Re: AI-GEOSTATS: Re: mixtures of populations

[Chaosheng Zhang]

Dear Isobel and all, Thanks for your clarification and the replies from several others. Well, I didn't mean to question what you said (or wrote, -:)), but just wanted to discuss with you and make this issue clearer as I saw so many messages in the list talking about "probability plot". Glad to know that I am not alone with such a concern. However, perhaps the appropriate way is to say that a probability plot is still very useful, but care should be taken when explain it. It may be still ok to visually identify outliers, even to explain different sections on the plot with scientific knowledge, but we cannot go too far. Since it is a "graphical" method, we may regard it as a "practical" way. Cheers, Chaosheng -------------------------------------------------------------------------- Dr. Chaosheng Zhang Lecturer in GIS Department of Geography National University of Ireland, Galway IRELAND Tel: +353-91-524411 x 2375 Fax: +353-91-525700 E-mail: [EMAIL PROTECTED] Web 1: www.nuigalway.ie/geography/zhang.html Web 2: www.nuigalway.ie/geography/gis/index.htm ---------------------------------------------------------------------------- ----- Original Message ----- From: "Isobel Clark" <[EMAIL PROTECTED]> To: "Chaosheng Zhang" <[EMAIL PROTECTED]> Cc: <[EMAIL PROTECTED]> Sent: Tuesday, March 09, 2004 11:34 PM 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. 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