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D.15.9.5 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
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