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D.15.8.5 maxPointsProb

Procedure from library maxlike.lib (see maxlike_lib).

Usage:
maxPointsProb(I,u,prec [, "nodisplay"]); ideal I, intvec u, int prec I represents the algebraic statistical model, u is the data vector under considerarion, and prec is the precision to be used in the computations

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, - LHESSIANS, the (modified) Hessians at those points, and - VALS, the resulting probability distributions (that is, the values of the polynomials given by I at the points in MPOINTS).
Also prints out the points in MPOINTS, unless a fourth argument is given.

Note:
Does not compute the likelihood ideal via elimination, but rather computes the critical points by projection.

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;
def R = maxPointsProb(I, u, 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,
==> //   LHESSIANS, containing the (modified) Hessians at those points, and
==> //   VALS, containing the probability distributions 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
VALS;
==> [1]:
==>    [1]:
==>       20.243238719806146087911442991419754815247336319519
==>    [2]:
==>       28.935759823693462080008172364852255160359484607139
==>    [3]:
==>       30.275887674726032286743188295434289374080381269447
==>    [4]:
==>       20.545113781774359545337196348293700650312797803894