butools.fitting.LikelihoodFromTrace¶

butools.fitting.LikelihoodFromTrace()¶

Matlab:	logli = LikelihoodFromTrace(trace, X, Y, prec)
Mathematica:	logli = LikelihoodFromTrace[trace, X, Y, prec]
Python/Numpy:	logli = LikelihoodFromTrace(trace, X, Y, prec)

Evaluates the log-likelihood of a trace with the given PH distribution or MAP. The result is divided by the length of the trace.

If X is a row vector, than (X,Y) is interpreted as a PH distribution, otherwise (X,Y) is considered to be a MAP.

Parameters:

trace : column vector, length K The samples of the trace X : matrix, shape (1,M) or (M,M) If X is a row vector, it is the initial probability vector of the PH distribution. If X is a square matrix, it is interpreted as the D0 matrix of a MAP Y : matrix, (M,M) If X is a row vector, Y is the transient generator of the PH distribution. If X is a square matrix, Y is interpreted as the D1 matrix of a MAP prec : double, optional Numerical precision used by the randomization. The default value is 1e-14.

Returns:

logli : double The log likelihood divided by the size of the trace

Notes

The procedure is much faster with PH distributions.

Examples

For Matlab:

>>> tr = dlmread('/home/gabor/github/butools/test/data/bctrace.iat');
>>> [alpha, A] = APHFrom3Moments(MarginalMomentsFromTrace(tr, 3));
>>> [D0, D1] = MAPFromFewMomentsAndCorrelations(MarginalMomentsFromTrace(tr, 3), LagCorrelationsFromTrace(tr, 1));
>>> logliPH = LikelihoodFromTrace(tr, alpha, A);
>>> disp(logliPH);
       4.8496
>>> logliMAP = LikelihoodFromTrace(tr, D0, D1);
>>> disp(logliMAP);
       4.6523

For Mathematica:

>>> tr = Flatten[Import["/home/gabor/github/butools/test/data/bctrace.iat","CSV"]];
>>> {alpha, A} = APHFrom3Moments[MarginalMomentsFromTrace[tr, 3]];
>>> {D0, D1} = MAPFromFewMomentsAndCorrelations[MarginalMomentsFromTrace[tr, 3], LagCorrelationsFromTrace[tr, 1][[1]]];
>>> logliPH = LikelihoodFromTrace[tr, alpha, A];
>>> Print[logliPH];
4.849635301970579
>>> logliMAP = LikelihoodFromTrace[tr, D0, D1];
>>> Print[logliMAP];
4.65234643278208

For Python/Numpy:

>>> tr = np.loadtxt("/home/gabor/github/butools/test/data/bctrace.iat")
>>> alpha, A = APHFrom3Moments(MarginalMomentsFromTrace(tr, 3))
>>> D0, D1 = MAPFromFewMomentsAndCorrelations(MarginalMomentsFromTrace(tr, 3), LagCorrelationsFromTrace(tr, 1)[0])
>>> logliPH = LikelihoodFromTrace(tr, alpha, A)
>>> print(logliPH)
4.84963530196
>>> logliMAP = LikelihoodFromTrace(tr, D0, D1)
>>> print(logliMAP)
4.652346100436191