[R] Overlapping distributions (populations) - assigning an individual to a population?
People, Say a particular measure of an attribute for individuals in different populations gives a set of overlapping normal distributions (one distribution per population). If I then measure this attribute in a new individual - how do I assess the likelihood of this new individual belonging to each of the different populations? Thanks, Phil. -- Philip Rhoades Pricom Pty Limited (ACN 003 252 275 ABN 91 003 252 275) GPO Box 3411 Sydney NSW 2001 Australia Fax: +61:(0)2-8221-9599 E-mail: [EMAIL PROTECTED] __ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
Re: [R] Overlapping distributions (populations) - assigning an individual to a population?
Rolf, On Wed, 2008-04-09 at 10:57 +1200, Rolf Turner wrote: On 9/04/2008, at 10:30 AM, Phil Rhoades wrote: People, Say a particular measure of an attribute for individuals in different populations gives a set of overlapping normal distributions (one distribution per population). If I then measure this attribute in a new individual - how do I assess the likelihood of this new individual belonging to each of the different populations? You have a mixture of distributions. Let the density be k f(x) = SUM lambda_i * f_i(x) i=1 where the f_i(x) are the densities for the individual components in the mixture, and the lambda_i are the mixing probabilities. The probability that an individual with observation x is from component i is lambda_i * f_i(x) - f(x) Thanks for the quick response but I think I need to put some numbers on this so I can see what you mean. Say I have two pops with individual values: 1 2 3 4 5 3 4 5 6 7 and a new individual with value 5 - what is the likelihood of assignment to each of the populations? BTW, I say populations, but to keep it simple I didn't go into more detail - there is no physical overlap in space or time of the populations/distributions - so there are no gradients from interbreeding of sub-populations or anything like that. Regards, Phil. -- Philip Rhoades Pricom Pty Limited (ACN 003 252 275 ABN 91 003 252 275) GPO Box 3411 Sydney NSW 2001 Australia Fax: +61:(0)2-8221-9599 E-mail: [EMAIL PROTECTED] __ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
Re: [R] Overlapping distributions (populations) - assigning an individual to a population?
Rolf, On Wed, 2008-04-09 at 10:57 +1200, Rolf Turner wrote: On 9/04/2008, at 10:30 AM, Phil Rhoades wrote: People, Say a particular measure of an attribute for individuals in different populations gives a set of overlapping normal distributions (one distribution per population). If I then measure this attribute in a new individual - how do I assess the likelihood of this new individual belonging to each of the different populations? You have a mixture of distributions. Let the density be k f(x) = SUM lambda_i * f_i(x) i=1 where the f_i(x) are the densities for the individual components in the mixture, and the lambda_i are the mixing probabilities. The probability that an individual with observation x is from component i is lambda_i * f_i(x) - f(x) Thanks for the quick response but I think I need to put some numbers on this so I can see what you mean. Say I have two pops with individual values: 1 2 3 4 5 3 4 5 6 7 and a new individual with value 5 - what is the likelihood of assignment to each of the populations? Phil, for an application and more detailed explanation you can check the article: A Test for Long-Term Cyclical Clustering of Stock Market Regimes John Powell, Rubén Roa, Jing Shi, Viliphonh Xayavong Australian Journal of Management, vol. 32(2), 2007, available for free download from the journal website: http://www.agsm.edu.au/~eajm/current.html I provide there a quotation to a book by Hamilton on time series, where this technique is further explained. By the way, the computation suggested is a conditional probability. Rubén __ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
