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Absmag (#149)
* Add spacing * Add various cleanups of the code * Add basic updates * Add
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Richard Stiskalek
GitHub
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4fa0e04f6e
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5336c0296c
@ -45,13 +45,13 @@ H0 = 100 # km / s / Mpc
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# JAX Flow model #
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###############################################################################
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def dist2redshift(dist, Omega_m):
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def dist2redshift(dist, Omega_m, h=1.):
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"""
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Convert comoving distance to cosmological redshift if the Universe is
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flat and z << 1.
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"""
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eta = 3 * Omega_m / 2
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return 1 / eta * (1 - (1 - 2 * H0 * dist / SPEED_OF_LIGHT * eta)**0.5)
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return 1 / eta * (1 - (1 - 2 * 100 * h * dist / SPEED_OF_LIGHT * eta)**0.5)
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def redshift2dist(z, Omega_m):
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@ -366,11 +366,6 @@ def sample_calibration(Vext_min, Vext_max, Vmono_min, Vmono_max, beta_min,
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}
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###############################################################################
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# PV calibration model #
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###############################################################################
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def sample_gaussian_hyperprior(param, name, xmin, xmax):
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"""Sample MNR Gaussian hyperprior mean and standard deviation."""
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mean = sample(f"{param}_mean_{name}", Uniform(xmin, xmax))
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@ -378,9 +373,15 @@ def sample_gaussian_hyperprior(param, name, xmin, xmax):
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return mean, std
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###############################################################################
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# PV calibration model without absolute calibration #
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###############################################################################
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class PV_LogLikelihood(BaseFlowValidationModel):
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"""
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Peculiar velocity validation model log-likelihood.
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Peculiar velocity validation model log-likelihood with numerical
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integration of the true distances.
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Parameters
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----------
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@ -408,11 +409,15 @@ class PV_LogLikelihood(BaseFlowValidationModel):
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Catalogue kind, either "TFR", "SN", or "simple".
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name : str
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Name of the catalogue.
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with_num_dist_marginalisation : bool, optional
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Whether to use numerical distance marginalisation, in which case
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the tracers cannot be coupled by a covariance matrix. By default
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`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):
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r_xrange, Omega_m, kind, name, with_num_dist_marginalisation):
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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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@ -433,8 +438,12 @@ class PV_LogLikelihood(BaseFlowValidationModel):
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self.kind = kind
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self.name = name
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self.Omega_m = Omega_m
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self.with_num_dist_marginalisation = with_num_dist_marginalisation
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self.norm = - self.ndata * jnp.log(self.num_sims)
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# TODO: Somewhere here prepare the interpolators in case of no
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# numerical marginalisation.
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if mag_selection is not None:
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self.mag_selection_kind = mag_selection["kind"]
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@ -485,6 +494,9 @@ class PV_LogLikelihood(BaseFlowValidationModel):
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Vmono = field_calibration_params["Vmono"]
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Vext_rad = project_Vext(Vext[0], Vext[1], Vext[2], self.RA, self.dec)
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# ------------------------------------------------------------
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# 1. Sample true observables and obtain the distance estimate
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# ------------------------------------------------------------
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e_mu = distmod_params["e_mu"]
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if self.kind == "SN":
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mag_cal = distmod_params["mag_cal"]
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@ -532,10 +544,6 @@ class PV_LogLikelihood(BaseFlowValidationModel):
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mu = distmod_SN(
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mag_true, x1_true, c_true, mag_cal, alpha_cal, beta_cal)
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if field_calibration_params["sample_h"]:
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raise NotImplementedError("H0 for SN not implemented.")
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elif self.kind == "TFR":
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a = distmod_params["a"]
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b = distmod_params["b"]
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@ -605,11 +613,6 @@ class PV_LogLikelihood(BaseFlowValidationModel):
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e2_mu = jnp.ones_like(mag_true) * e_mu**2
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mu = distmod_TFR(mag_true, eta_true, a, b, c)
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if field_calibration_params["sample_h"]:
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raise NotImplementedError("H0 for TFR not implemented.")
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# mu -= 5 * jnp.log10(field_calibration_params["h"])
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elif self.kind == "simple":
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dmu = distmod_params["dmu"]
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@ -628,61 +631,73 @@ class PV_LogLikelihood(BaseFlowValidationModel):
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e2_mu = jnp.ones_like(mag_true) * e_mu**2
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mu = mu_true + dmu
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if field_calibration_params["sample_h"]:
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raise NotImplementedError("H0 for simple not implemented.")
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else:
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raise ValueError(f"Unknown kind: `{self.kind}`.")
