<SYSTEM_TASK:>
Solve the following problem using Python, implementing the functions described below, one line at a time
<END_TASK>
<USER_TASK:>
Description:

def fgmc(log_fg_ratios, mu_log_vt, sigma_log_vt, Rf, maxfg):
    '''
    Function to fit the likelihood Fixme
    '''

    Lb = np.random.uniform(0., maxfg, len(Rf))
    pquit = 0

    while pquit < 0.1:
        # quit when the posterior on Lf is very close to its prior

        nsamp = len(Lb)
        Rf_sel = np.random.choice(Rf, nsamp)
        vt = np.random.lognormal(mu_log_vt, sigma_log_vt, len(Rf_sel))

        Lf = Rf_sel * vt

        log_Lf, log_Lb = log(Lf), log(Lb)

        plR = 0
        for lfr in log_fg_ratios:
            plR += np.logaddexp(lfr + log_Lf, log_Lb)

        plR -= (Lf + Lb)
        plRn = plR - max(plR)

        idx = np.exp(plRn) > np.random.random(len(plRn))

        pquit = ss.stats.ks_2samp(Lb, Lb[idx])[1]

        Lb = Lb[idx]

    return Rf_sel[idx], Lf[idx], Lb