Log10Likelihood¶

The purpose of this class is to provide an interface for maximizing the likelihood. It computes, for a given set of observed open and shut intervals, the likelihood \(\frac{\ln(L(Q))}{ln 10}\), where \(L(Q)\) is declared in the likelihood equation.

Likelihood of a set of bursts.

This functor takes as input a Q-matrix and returns the likelihood for a given set of bursts. It is, in practice, a convenience object with which to perform likelihood optimization.

At each call, it creates a likelihood object MissedEventsG using the input parameters given during initialization, and the Q-matrix given on input. It then returns the log10 likelihood for the set of bursts given on input.

Public Functions

Log10Likelihood(t_Bursts const & _bursts, t_uint _nopen, t_real _tau, t_real _tcritical = -1e0, t_uint _nmax = 2, t_real _xtol = 1e-10, t_real _rtol = 1e-10, t_uint _itermax = 100, t_real _lowerbound = quiet_nan, t_real _upperbound = quiet_nan)

Constructor

Parameters

• _bursts -

  A vector of bursts. Each burst is a vector of intervals, starting with an open interval. The intervals should be prefiltered for the maximum missed-event length.

• _nopen -

  Number of open states. The open states must be in the top left corner of the Q-matrix.

• _tau -

  Maximum length of the missed events

• _tcritical -

  Parameter for CHS vectors (see[2]) if positive. If negative, then equilibrium occupancies will be used as initial and final states (as in[1])

• _nmax -

  The exact missed-event likelihood will be computed for \( t < n_{\mathrm{max}} \tau\)

• _xtol -

  Tolerance criteria for brentq().

• _rtol -

  Tolerance criteria for brentq().

• _itermax -

  Maximum number of iteration when calling brentq().

• _lowerbound -

  Lower bound of the interval bracketing all roots. If None, the lower bound is obtained from find_lower_bound_for_roots().

• _upperbound -

  Upper bound of the interval bracketing all roots. If None, the upper bound is obtained from find_upper_bound_for_roots().

t_rvector vector(t_rmatrix const & _Q)

Computes likelihood for each burst.

Return

a DCProgs::t_rvector

t_rvector vector(QMatrix const & _Q)

Computes likelihood for each burst.

Return

a DCProgs::t_rvector

t_real operator()(t_rmatrix const & _Q)

Log-likelihood.

t_real operator()(QMatrix const & _Q)

Log-likelihood.

Public Members

t_Bursts bursts

Set of bursts for which to compute the likelihood.

t_uint nopen

Number of open states.

t_real tau

Max length of missed events.

t_real tcritical

\(t_{\mathrm{crit}}\).

If negative or null, will use equilibrium occupancies rather than CHS occupancies.

t_uint nmax

Number of intervals for which to compute exact result.

t_real xtol

Tolerance for root finding.

t_real rtol

Tolerance for root finding.

t_uint itermax

Maximum number of iterations for root finding.

t_real lower_bound

Lower bound bracketing all roots.

t_real upper_bound

Upper bound bracketing all roots.