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# Calculate p(r) (Malmquist bias). Shape is (ndata, nxrange)
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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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# h = field_calibration_params["h"]
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# ----------------------------------------------------------------
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# 2. Log-likelihood of the true distance and observed redshifts.
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# The marginalisation of the true distance can be done numerically.
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# ----------------------------------------------------------------
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if self.with_num_dist_marginalisation:
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# Inhomogeneous Malmquist bias. Shape is (n_sims, ndata, nxrange)
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alpha = distmod_params["alpha"]
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log_ptilde = log_ptilde[None, ...] + alpha * self.log_los_density
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if field_calibration_params["sample_h"]:
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raise NotImplementedError("Sampling of h not implemented.")
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# Rescale the grid to account for the sampled H0. For distance
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# modulus going from Mpc / h to Mpc implies larger numerical
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# values, so there has to be a minus sign since h < 1.
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# mu_xrange = self.mu_xrange - 5 * jnp.log(h)
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ptilde = jnp.exp(log_ptilde)
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# The redshift should also be boosted since now the object are
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# further away?
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# Normalization of p(r). Shape is (n_sims, ndata)
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pnorm = simpson(ptilde, x=self.r_xrange, axis=-1)
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# Actually, the redshift ought to remain the same?
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else:
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mu_xrange = self.mu_xrange
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# Calculate z_obs at each distance. Shape is (n_sims, ndata, nxrange)
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vrad = field_calibration_params["beta"] * self.los_velocity
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vrad += (Vext_rad[None, :, None] + Vmono)
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zobs = (1 + self.z_xrange[None, None, :]) * (1 + vrad / SPEED_OF_LIGHT)
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zobs -= 1.
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# Calculate p(r) (Malmquist bias). Shape is (ndata, nxrange)
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log_ptilde = log_ptilde_wo_bias(
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mu_xrange[None, :], mu[:, None], e2_mu[:, None],
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self.log_r2_xrange[None, :])
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# Shape remains (n_sims, ndata, nxrange)
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ptilde *= likelihood_zobs(
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self.z_obs[None, :, None], zobs, e2_cz[None, :, None])
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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 * self.log_los_density
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if self.with_absolute_calibration:
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raise NotImplementedError("Absolute calibration not implemented.")
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# Absolute calibration likelihood, the shape is now
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# (ndata_with_calibration, ncalib, nxrange)
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# ll_calibration = normal_logpdf(
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# self.mu_xrange[None, None, :],
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# self.calibration_distmod[..., None],
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# self.calibration_edistmod[..., None])
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ptilde = jnp.exp(log_ptilde)
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# # Average the likelihood over the calibration points. The shape
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# is
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# # now (ndata, nxrange)
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# ll_calibration = logsumexp(
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# jnp.nan_to_num(ll_calibration, nan=-jnp.inf), axis=1)
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# # This is the normalisation because we want the *average*.
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# ll_calibration -= self.log_length_calibration[:, None]
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# Normalization of p(r). Shape: (nsims, ndata)
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pnorm = simpson(ptilde, x=self.r_xrange, axis=-1)
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# ptilde = ptilde.at[:, self.data_with_calibration, :].
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# multiply(jnp.exp(ll_calibration))
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# Calculate z_obs at each distance. Shape: (nsims, ndata, nxrange)
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vrad = field_calibration_params["beta"] * self.los_velocity
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vrad += (Vext_rad[None, :, None] + Vmono)
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zobs = 1 + self.z_xrange[None, None, :]
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zobs *= 1 + vrad / SPEED_OF_LIGHT
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zobs -= 1.
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# Integrate over the radial distance. Shape is (n_sims, ndata)
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ll = jnp.log(simpson(ptilde, x=self.r_xrange, axis=-1))
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ll -= jnp.log(pnorm)
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# Shape remains (nsims, ndata, nxrange)
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ptilde *= likelihood_zobs(
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self.z_obs[None, :, None], zobs, e2_cz[None, :, None])
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return ll0 + jnp.sum(logsumexp(ll, axis=0)) + self.norm
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if self.with_absolute_calibration:
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raise NotImplementedError(
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"Absolute calibration not implemented for this model. "
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"Use `PV_LogLikelihood_NoDistMarg` instead.")
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# Integrate over the radial distance. Shape: (nsims, ndata)
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ll = jnp.log(simpson(ptilde, x=self.r_xrange, axis=-1))
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ll -= jnp.log(pnorm)
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return ll0 + jnp.sum(logsumexp(ll, axis=0)) + self.norm
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else:
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raise NotImplementedError(
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"No distance marginalisation not implemented yet.")
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###############################################################################
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# Combining several catalogues #
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###############################################################################
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def PV_validation_model(models, distmod_hyperparams_per_model,
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