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MathGroup Archive 1997

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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}]


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