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Add Jeffrey priors
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rstiskalek
parent
498cca52b7
commit
53b48363a1
1 changed files with 29 additions and 58 deletions
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@ -31,9 +31,7 @@ from jax import jit
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from jax import numpy as jnp
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from jax.scipy.special import erf, logsumexp
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from numpyro import factor, plate, sample
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from numpyro.distributions import (Distribution, MultivariateNormal, Normal,
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Uniform, constraints)
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from numpyro.distributions.util import promote_shapes
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from numpyro.distributions import MultivariateNormal, Normal, Uniform
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from quadax import simpson
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from tqdm import trange
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@ -152,35 +150,6 @@ def upper_truncated_normal_logpdf(x, loc, scale, xmax):
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return normal_logpdf(x, loc, scale) - jnp.log(norm)
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###############################################################################
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# Inverse distribution #
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###############################################################################
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class InverseDistribution(Distribution):
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"""Inverse distribution."""
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support = constraints.positive
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args_contraints = {
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"low": constraints.positive,
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"high": constraints.positive,
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"fiducial_scale": constraints.positive,
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}
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reparametrized_params = ["low", "high"]
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def __init__(self, low, high, fiducial_scale=1.):
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self.low, self.high = promote_shapes(low, high)
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self.log_fiducial_scale = jnp.log(fiducial_scale)
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super(InverseDistribution, self).__init__(batch_shape=())
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def sample(self, key, sample_shape=()):
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z = Uniform(0, 1).sample(key, sample_shape)
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return self.high * (self.low / self.high)**z
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def log_prob(self, value):
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return - (jnp.log(value) - self.log_fiducial_scale)
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###############################################################################
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# Base flow validation #
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###############################################################################
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@ -345,13 +314,11 @@ def e2_distmod_SN(e2_mag, e2_x1, e2_c, alpha_cal, beta_cal, e_mu_intrinsic):
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+ e_mu_intrinsic**2)
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def sample_SN(mag_cal_mean, mag_cal_std, alpha_cal_mean, alpha_cal_std,
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beta_cal_mean, beta_cal_std, alpha_min, alpha_max,
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def sample_SN(e_mu_min, e_mu_max, mag_cal_mean, mag_cal_std, alpha_cal_mean,
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alpha_cal_std, beta_cal_mean, beta_cal_std, alpha_min, alpha_max,
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sample_alpha, name):
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"""Sample SNIe Tripp parameters."""
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# The low/high are used only to generate an initial guess, they only
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# have to be in the right order of magnitude so that's why hardcoded.
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e_mu = sample(f"e_mu_{name}", InverseDistribution(0.2, 0.5, 0.15))
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e_mu = sample(f"e_mu_{name}", Uniform(e_mu_min, e_mu_max))
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mag_cal = sample(f"mag_cal_{name}", Normal(mag_cal_mean, mag_cal_std))
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alpha_cal = sample(
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f"alpha_cal_{name}", Normal(alpha_cal_mean, alpha_cal_std))
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@ -383,18 +350,15 @@ def e2_distmod_TFR(e2_mag, e2_eta, eta, b, c, e_mu_intrinsic):
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return e2_mag + (b + 2 * c * eta)**2 * e2_eta + e_mu_intrinsic**2
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def sample_TFR(a_mean, a_std, b_mean, b_std, c_mean, c_std, alpha_min,
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alpha_max, sample_alpha, a_dipole_mean, a_dipole_std,
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sample_a_dipole, name):
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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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"""Sample Tully-Fisher calibration parameters."""
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# The low/high are used only to generate an initial guess, they only
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# have to be in the right order of magnitude so that's why hardcoded.
