Data Models¶

Parameter Space¶

class master_thesis_code.datamodels.parameter_space.Parameter(symbol, unit, lower_limit, upper_limit, value=0.0, derivative_epsilon=1e-06, is_fixed=False, randomize_by_distribution=<function uniform>)[source]¶

Bases: object

Main class for parameters.

Parameters:

symbol (str)
unit (str)
lower_limit (float)
upper_limit (float)
value (float)
derivative_epsilon (float)
is_fixed (bool)
randomize_by_distribution (Callable[[float, float, Generator], float])

derivative_epsilon: float = 1e-06¶

is_fixed: bool = False¶

lower_limit: float¶

randomize_by_distribution(upper_limit, rng)¶

Parameters:

lower_limit (float)
upper_limit (float)
rng (Generator)

Return type:

float

symbol: str¶

unit: str¶

upper_limit: float¶

value: float = 0.0¶

class master_thesis_code.datamodels.parameter_space.ParameterSpace(M=<factory>, mu=<factory>, a=<factory>, p0=<factory>, e0=<factory>, x0=<factory>, luminosity_distance=<factory>, qS=<factory>, phiS=<factory>, qK=<factory>, phiK=<factory>, Phi_phi0=<factory>, Phi_theta0=<factory>, Phi_r0=<factory>)[source]¶

Bases: object

Dataclass to manage the parameter space of a simulation.

Parameters:

M (Parameter)
mu (Parameter)
a (Parameter)
p0 (Parameter)
e0 (Parameter)
x0 (Parameter)
luminosity_distance (Parameter)
qS (Parameter)
phiS (Parameter)
qK (Parameter)
phiK (Parameter)
Phi_phi0 (Parameter)
Phi_theta0 (Parameter)
Phi_r0 (Parameter)

M: Parameter¶

Phi_phi0: Parameter¶

Phi_r0: Parameter¶

Phi_theta0: Parameter¶

a: Parameter¶

e0: Parameter¶

luminosity_distance: Parameter¶

mu: Parameter¶

p0: Parameter¶

phiK: Parameter¶

phiS: Parameter¶

qK: Parameter¶

qS: Parameter¶

randomize_parameter(parameter, rng)[source]¶

Parameters:

parameter (Parameter)
rng (Generator)

Return type:

None

randomize_parameters(rng=None)[source]¶

Parameters:: rng (Generator | None)
Return type:: None

set_host_galaxy_parameters(host_galaxy)[source]¶

Parameters:: host_galaxy (HostGalaxy)
Return type:: None

x0: Parameter¶

master_thesis_code.datamodels.parameter_space.log_uniform(lower_limit, upper_limit, rng)[source]¶

Parameters:

lower_limit (float)
upper_limit (float)
rng (Generator)

Return type:

float

master_thesis_code.datamodels.parameter_space.polar_angle_distribution(lower_limit, upper_limit, rng)[source]¶

Parameters:

lower_limit (float)
upper_limit (float)
rng (Generator)

Return type:

float

master_thesis_code.datamodels.parameter_space.uniform(lower_limit, upper_limit, rng)[source]¶

Parameters:

lower_limit (float)
upper_limit (float)
rng (Generator)

Return type:

float

Galaxy Catalog¶

Galaxy and GalaxyCatalog datamodels for Bayesian H₀ inference.

class master_thesis_code.datamodels.galaxy.Galaxy(redshift, central_black_hole_mass, right_ascension, declination)[source]¶

Bases: object

A galaxy in the catalog with a central massive black hole.

Variables:

redshift (float) – Spectroscopic redshift \(z\) (dimensionless).
central_black_hole_mass (float) – Central MBH mass in solar masses \(M_\odot\).
right_ascension (float) – Ecliptic azimuthal angle in radians \([0, 2\pi)\).
declination (float) – Ecliptic polar angle in radians \([0, \pi]\).

