def numerator_integrand(r):
out = np.zeros_like(r)
vesc = m.vesc_model(r,0.,0.,params,model)
out[vesc<=v] = 0.
out[vesc>v] = (m.vesc_model(r[vesc>v],0.,0.,params,model) - v)**(k+1.) * spline(r[vesc>v])
return out
def outlier_probabilities(params, data, vmin, model):
"""
Likelihood function template for given model.
Arguments
---------
params: array_like
the model parameters
data: list
the output of sample_distances_multiple_tracers
vmin: float
the minimum radial velocity considered
Returns
-------
logL: array_like
the sum of the log-likelihoods for this set of parameters.
"""
kbhb,kkgiant,kms,f = params[:4]
pot_params = params[4:]
outlier_probabilities = [None,None,None]
k = [kbhb,kkgiant,kms]
outlier_normalisation = ( .5*m.erfc( vmin / (np.sqrt(2.)*1000.) ) )**-1.
for i,tracer in enumerate(data):
l,b,v,s = tracer
x,y,z = gu.galactic2cartesian(s,b,l)
vesc = m.vesc_model(x,y,z,pot_params,model)
out = np.zeros_like(v)
with m.warnings.catch_warnings():
#deliberately getting NaNs here so stop python from telling us about it
m.warnings.simplefilter("ignore",category=RuntimeWarning)
out = (1.-f)*(k[i]+2)*(vesc - np.abs(v))**(k[i]+1.) / (vesc - vmin)**(k[i]+2.) + \
f*outlier_normalisation*m.Gaussian(np.abs(v),0.,1000.)
out[np.isnan(out)] = f*outlier_normalisation*m.Gaussian(np.abs(v[np.isnan(out)]),0.,1000.)
outlier = f*outlier_normalisation*m.Gaussian(np.abs(v),0.,1000.)
outlier_probabilities[i] = np.mean(outlier,axis=1) / np.mean(out, axis=1)
return outlier_probabilities
def denominator_integrand(r):
return spline(r)*(m.vesc_model(r,0.,0.,params,model) - vmin)**(k+2.) / (k+2.)
def m_vesc(r, params):
return -m.vesc_model(r, 0., 0., params, model)
def vesc(r, params):
return m.vesc_model(r, 0., 0., params, model)