On 11-Oct-06 Njeri Wabiri wrote: > Dear list > Just a newbabie question > What is the statistical interpretation of the Lagrange > multiplier in kriging. > At least I know if its positive we have a high kriging > variance and vice versa. > > Grateful for a response and a reference > > Njeri
The general interpretation of a Langrange multiplier is as follows. In the context of an extremal problem (find the max/min) of a function f(x1,x2,...,xk) subject to a constraint g(x1,x2,...,xk) = c when you express it as solving the extremal problem for f(x1,x2,...,xk) - L*g(x1,x2,...,xk) (and then using the constraint equation to eliminate L), the value of L is equal to the rate of change of the extremal value of f (as so found) with respect to variation in the value of c. Otherwise put: for a particular value of c, the extremal value of f is (say) fmax(c). Then L = dfmax(c)/dc. The same is true with several constraints (and a corresponding number of lagrange multipliers), in that the i-th L is equal to the partial derivative of fmax(c1,c2,...,cr) with respect to ci. [This assumes that the function f has a max/min which can be found analytically by solving the equation[s] obtained by setting derivative[s] equal to 0. The above is not quite so directly true when the maximum is attained on the boundary of the region defined by the constraints, as in a Linear Programming problem, for instance; though something similar is also true there.] I can supply a demonstration of the above, if requested. So, if (in a statistical context) a sum of squares if minimised, or a likelihood is maximised, subject to constraints, then the above applies to the sum of squares, or likelihood, or whatever. Hoping this helps, Ted. -------------------------------------------------------------------- E-Mail: (Ted Harding) <[EMAIL PROTECTED]> Fax-to-email: +44 (0)870 094 0861 Date: 11-Oct-06 Time: 21:27:33 ------------------------------ XFMail ------------------------------ + + To post a message to the list, send it to ai-geostats@jrc.it + To unsubscribe, send email to majordomo@ jrc.it with no subject and "unsubscribe ai-geostats" in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list + As a general service to list users, please remember to post a summary of any useful responses to your questions. + Support to the forum can be found at http://www.ai-geostats.org/