Parameters:

redshift (float)
central_black_hole_mass (float)
right_ascension (float)
declination (float)

central_black_hole_mass: float¶

property central_black_hole_mass_uncertainty: float¶

declination: float¶

redshift: float¶

property redshift_uncertainty: float¶

right_ascension: float¶

classmethod with_random_skylocalization(redshift, central_black_hole_mass, rng=None)[source]¶

Parameters:

redshift (float)
central_black_hole_mass (float)
rng (Generator | None)

Return type:

Galaxy

class master_thesis_code.datamodels.galaxy.GalaxyCatalog(use_truncnorm=True, use_comoving_volume=True, h0=TRUE_HUBBLE_CONSTANT)[source]¶

Bases: object

Synthetic galaxy catalog for Bayesian H₀ inference.

Holds a list of Galaxy objects and provides redshift/mass probability distributions used by BayesianInference.

Variables:

lower_mass_limit (float) – Minimum central BH mass in \(M_\odot\).
upper_mass_limit (float) – Maximum central BH mass in \(M_\odot\).
redshift_lower_limit (float) – Minimum redshift in the catalog.
redshift_upper_limit (float) – Maximum redshift in the catalog.
catalog (list[master_thesis_code.datamodels.galaxy.Galaxy]) – List of Galaxy instances.

Parameters:

use_truncnorm (bool)
use_comoving_volume (bool)
h0 (float)

add_host_galaxy(rng=None)[source]¶

Parameters:: rng (Generator | None)
Return type:: Galaxy

add_random_galaxy(rng=None)[source]¶

Parameters:: rng (Generator | None)
Return type:: None

add_unique_host_galaxies_from_catalog(number_of_host_galaxies_to_add, used_host_galaxies, rng=None)[source]¶

Parameters:

number_of_host_galaxies_to_add (int)
used_host_galaxies (list[Galaxy])
rng (Generator | None)

Return type:

list[Galaxy]

append_galaxy_to_galaxy_distribution(galaxy)[source]¶

Parameters:: galaxy (Galaxy)
Return type:: None

append_galaxy_to_galaxy_mass_distribution(galaxy)[source]¶

Parameters:: galaxy (Galaxy)
Return type:: None

catalog: list[Galaxy]¶

comoving_volume_element(redshift)[source]¶

Comoving volume element dV_c/dz at the given redshift.

Parameters:: redshift (float)
Return type:: float

create_random_catalog(number_of_galaxies, rng=None)[source]¶

Parameters:

number_of_galaxies (int)
rng (Generator | None)

Return type:

None

evaluate_galaxy_distribution(redshift)[source]¶

Parameters:: redshift (float)
Return type:: ndarray[tuple[Any, …], dtype[float64]]

evaluate_galaxy_mass_distribution(mass)[source]¶

Parameters:: mass (float)
Return type:: ndarray[tuple[Any, …], dtype[float64]]

galaxy_distribution: list[NormalDist | rv_continuous]¶

galaxy_mass_distribution: list[NormalDist | rv_continuous]¶

get_possible_host_galaxies()[source]¶

Return type:: list[Galaxy]

get_samples_from_comoving_volume_element(number_of_samples, rng=None)[source]¶

Parameters:

number_of_samples (int)
rng (Generator | None)

Return type:

ndarray

get_unique_host_galaxies_from_catalog(number_of_host_galaxies, rng=None)[source]¶

Parameters:

number_of_host_galaxies (int)
rng (Generator | None)

Return type:

list[Galaxy]

log_comoving_volume_element(redshift)[source]¶

Parameters:: redshift (float)
Return type:: float

lower_mass_limit: float = 10000¶

redshift_lower_limit: float = 1e-05¶

redshift_upper_limit: float = 0.55¶

remove_all_galaxies()[source]¶

Return type:: None

setup_galaxy_distribution()[source]¶

Return type:: None

setup_galaxy_mass_distribution()[source]¶

Return type:: None

upper_mass_limit: float = 10000000¶

EMRI Detection¶

EMRIDetection datamodel for Bayesian H₀ inference.

class master_thesis_code.datamodels.emri_detection.EMRIDetection(measured_luminosity_distance, measured_redshifted_mass, measured_right_ascension, measured_declination)[source]¶

Bases: object

A simulated EMRI detection with noisy measured observables.

Holds the LISA-measured quantities that enter the Bayesian H₀ likelihood. All angular quantities use ecliptic coordinates.

