much simpler if you use variances than if you use any other function of differences. Isobel http://geoecosse.bizland.com/news.html __________________________________________________ Do You Yahoo!? Everything you'll ever need on one web page from News and Sport to Email and Music Charts http://uk.my.yahoo.com -- * To post a message to the list, send it to [EMAIL PROTECTED] * As a general service to the users, please remember to post a summary of any useful responses to your questions. * To unsubscribe, send an email to [EMAIL PROTECTED] with no subject and "unsubscribe ai-geostats" followed by "end" on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list * Support to the list is provided at http://www.ai-geostats.org