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e_mu = sample(f"e_mu_{name}", InverseDistribution(0.2, 0.5, 0.15))
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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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if sample_a_dipole:
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ax, ay, az = sample(f"a_dipole_{name}", Normal(
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a_dipole_mean, a_dipole_std).expand([3]))
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ax, ay, az = sample(f"a_dipole_{name}", Normal(a_dipole_mean, a_dipole_std).expand([3])) # noqa
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else:
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ax, ay, az = 0.0, 0.0, 0.0
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@ -417,13 +381,11 @@ def sample_TFR(a_mean, a_std, b_mean, b_std, c_mean, c_std, alpha_min,
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# Simple calibration parameters sampling #
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###############################################################################
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def sample_simple(dmu_min, dmu_max, alpha_min, alpha_max, dmu_dipole_mean,
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dmu_dipole_std, sample_alpha, sample_dmu_dipole, name):
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def sample_simple(e_mu_min, e_mu_max, dmu_min, dmu_max, alpha_min, alpha_max,
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dmu_dipole_mean, dmu_dipole_std, sample_alpha,
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sample_dmu_dipole, name):
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"""Sample simple calibration parameters."""
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# The low/high are used only to generate an initial guess, they only
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# have to be in the right order of magnitude so that's why hardcoded.
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e_mu = sample(f"e_mu_{name}", InverseDistribution(0.2, 0.5, 0.15))
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e_mu = sample(f"e_mu_{name}", Uniform(e_mu_min, e_mu_max))
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dmu = sample(f"dmu_{name}", Uniform(dmu_min, dmu_max))
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alpha = sample_alpha_bias(name, alpha_min, alpha_max, sample_alpha)
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@ -447,13 +409,11 @@ def sample_simple(dmu_min, dmu_max, alpha_min, alpha_max, dmu_dipole_mean,
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def sample_calibration(Vext_min, Vext_max, Vmono_min, Vmono_max, beta_min,
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beta_max, h_min, h_max, rLG_min, rLG_max, no_Vext,
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sample_Vmono, sample_beta, sample_h, sample_rLG,
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sample_Vmag_vax):
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beta_max, sigma_v_min, sigma_v_max, h_min, h_max,
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rLG_min, rLG_max, no_Vext, sample_Vmono, sample_beta,
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sample_h, sample_rLG, sample_Vmag_vax):
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"""Sample the flow calibration."""
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# The low/high are used only to generate an initial guess, they only
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# have to be in the right order of magnitude so that's why hardcoded.
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sigma_v = sample("sigma_v", InverseDistribution(100, 1000., 150.))
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sigma_v = sample("sigma_v", Uniform(sigma_v_min, sigma_v_max))
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if sample_beta:
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beta = sample("beta", Uniform(beta_min, beta_max))
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@ -647,10 +607,15 @@ 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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e_mu = distmod_params["e_mu"]
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# Jeffrey's prior on sigma_v and the intrinsic scatter, they are above
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# "sampled" from uniform distributions.
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ll0 -= jnp.log(sigma_v) + jnp.log(e_mu)
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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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alpha_cal = distmod_params["alpha_cal"]
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@ -664,6 +629,9 @@ class PV_LogLikelihood(BaseFlowValidationModel):
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c_mean, c_std = sample_gaussian_hyperprior(
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"c", self.name, self.c_min, self.c_max)
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# Jeffrey's prior on the the MNR hyperprior widths.
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ll0 -= jnp.log(mag_std) + jnp.log(x1_std) + jnp.log(c_std)
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# NOTE: that the true variables are currently uncorrelated.
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with plate(f"true_SN_{self.name}", self.ndata):
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mag_true = sample(
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@ -715,6 +683,9 @@ class PV_LogLikelihood(BaseFlowValidationModel):
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corr_mag_eta = sample(
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f"corr_mag_eta_{self.name}", Uniform(-1, 1))
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# Jeffrey's prior on the the MNR hyperprior widths.
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ll0 -= jnp.log(mag_std) + jnp.log(eta_std)
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loc = jnp.array([mag_mean, eta_mean])
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cov = jnp.array(
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[[mag_std**2, corr_mag_eta * mag_std * eta_std],
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