To add to this discussion, one of Peter MacDonald's students changed MIX to Rmix using the Free R-package with nlm for the mle optimization. So it is free(but it is good for Peter if you want to spend some money to buy MIX) and excellent for mixture population from my view.
As for plateau/kinks/breakpoints, it depends on the proportions of each subpopulation in the mixture. Furthermore, the goodness-of-fit statistics in Rmix will give you some directions on how many subpopulations in the mixture. Din -----Original Message----- From: Isobel Clark [mailto:[EMAIL PROTECTED] Sent: Tuesday, March 09, 2004 3:34 PM To: Chaosheng Zhang Cc: [EMAIL PROTECTED] Subject: AI-GEOSTATS: Re: mixtures of populations AH me, the English language slips away from me again. I said that the PRESENCE {pardon the capitals, no way to italicise email} of more than one population is indicated by the points of inflexion on the probability plot. Not that these were breakpoints between populations. Normal (or lognormal) populations overlap. The break point in the probability plot allows us to distinguish between data which are skewed and multiple populations. Skewed data give curved probability plots. Mixtures of populations give plots with abrupt changes in slope. These are very rarely equivalent to 'equal probability' points - that is, statistical break points between the population. But, they are a good place to start looking ;-) Once you have deduced that multiple populations are present there are lots of things you can do, including simple stuff like post-plotting an indicator transform of the data at various threshholds just to see if there is any spatial pattern obvious to the naked eye. In many cases, ordinary kriging can proceed even with a mixture, since it only requires second-order stationarity not the existance of one single population. In 34 years of searching, I have never seen a probability plot with breakpoint(s) which did not have a matching multiple population explanation. The number of times I have argued with a 'customer' about this is legion. In some cases, we have found more populations than expected (witness my 1993 IGMC paper). In environmental studies, as in many geological situations, one would normally expect a broad background population of readings with the 'pollution' showing as a more cohesive, generally higher valued overlying one. Where both exist in the same locality, it is often difficult to separate them in the data set because you need both to characterise that area. This is the case where you would co-krige an indicator and two populations to get one estimate. Peter MacDonald's work is pretty definitive in North America and his MIX program for separating a histogram out into components has been around for 30 years, to my knowledge (I met him in 1976 at a Biometrics Congress!). There is a great monograph by Alistair Sinclair called "Application of Probability Plots in Mineral Exploration" which costs around $10 from the Association of Exploration Geochemists and was first published about 30 years ago. The task of identifying mineral targets is very like that of identifying pollution sources or other types of 'secondary' populations. It is much better to identify multiple populations from other knwledge of the site, but this is not always possible. If you don't know whether or not you have a mixture, statistical plots are one way of checking - and very quick and easy to produce nowadays. I am open to any other suggestions on how to identify multiple populations when all you have is the sample data. Isobel Clark http://uk.geocities.com/drisobelclark ___________________________________________________________ Yahoo! Messenger - Communicate instantly..."Ping" your friends today! Download Messenger Now http://uk.messenger.yahoo.com/download/index.html -- * 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 -- * 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
