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Add SN calibration model
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rstiskalek
parent
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commit
088b15429b
1 changed files with 164 additions and 72 deletions
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@ -538,13 +538,15 @@ class SD_PV_validation_model:
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def __init__(self, los_density, los_velocity, RA, dec, z_obs,
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def __init__(self, los_density, los_velocity, RA, dec, z_obs,
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r_hMpc, e_r_hMpc, r_xrange, Omega_m):
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r_hMpc, e_r_hMpc, r_xrange, Omega_m):
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# Convert everything to JAX arrays.
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dt = jnp.float32
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dt = jnp.float32
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# Convert everything to JAX arrays.
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self._los_density = jnp.asarray(los_density, dtype=dt)
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self._los_density = jnp.asarray(los_density, dtype=dt)
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self._los_velocity = jnp.asarray(los_velocity, dtype=dt)
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self._los_velocity = jnp.asarray(los_velocity, dtype=dt)
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self._RA = jnp.asarray(np.deg2rad(RA), dtype=dt)
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self._RA = jnp.asarray(np.deg2rad(RA), dtype=dt)
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self._dec = jnp.asarray(np.deg2rad(dec), dtype=dt)
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self._dec = jnp.asarray(np.deg2rad(dec), dtype=dt)
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self._z_obs = jnp.asarray(z_obs, dtype=dt)
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self._z_obs = jnp.asarray(z_obs, dtype=dt)
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self._r_hMpc = jnp.asarray(r_hMpc, dtype=dt)
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self._r_hMpc = jnp.asarray(r_hMpc, dtype=dt)
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self._e_rhMpc = jnp.asarray(e_r_hMpc, dtype=dt)
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self._e_rhMpc = jnp.asarray(e_r_hMpc, dtype=dt)
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@ -564,37 +566,39 @@ class SD_PV_validation_model:
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self._vmap_zobs = vmap(lambda beta, Vr, vpec_rad: predict_zobs(r_xrange, beta, Vr, vpec_rad, Omega_m), in_axes=(None, 0, 0)) # noqa
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self._vmap_zobs = vmap(lambda beta, Vr, vpec_rad: predict_zobs(r_xrange, beta, Vr, vpec_rad, Omega_m), in_axes=(None, 0, 0)) # noqa
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self._vmap_ll_zobs = vmap(lambda zobs, zobs_pred, sigma_v: calculate_ll_zobs(zobs, zobs_pred, sigma_v), in_axes=(0, 0, None)) # noqa
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self._vmap_ll_zobs = vmap(lambda zobs, zobs_pred, sigma_v: calculate_ll_zobs(zobs, zobs_pred, sigma_v), in_axes=(0, 0, None)) # noqa
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# Vext_x, Vext_y, Vext_z: external velocity components
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# Distribution of external velocity components
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self._dist_Vext = dist.Uniform(-1000, 1000)
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self._Vext = dist.Uniform(-1000, 1000)
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# We want sigma_v to be 150 +- 100 km / s (lognormal)
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# Distribution of density, velocity and location bias parameters
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self._dist_sigma_v = dist.LogNormal(
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self._alpha = dist.LogNormal(*lognorm_mean_std_to_loc_scale(1.0, 0.5)) # noqa
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*lognorm_mean_std_to_loc_scale(150, 100))
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self._beta = dist.Normal(1., 0.5)
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# Density power-law bias
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self._h = dist.LogNormal(*lognorm_mean_std_to_loc_scale(1.0, 0.5))
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self._dist_alpha = dist.LogNormal(
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# Distribution of velocity uncertainty sigma_v
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*lognorm_mean_std_to_loc_scale(1.0, 0.5))
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self._sv = dist.LogNormal(*lognorm_mean_std_to_loc_scale(150, 100))
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# Velocity bias
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self._dist_beta = dist.Normal(1., 0.5)
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def __call__(self):
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def __call__(self, sample_alpha=False, scale_distance=False):
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"""
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"""
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The simple distance NumPyro PV validation model. Samples the following
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The simple distance NumPyro PV validation model.
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parameters:
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- `Vext_x`, `Vext_y`, `Vext_z`: external velocity components
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Parameters
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- `alpha`: density bias parameter
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----------
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- `beta`: velocity bias parameter
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sample_alpha : bool, optional
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- `sigma_v`: velocity uncertainty
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Whether to sample the density bias parameter `alpha`, otherwise
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it is fixed to 1.
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scale_distance : bool, optional
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Whether to scale the distance by `h`, otherwise it is fixed to 1.
