How to use the pymc.invlogit function in pymc

        @mc.deterministic(name=key)
        def rate_stoch(mu=mu):
            return mc.invlogit(mu)

        @mc.deterministic(name=key)
        def rate_stoch(logit_rate=logit_rate):
            return interpolate(param_mesh, mc.invlogit(logit_rate), est_mesh)

    @mc.deterministic
    def C_0(logit_C_0=logit_C_0):
        return mc.invlogit(logit_C_0)

# make sure that there is something to observe
        if mesh == []:
            continue
        
        # uncomment the following line to make more inferences than
        # are valid from the data
        #gp.observe(M, C, mesh, obs, V)

        # uncomment the following 2 lines to make less inferences than
        # possible: it may be better to waste information than have
        # false confidence
        ii = len(mesh)/2
        gp.observe(M, C, [mesh[ii]], [obs[ii]], [V[ii]])

    x = asrf.fit['out_age_mesh']
    na_rate = mc.invlogit(M(x))
    asrf.fit['normal_approx'] = list(na_rate)
    asrf.save()

    return M, C

def theta(a=alpha, b=beta):
    """theta = logit^{-1}(a+b)"""
    return pymc.invlogit(a + b * x)

XX_pred = sm.add_constant(X_pred)


model = sm.OLS(Y, XX)
results = model.fit()
Y_pred = model.predict(XX_pred)

pl.plot(X_pred, Y_pred, 'k-', linewidth=2, label='Predicted by OLS')


Y = mc.logit(df['Parameter Value'].__array__())
model = sm.OLS(Y, XX)
results = model.fit()
Y_pred = model.predict(XX_pred)

pl.plot(X_pred, mc.invlogit(Y_pred), 'k--', linewidth=2, label='Predicted by logit-transformed OLS')


pl.xlabel('Age (Years)')
pl.ylabel('Seroprevalence (Per 1)')
pl.legend(loc='lower right', fancybox=True, shadow=True)
pl.axis([-5, 55, 0, 1.2])
pl.grid()

pl.savefig('vzv_forest.pdf')

### setup the generic disease model (without prevalence data)
    import dismod3.gbd_disease_model as model
    keys = dismod3.utils.gbd_keys(region_list=[region], year_list=[year], sex_list=[sex])
    dm.calc_effective_sample_size(dm.data)
    dm.vars = model.setup(dm, keys)


    ## override the birth prevalence prior, based on the withheld prevalence data
    logit_C_0 = dm.vars[dismod3.utils.gbd_key_for('bins', region, year, sex)]['initial']['logit_C_0']
    assert len(prev_data) == 1, 'should be a single prevalance datum'
    d = prev_data[0]

    mu_logit_C_0 = mc.logit(dm.value_per_1(d)+dismod3.settings.NEARLY_ZERO)
    lb, ub = dm.bounds_per_1(d)
    sigma_logit_C_0 = (mc.logit(ub+dismod3.settings.NEARLY_ZERO) - mc.logit(lb+dismod3.settings.NEARLY_ZERO)) / (2 * 1.96)
    print 'mu_C_0_pri:', mc.invlogit(mu_logit_C_0)
    print 'ui_C_0_pri:', lb, ub

    # override the excess-mortality, based on the relative-risk data
    mu_rr = 1.01*np.ones(dismod3.settings.MAX_AGE)
    sigma_rr = .01*np.ones(dismod3.settings.MAX_AGE)
    for d in rr_data:
        mu_rr[d['age_start']:(d['age_end']+1)] = dm.value_per_1(d)
        sigma_rr[d['age_start']:(d['age_end']+1)] = dm.se_per_1(d)
    print 'mu_rr:', mu_rr.round(2)
    #print 'sigma_rr:', sigma_rr.round(2)

    log_f = dm.vars[dismod3.utils.gbd_key_for('excess-mortality', region, year, sex)]['age_coeffs']
    log_f_mesh = log_f.parents['gamma_mesh']
    param_mesh = log_f.parents['param_mesh']
    
    m_all = dm.vars[dismod3.utils.gbd_key_for('all-cause_mortality', region, year, sex)]

    @mc.deterministic(name=key)
    def rate_stoch(logit_rate=logit_rate, age_intervals=aa):
        return mc.invlogit(logit_rate(age_intervals))