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D.15.8.2 logHessian
Procedure from library maxlike.lib (see maxlike_lib).
- Usage:
- logHessian(I,u); ideal I, intvec u
I represents the algebraic statistical model and u is the data vector under
considerarion.
- Return:
- matrix: a modified version of the Hessian matrix of the loglikelihood function
defined by u and (the given generators of) I.
- Note:
- This matrix has the following property: if it is negative definite at a point,
then the actual Hessian is also negative definite at that point. The same holds
for positive definiteness.
Example:
| | LIB "maxlike.lib";
ring r = 0,(x,y),dp;
poly pA = -10x+2y+25;
poly pC = 8x-y+25;
poly pG = 11x-2y+25;
poly pT = -9x+y+25;
intvec u = 10,14,15,10;
ideal I = pA,pC,pG,pT;
matrix H = logHessian(I,u); H;
==> H[1,1]=-689040x3+314898x2y-44808xy2+1974y3+9619350x2-2949075xy+240975y2+6\
151875x-1072500y-70640625
==> H[1,2]=110880x3-51936x2y+7596xy2-348y3-1489200x2+431400xy-33450y2-1072500\
x+176250y+11437500
==> H[2,1]=110880x3-51936x2y+7596xy2-348y3-1489200x2+431400xy-33450y2-1072500\
x+176250y+11437500
==> H[2,2]=-16580x3+7972x2y-1192xy2+56y3+243150x2-66800xy+4900y2+176250x-2750\
0y-1937500
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