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Control over Malmquist
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1 changed files with 40 additions and 17 deletions
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@ -356,7 +356,8 @@ def e2_distmod_TFR(e2_mag, e2_eta, eta, b, c, e_mu_intrinsic):
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def sample_TFR(e_mu_min, e_mu_max, a_mean, a_std, b_mean, b_std,
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c_mean, c_std, alpha_min, alpha_max, sample_alpha,
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a_dipole_mean, a_dipole_std, sample_a_dipole, name):
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a_dipole_mean, a_dipole_std, sample_a_dipole,
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sample_curvature, name):
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"""Sample Tully-Fisher calibration parameters."""
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e_mu = sample(f"e_mu_{name}", Uniform(e_mu_min, e_mu_max))
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a = sample(f"a_{name}", Normal(a_mean, a_std))
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@ -367,7 +368,11 @@ def sample_TFR(e_mu_min, e_mu_max, a_mean, a_std, b_mean, b_std,
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ax, ay, az = 0.0, 0.0, 0.0
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b = sample(f"b_{name}", Normal(b_mean, b_std))
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if sample_curvature:
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c = sample(f"c_{name}", Normal(c_mean, c_std))
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else:
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c = 0.
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alpha = sample_alpha_bias(name, alpha_min, alpha_max, sample_alpha)
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@ -513,12 +518,18 @@ class PV_LogLikelihood(BaseFlowValidationModel):
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Whether to directly sample the distance without numerical
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marginalisation. in which case the tracers can be coupled by a
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covariance matrix. By default `False`.
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with_homogeneous_malmquist : bool, optional
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Whether to include the homogeneous Malmquist bias. By default `True`.
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with_inhomogeneous_malmquist : bool, optional
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Whether to include the inhomogeneous Malmquist bias. By default `True`.
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"""
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def __init__(self, los_density, los_velocity, RA, dec, z_obs, e_zobs,
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calibration_params, abs_calibration_params, mag_selection,
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r_xrange, Omega_m, kind, name, void_kwargs=None,
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wo_num_dist_marginalisation=False):
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wo_num_dist_marginalisation=False,
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with_homogeneous_malmquist=True,
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with_inhomogeneous_malmquist=True):
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if e_zobs is not None:
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e2_cz_obs = jnp.asarray((SPEED_OF_LIGHT * e_zobs)**2)
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else:
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@ -557,6 +568,8 @@ class PV_LogLikelihood(BaseFlowValidationModel):
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self.name = name
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self.Omega_m = Omega_m
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self.wo_num_dist_marginalisation = wo_num_dist_marginalisation
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self.with_homogeneous_malmquist = with_homogeneous_malmquist
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self.with_inhomogeneous_malmquist = with_inhomogeneous_malmquist
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self.norm = - self.ndata * jnp.log(self.num_sims)
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if mag_selection is not None:
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@ -771,9 +784,14 @@ class PV_LogLikelihood(BaseFlowValidationModel):
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"marginalising the true distance.")
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# Calculate p(r) (Malmquist bias). Shape is (ndata, nxrange)
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if self.with_homogeneous_malmquist:
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log_ptilde = log_ptilde_wo_bias(
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self.mu_xrange[None, :], mu[:, None], e2_mu[:, None],
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self.log_r2_xrange[None, :])
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else:
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log_ptilde = log_ptilde_wo_bias(
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self.mu_xrange[None, :], mu[:, None], e2_mu[:, None],
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0.)
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if self.is_void_data:
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rLG = field_calibration_params["rLG"]
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@ -785,7 +803,9 @@ class PV_LogLikelihood(BaseFlowValidationModel):
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# Inhomogeneous Malmquist bias. Shape: (nsims, ndata, nxrange)
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alpha = distmod_params["alpha"]
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log_ptilde = log_ptilde[None, ...] + alpha * log_los_density
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log_ptilde = log_ptilde[None, ...]
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if self.with_inhomogeneous_malmquist:
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log_ptilde += alpha * log_los_density
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ptilde = jnp.exp(log_ptilde)
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# Normalization of p(r). Shape: (nsims, ndata)
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@ -840,11 +860,13 @@ class PV_LogLikelihood(BaseFlowValidationModel):
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alpha = distmod_params["alpha"]
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# Normalisation of p(mu), shape is `(n_sims, n_data, n_rad)`
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pnorm = (
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+ self.log_r2_xrange[None, None, :]
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+ alpha * log_los_density_grid
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+ normal_logpdf(
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self.mu_xrange[None, :], mu[:, None], e_mu[:, None])[None, ...]) # noqa
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pnorm = normal_logpdf(
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self.mu_xrange[None, :], mu[:, None], e_mu[:, None])[None, ...]
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if self.with_homogeneous_malmquist:
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pnorm += self.log_r2_xrange[None, None, :]
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if self.with_inhomogeneous_malmquist:
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pnorm += alpha * log_los_density_grid
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pnorm = jnp.exp(pnorm)
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# Now integrate over the radial steps. Shape is `(nsims, ndata)`.
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# No Jacobian here because I integrate over distance, not the
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@ -855,11 +877,12 @@ class PV_LogLikelihood(BaseFlowValidationModel):
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jac = jnp.abs(distmod2dist_gradient(mu_true, self.Omega_m))
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# Calculate unnormalized log p(mu). Shape is (nsims, ndata)
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ll = (
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+ jnp.log(jac)[None, :]
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+ (2 * jnp.log(r_true) - self.log_r2_xrange_mean)[None, :]
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+ alpha * log_density
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)
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ll = 0.
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if self.with_homogeneous_malmquist:
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ll = (+ jnp.log(jac)
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+ (2 * jnp.log(r_true) - self.log_r2_xrange_mean))
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if self.with_inhomogeneous_malmquist:
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ll += alpha * log_density
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# Subtract the normalization. Shape remains (nsims, ndata)
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ll -= jnp.log(pnorm)
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