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"""
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"""
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Vx = numpyro.sample("Vext_x", self._dist_Vext)
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Vx = numpyro.sample("Vext_x", self._Vext)
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Vy = numpyro.sample("Vext_y", self._dist_Vext)
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Vy = numpyro.sample("Vext_y", self._Vext)
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Vz = numpyro.sample("Vext_z", self._dist_Vext)
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Vz = numpyro.sample("Vext_z", self._Vext)
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alpha = numpyro.sample("alpha", self._dist_alpha)
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alpha = numpyro.sample("alpha", self._alpha) if sample_alpha else 1.0
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beta = numpyro.sample("beta", self._dist_beta)
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beta = numpyro.sample("beta", self._beta)
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sigma_v = numpyro.sample("sigma_v", self._dist_sigma_v)
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h = numpyro.sample("h", self._h) if scale_distance else 1.0
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sigma_v = numpyro.sample("sigma_v", self._sv)
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Vext_rad = project_Vext(Vx, Vy, Vz, self._RA, self._dec)
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Vext_rad = project_Vext(Vx, Vy, Vz, self._RA, self._dec)
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# Calculate p(r) and multiply it by the galaxy bias
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# Calculate p(r) and multiply it by the galaxy bias
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ptilde = self._vmap_ptilde_wo_bias(self._r_hMpc, self._e_rhMpc)
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ptilde = self._vmap_ptilde_wo_bias(h * self._r_hMpc, h * self._e_rhMpc)
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ptilde *= self._los_density**alpha
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ptilde *= self._los_density**alpha
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# Normalization of p(r)
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# Normalization of p(r)
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@ -608,50 +612,138 @@ class SD_PV_validation_model:
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numpyro.factor("ll", ll)
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numpyro.factor("ll", ll)
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# def SN_PV_wcal_validation_model(los_overdensity=None, los_velocity=None,
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class SN_PV_validation_model:
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# RA=None, dec=None, z_CMB=None,
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"""
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# mB=None, x1=None, c=None,
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Supernova peculiar velocity (PV) validation model that includes the
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# e_mB=None, e_x1=None, e_c=None,
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calibration of the SALT2 light curve parameters.
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# mu_xrange=None, r_xrange=None,
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# norm_r2_xrange=None, Omega_m=None, dr=None):
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Parameters
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# """
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----------
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# Pass
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los_density : 2-dimensional array of shape (n_objects, n_steps)
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# """
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LOS density field.
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# Vx = numpyro.sample("Vext_x", dist.Uniform(-1000, 1000))
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los_velocity : 3-dimensional array of shape (n_objects, n_steps)
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# Vy = numpyro.sample("Vext_y", dist.Uniform(-1000, 1000))
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LOS radial velocity field.
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# Vz = numpyro.sample("Vext_z", dist.Uniform(-1000, 1000))
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RA, dec : 1-dimensional arrays of shape (n_objects)
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# beta = numpyro.sample("beta", dist.Uniform(-10, 10))
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Right ascension and declination in degrees.
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#
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z_obs : 1-dimensional array of shape (n_objects)
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# # TODO: Later sample these as well.
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Observed redshifts.
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# e_mu_intrinsic = 0.064
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mB, x1, c : 1-dimensional arrays of shape (n_objects)
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# alpha_cal = 0.135
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SALT2 light curve parameters.
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# beta_cal = 2.9
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e_mB, e_x1, e_c : 1-dimensional arrays of shape (n_objects)
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# mag_cal = -18.555
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Errors on the SALT2 light curve parameters.
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# sigma_v = 112
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r_xrange : 1-dimensional array
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#
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Radial distances where the field was interpolated for each object.
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# # TODO: Check these for fiducial values.
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Omega_m : float
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# mu = mB - mag_cal + alpha_cal * x1 - beta_cal * c
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Matter density parameter.
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# squared_e_mu = e_mB**2 + alpha_cal**2 * e_x1**2 + beta_cal**2 * e_c**2
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"""
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#
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# squared_e_mu += e_mu_intrinsic**2
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def __init__(self, los_density, los_velocity, RA, dec, z_obs,
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# ll = 0.
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mB, x1, c, e_mB, e_x1, e_c, r_xrange, Omega_m):
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# for i in range(len(los_overdensity)):
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dt = jnp.float32
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# # Project the external velocity for this galaxy.
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# Convert everything to JAX arrays.
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# Vext_rad = project_Vext(Vx, Vy, Vz, RA[i], dec[i])
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self._los_density = jnp.asarray(los_density, dtype=dt)
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#
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self._los_velocity = jnp.asarray(los_velocity, dtype=dt)
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# dmu = mu_xrange - mu[i]
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# ptilde = norm_r2_xrange * jnp.exp(-0.5 * dmu**2 / squared_e_mu[i])
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self._RA = jnp.asarray(np.deg2rad(RA), dtype=dt)
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# # TODO: Add some bias
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self._dec = jnp.asarray(np.deg2rad(dec), dtype=dt)
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# ptilde *= (1 + los_overdensity[i])
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self._z_obs = jnp.asarray(z_obs, dtype=dt)
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#
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# zobs_pred = predict_zobs(r_xrange, beta, Vext_rad, los_velocity[i],
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self._mB = jnp.asarray(mB, dtype=dt)
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# Omega_m)
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self._x1 = jnp.asarray(x1, dtype=dt)
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#
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self._c = jnp.asarray(c, dtype=dt)
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# dczobs = SPEED_OF_LIGHT * (z_CMB[i] - zobs_pred)
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self._e2_mB = jnp.asarray(e_mB**2, dtype=dt)
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#
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self._e2_x1 = jnp.asarray(e_x1**2, dtype=dt)
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# ll_zobs = jnp.exp(-0.5 * (dczobs / sigma_v)**2) / sigma_v
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self._e2_c = jnp.asarray(e_c**2, dtype=dt)
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#
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# ll += jnp.log(simps(ptilde * ll_zobs, dr))
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# Get radius squared
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# ll -= jnp.log(simps(ptilde, dr))
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r2_xrange = r_xrange**2
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#
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r2_xrange /= r2_xrange.mean()
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# numpyro.factor("ll", ll)
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mu_xrange = dist2distmodulus(r_xrange, Omega_m)
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# Get the stepsize, we need it to be constant for Simpson's rule.
