By default, solverMLE outputs the MLE for the covariance matrix. By setting solverMLE(...,ConcentrationMatrix=>...) to true, solverMLE provides the MLE for the concentration matrix.
Note that both the maximum value attained in the log-likelihood function and the ML-degree remain the same.
i1 : G= mixedGraph(graph{{a,b},{b,c}},digraph {{a,d},{c,e},{f,g}},bigraph {{d,e}}) o1 = MixedGraph{Bigraph => Bigraph{d => {e}}} e => {d} Digraph => Digraph{a => {d}} c => {e} d => {} e => {} f => {g} g => {} Graph => Graph{a => {b} } b => {a, c} c => {b} o1 : MixedGraph |
i2 : solverMLE (G, random(QQ^7,QQ^7)) o2 = (-8.88546, | 1.76276 -.132596 .0588765 1.19122 -.0121464 0 0 |, 5) | -.132596 .406406 -.180456 -.0896046 .0372285 0 0 | | .0588765 -.180456 4.53915 .0397869 -.93644 0 0 | | 1.19122 -.0896046 .0397869 4.6897 5.61757 0 0 | | -.0121464 .0372285 -.93644 5.61757 9.69158 0 0 | | 0 0 0 0 0 2.42434 -.115437 | | 0 0 0 0 0 -.115437 .171669 | o2 : Sequence |
i3 : solverMLE (G, random(QQ^7,QQ^7), ConcentrationMatrix=>true) o3 = (-6.95349, | 2.63818 .250925 -.421645 1.01192 .164301 0 0 |, 5) | .250925 .493839 .0300089 0 0 0 0 | | -.421645 .0300089 6.42505 -.309127 -.386315 0 0 | | 1.01192 0 -.309127 .741884 .120456 0 0 | | .164301 0 -.386315 .120456 .150534 0 0 | | 0 0 0 0 0 2.54322 -2.42347 | | 0 0 0 0 0 -2.42347 3.70744 | o3 : Sequence |