In the following application I implemented a popular alternative to the Gauss-Newton method for performing least squares fitting of the cases of H1N1 flu strain.
The Levenberg-Marquardt is an efficient, fast and robust method for finding the minimum of the Sigmoidal function that is a sum of squares of nonlinear functions. The optimization routine uses a search direction that is a cross between the Gauss-Newton direction and the steepest descent.
The best fit approximation to the logarithm of cases, selecting rr, K, A and b to get a minimum least squares fit to: f(x) = log(cases) = K { 1 – A*exp(-rr*x) }b
From April 2009 to July 2009 the Best Fit =
EVENTUAL VALUE: 431,556
EVENTUAL LOWER BOUND: 379,000
EVENTUAL UPPER BOUND: 491,000
DATE: 14-Sep-09
PREDICTION: 270,580
LOWER BOUND: 240,077
UPPER BOUND: 304,917
AS OF SEPT. 6, 2009, THE NUMBER OF CASES IS 277,607
For the Spreadsheet Application Click Here
nico
Here we started with a complex system, then we ignore the hard parts so the problem is amenable to a mathematical analysis, then we solve the simpler problem, then we pray that it’s a reasonable approximation to the actual cases of the Swine Flu………