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dr = np.diff(r_xrange)
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if not np.all(np.isclose(dr, dr[0], atol=1e-5)):
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raise ValueError("The radial step size must be constant.")
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dr = dr[0]
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# Get the various vmapped functions
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self._vmap_ptilde_wo_bias = vmap(lambda mu, err: calculate_ptilde_wo_bias(mu_xrange, mu, err, r2_xrange)) # noqa
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self._vmap_simps = vmap(lambda y: simps(y, dr))
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self._vmap_zobs = vmap(lambda beta, Vr, vpec_rad: predict_zobs(r_xrange, beta, Vr, vpec_rad, Omega_m), in_axes=(None, 0, 0)) # noqa
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self._vmap_ll_zobs = vmap(lambda zobs, zobs_pred, sigma_v: calculate_ll_zobs(zobs, zobs_pred, sigma_v), in_axes=(0, 0, None)) # noqa
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# Distribution of external velocity components
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self._dist_Vext = dist.Uniform(-1000, 1000)
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# Distribution of velocity and density bias parameters
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self._dist_alpha = dist.LogNormal(*lognorm_mean_std_to_loc_scale(1.0, 0.5)) # noqa
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self._dist_beta = dist.Normal(1., 0.5)
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# Distribution of velocity uncertainty
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self._dist_sigma_v = dist.LogNormal(*lognorm_mean_std_to_loc_scale(150, 100)) # noqa
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# Distribution of light curve calibration parameters
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self._dist_mag_cal = dist.Normal(-18.25, 1.0)
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self._dist_alpha_cal = dist.Normal(0.1, 0.5)
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self._dist_beta_cal = dist.Normal(3.0, 1.0)
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self._dist_e_mu = dist.LogNormal(*lognorm_mean_std_to_loc_scale(0.1, 0.05)) # noqa
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def __call__(self, sample_alpha=False, fix_calibration=False):
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"""
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The supernova NumPyro PV validation model with SALT2 calibration.
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Parameters
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----------
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sample_alpha : bool, optional
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Whether to sample the density bias parameter `alpha`, otherwise
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it is fixed to 1.
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"""
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Vx = numpyro.sample("Vext_x", self._dist_Vext)
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Vy = numpyro.sample("Vext_y", self._dist_Vext)
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Vz = numpyro.sample("Vext_z", self._dist_Vext)
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if sample_alpha:
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alpha = numpyro.sample("alpha", self._dist_alpha)
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else:
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alpha = 1.0
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beta = numpyro.sample("beta", self._dist_beta)
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sigma_v = numpyro.sample("sigma_v", self._dist_sigma_v)
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if fix_calibration == "Foundation":
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# Foundation inverse best parameters
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e_mu_intrinsic = 0.064
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alpha_cal = 0.135
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beta_cal = 2.9
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sigma_v = 140
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mag_cal = -18.555
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elif fix_calibration == "LOSS":
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# LOSS inverse best parameters
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e_mu_intrinsic = 0.123
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alpha_cal = 0.123
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beta_cal = 3.52
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mag_cal = -18.195
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sigma_v = 140
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else:
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e_mu_intrinsic = numpyro.sample("e_mu_intrinsic", self._dist_e_mu)
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mag_cal = numpyro.sample("mag_cal", self._dist_mag_cal)
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alpha_cal = numpyro.sample("alpha_cal", self._dist_alpha_cal)
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beta_cal = numpyro.sample("beta_cal", self._dist_beta_cal)
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Vext_rad = project_Vext(Vx, Vy, Vz, self._RA, self._dec)
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mu = self._mB - mag_cal + alpha_cal * self._x1 - beta_cal * self._c
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squared_e_mu = (self._e2_mB
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+ alpha_cal**2 * self._e2_x1
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+ beta_cal**2 * self._e2_c)
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squared_e_mu += e_mu_intrinsic**2
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# Calculate p(r) and multiply it by the galaxy bias
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ptilde = self._vmap_ptilde_wo_bias(mu, squared_e_mu**0.5)
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ptilde *= self._los_density**alpha
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# Normalization of p(r)
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pnorm = self._vmap_simps(ptilde)
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# Calculate p(z_obs) and multiply it by p(r)
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zobs_pred = self._vmap_zobs(beta, Vext_rad, self._los_velocity)
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ptilde *= self._vmap_ll_zobs(self._z_obs, zobs_pred, sigma_v)
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ll = jnp.sum(jnp.log(self._vmap_simps(ptilde) / pnorm))
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numpyro.factor("ll", ll)
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