Plot3D precision limits?

*To*: mathgroup at smc.vnet.net*Subject*: [mg6504] Plot3D precision limits?*From*: Jim Hicks <jim at cern36.ce.uiuc.edu>*Date*: Thu, 27 Mar 1997 02:42:45 -0500 (EST)*Organization*: University of Illinois at Urbana-Champaign*Sender*: owner-wri-mathgroup at wolfram.com

I have two questions regarding the statements listed below that find the numerical solution to a system of two equations and two unknowns (x and y). This solution happens to be a maximum likelihood solution to the problem of estimating two unknown parameters, x and y. The solution provided by FindRoot using Mathematica 3.0 under Solaris 2.5 for SPARC is the following: {x-> -0.237575444848816, y-> -0.0531098274657849} I am interested in visualizing the surface of the log-likelihood function in the immediate vicinity of the optimal solution. As you can see, I have used Plot3D to plot this function near the solution. Question 1: As I increase the number of digits specified for the ranges of x and y to zoom in closer to the actual solution, Plot3D produces a non-smooth surface. Plot3D produces a smooth surface if fewer digits are specified following the decimal for the plot ranges. I assume that I am crossing some machine precision threshold. Is this true and is there anyway to overcome it so that I can see an accurate representation of the surface near the solution given by x and y above? Question 2: If you reproduce the plot that I am considering, you will notice that all the axis labels are printed with up to 6 digits after the decimal. Is it possible to change this by some option such that for example, as many as 15 digits would be displayed? Thank you very much for your consideration of my questions. Jim je-hicks at uiuc.edu a={52.9,4.1,4.1,56.2,51.8,0.2,27.6,89.9,41.5,95.,99.1,18.5,82.,8.6,22.5,51.4,81.,51.,62.2,95.1,41.6} b={4.4,28.5,86.9,31.6,20.2,91.2,79.7,2.2,24.5,43.5,8.4,84.,38.,1.6,74.1,83.8,19.2,85.,90.1,22.2,91.5} c={0,0,1,0,0,1,1,0,0,0,0,1,1,0,1,1,0,1,1,0,1} p=1/(1+Exp[-x+y(b-a)]) FindRoot[{Sum[c[[i]]-p[[i]],{i,1,21}], Sum[(c[[i]]-p[[i]])(a[[i]]-b[[i]]),{i,1,21}]},{x,0},{y,0}] Plot3D[Sum[c[[i]]Log[p[[i]]]+(1-c[[i]])Log[1-p[[i]]],{i,1,21}], {x,-.23757544485,-.23757544484},{y,-.05310983,-.05310982}, PlotPoints->15, BoxRatios->{1.0,1.0,0.4}]