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D.15.9.3 getMaxPoints
Procedure from library maxlike.lib (see maxlike_lib).
- Usage:
- getMaxPoints(Iu, H, prec [, "nodisplay"]); ideal Iu, matrix H, int prec, int k
Iu the likelihood ideal, H the (modified) Hessian of the considered algebraic
statistical model, prec the precision with which to compute the maximum
likelihood estimates
- Return:
- ring: a complex ring R in which you can find the following two lists:
- MPOINTS, points in which the loglikelihood function has a local maximum, and
- LHESSIANS, the (modified) Hessians at those points
also prints out the points in MPOINTS, unless a fourth argument is given
- Note:
- it is assumed that the likelihood ideal is 0-dimensional
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;
ideal L = likeIdeal(I,u);
matrix H = logHessian(I,u);
def R = getMaxPoints(L, H, 50);
==> [1]:
==> [1]:
==> 0.51912639453217837465463128685404418932771758896637
==> [2]:
==> 0.21725133256396491722887792998009835426225610459149
==>
==> // In the ring created by getmaxpoints you can find the lists
==> // MPOINTS, containing points in which the loglikelihood function has a\
local maximum, and
==> // LHESSIANS, containing the (modified) Hessians at those points.
==>
setring R;
MPOINTS;
==> [1]:
==> [1]:
==> 0.51912639453217837465463128685404418932771758896637
==> [2]:
==> 0.21725133256396491722887792998009835426225610459149
LHESSIANS;
==> [1]:
==> _[1,1]=-65487950.391931360088969690060635799847590217779318
==> _[1,2]=10577428.579689959415257134363650588464921754723022
==> _[2,1]=10577428.579689959415257134363650588464921754723022
==> _[2,2]=-1795635.2877514452321365400508526832132830781483598
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