double QUpdater::GraphLogLikelihood(curr_par_obj* current_values, global_par_obj* global_pars)
{
double loglike;
double l, u, kappa, theta;
lb = hyperpar[0];
ub = hyperpar[1];
kappa = hyperpar[2];
theta = hyperpar[3];
loglike = distributions->LogDensity(4,current_values->q, kappa, theta) - log(gsl_cdf_gamma_Q(l, kappa, theta));
if( (current_values->q < l) || (current_values->q > u) )
loglike = -1.0*INFINITY;
return loglike;
}
double
gsl_cdf_poisson_P (const unsigned int k, const double mu)
{
double P;
double a;
if (mu <= 0.0)
{
CDF_ERROR ("mu <= 0", GSL_EDOM);
}
a = (double) k + 1.0;
P = gsl_cdf_gamma_Q (mu, a, 1.0);
return P;
}
double
gsl_cdf_gamma_Qinv (const double Q, const double a, const double b)
{
double x;
if (Q == 1.0)
{
return 0.0;
}
else if (Q == 0.0)
{
return GSL_POSINF;
}
/* Consider, small, large and intermediate cases separately. The
boundaries at 0.05 and 0.95 have not been optimised, but seem ok
for an initial approximation. */
if (Q < 0.05)
{
double x0 = -log (Q) + gsl_sf_lngamma (a);
x = x0;
}
else if (Q > 0.95)
{
double x0 = exp ((gsl_sf_lngamma (a) + log1p (-Q)) / a);
x = x0;
}
else
{
double xg = gsl_cdf_ugaussian_Qinv (Q);
double x0 = (xg < -0.5*sqrt (a)) ? a : sqrt (a) * xg + a;
x = x0;
}
/* Use Lagrange's interpolation for E(x)/phi(x0) to work backwards
to an improved value of x (Abramowitz & Stegun, 3.6.6)
where E(x)=P-integ(phi(u),u,x0,x) and phi(u) is the pdf.
*/
{
double lambda, dQ, phi;
unsigned int n = 0;
start:
dQ = Q - gsl_cdf_gamma_Q (x, a, 1.0);
phi = gsl_ran_gamma_pdf (x, a, 1.0);
if (dQ == 0.0 || n++ > 32)
goto end;
lambda = -dQ / GSL_MAX (2 * fabs (dQ / x), phi);
{
double step0 = lambda;
double step1 = -((a - 1) / x - 1) * lambda * lambda / 4.0;
double step = step0;
if (fabs (step1) < 0.5 * fabs (step0))
step += step1;
if (x + step > 0)
x += step;
else
{
x /= 2.0;
}
if (fabs (step0) > 1e-10 * x)
goto start;
}
}
end:
return b * x;
}
double
gsl_cdf_chisq_Q (const double x, const double nu)
{
return gsl_cdf_gamma_Q (x, nu / 2, 2.0);
}