Variables:

measured_luminosity_distance (float) – Measured luminosity distance \(\hat{d}_L\) in Gpc.
measured_redshifted_mass (float) – Measured redshifted central BH mass \(\hat{M}_z = M(1+z)\) in solar masses.
measured_right_ascension (float) – Measured sky azimuthal angle in radians.
measured_declination (float) – Measured sky polar angle in radians.

Parameters:

measured_luminosity_distance (float)
measured_redshifted_mass (float)
measured_right_ascension (float)
measured_declination (float)

classmethod from_host_galaxy(host_galaxy, use_measurement_noise=True, rng=None)[source]¶

Parameters:

host_galaxy (Galaxy)
use_measurement_noise (bool)
rng (Generator | None)

Return type:

EMRIDetection

measured_declination: float¶

measured_luminosity_distance: float¶

measured_redshifted_mass: float¶

measured_right_ascension: float¶

Detection (Cramér-Rao)¶

Detection datamodel for Cramér-Rao bounds based EMRI inference.

class master_thesis_code.datamodels.detection.Detection(parameters)[source]¶

Bases: object

EMRI detection parsed from Cramér-Rao bounds CSV output.

Stores the maximum-likelihood parameter estimates and their 1-σ errors derived from the Fisher information matrix for a single detected EMRI event.

Variables:

d_L (float) – Luminosity distance \(d_L\) in Gpc.
d_L_uncertainty (float) – 1-σ error on \(d_L\) in Gpc, equal to \(\sqrt{\Gamma^{-1}_{d_L d_L}}\).
phi (float) – Sky azimuthal angle \(\phi_S\) in radians.
phi_error (float) – 1-σ error on \(\phi_S\) in radians.
theta (float) – Sky polar angle \(\theta_S\) (= \(q_S\)) in radians.
theta_error (float) – 1-σ error on \(\theta_S\) in radians.
M (float) – Redshifted central BH mass \(M_z\) in solar masses.
M_uncertainty (float) – 1-σ error on \(M_z\) in solar masses.
theta_phi_covariance (float) – Off-diagonal Cramér-Rao element \(C_{\theta\phi}\) in rad².
M_phi_covariance (float) – Off-diagonal element \(C_{M\phi}\) in \(M_\odot \cdot \mathrm{rad}\).
M_theta_covariance (float) – Off-diagonal element \(C_{M\theta}\) in \(M_\odot \cdot \mathrm{rad}\).
d_L_M_covariance (float) – Off-diagonal element \(C_{d_L M}\) in \(\mathrm{Gpc} \cdot M_\odot\).
d_L_theta_covariance (float) – Off-diagonal element \(C_{d_L\theta}\) in \(\mathrm{Gpc} \cdot \mathrm{rad}\).
d_L_phi_covariance (float) – Off-diagonal element \(C_{d_L\phi}\) in \(\mathrm{Gpc} \cdot \mathrm{rad}\).
host_galaxy_index (int) – Index of the host galaxy in the galaxy catalog.
snr (float) – Signal-to-noise ratio (dimensionless).
WL_uncertainty (float) – Weak-lensing contribution to the \(d_L\) uncertainty in Gpc.

Parameters:

parameters (Series)

M: float¶

M_phi_covariance: float¶

M_theta_covariance: float¶

M_uncertainty: float¶

WL_uncertainty: float = 0.0¶

convert_to_best_guess_parameters(rng=None)[source]¶

Draw simulated measured parameters from the Fisher-matrix posterior.

When rng is provided, draws a single correlated sample from the 4-dimensional multivariate normal defined by the full Cramér-Rao covariance sub-matrix for (phi, theta, d_L, M) and clips to physical bounds. This is the standard procedure in the GW literature (Cutler & Flanagan 1994; Vallisneri 2008, arXiv:gr-qc/0703086).

When rng is None the legacy behaviour is preserved: four independent truncated-normal draws from the marginal distributions.

Parameters:: rng (Generator | None) – NumPy random generator for reproducible, correlated draws. Pass None to keep the legacy independent-sampling path.
Return type:: None