util_ConstructIntrinsicPosterior_GenericCoordinates

The util_ConstructIntrinsicPosterior_GenericCoordinates executable loads marginalized likelihood data (typically from integrate_likelihood_extrinsic), fits the peak using various interpolation methods, and generates posterior samples for the intrinsic parameters.

Overview

This tool represents the “Construct Intrinsic Posterior” (CIP) stage of the RIFT pipeline. After integrate_likelihood_extrinsic has computed the marginalized likelihood for a grid of intrinsic parameters, util_ConstructIntrinsicPosterior_GenericCoordinates takes that grid and: 1. Fits a continuous surface to the discrete log-likelihood ($ln mathcal{L}$) data. 2. Uses a Monte Carlo sampler to draw posterior samples based on the fit and a specified prior. 3. Performs coordinate transformations and adds derived quantities to the resulting samples.

Usage

Basic Command Line

util_ConstructIntrinsicPosterior_GenericCoordinates [options]

Primary Options

Input/Output

--fname: Filename of the *.dat file containing the marginalized likelihood data (standard ILE output).
--fname-output-samples: Filename for the resulting posterior samples (default: output-ILE-samples).
--fname-output-integral: Filename for the resulting integral result (default: integral_result).
--n-output-samples: Number of posterior samples to generate (default: 3000).

Fitting Configuration

--fit-method: Method used to interpolate the likelihood surface. Options include:
- rf: Random Forest (default)
- gp: Gaussian Process
- quadratic: Quadratic fit to the peak
- polynomial: General polynomial fit
- kde: Kernel Density Estimation
--fit-order: Order of the polynomial fit (default: 2 for quadratic).
--lnL-offset: Threshold relative to the peak ($ln mathcal{L}_{max} - text{offset}$) used to filter data points for the fit.

Parameter and Prior Configuration

--parameter: List of parameters to be used as fitting parameters and varied for the posterior.
--parameter-implied: Parameters used in the fit but not independently varied for MC.
--mc-range, --eta-range, --mtot-range: Manual ranges for the Monte Carlo sampling to avoid wasting time in low-probability regions.
--aligned-prior: Prior for aligned spins (uniform, volumetric, alignedspin-zprior).
--transverse-prior: Prior for transverse spins (uniform, uniform-mag, taper-down, sqrt-prior, etc.).
--prior-gaussian-mass-ratio: Applies a Gaussian mass ratio prior.

Advanced Analysis

--downselect-parameter & --downselect-parameter-range: Used to eliminate grid points that fall outside specified ranges.
--fname-lalinference: Filename of LALInference posterior samples to overlay on corner plots for comparison.

Functional Logic

Data Loading: Reads the marginalized likelihood grid from the input file.
Downselection: Filters out points based on the --downselect-parameter criteria or EOS-based constraints.
Fitting:
- Applies the chosen --fit-method (e.g., Gaussian Process or Random Forest) to create a continuous representation of the $ln mathcal{L}$ surface.
- Optionally shifts the $ln mathcal{L}$ values to prevent numerical overflow.
Sample Generation:
- Uses an integrator (like adaptive_cartesian or GMM) to draw samples proportional to $mathcal{L}_{fit}(theta) times text{Prior}(theta)$.
- This converts the fitted surface into a set of posterior samples.
Post-Processing:
- Transforms samples into requested coordinate systems.
- Calculates derived parameters (e.g., $chi_{eff}$, $chi_{minus}$).
- Writes the samples to the output file and computes the total evidence (integral).

Output Details

The primary output is a structured numpy array (or XML/HDF5 file) containing the posterior samples of the intrinsic parameters. It also produces an integral result representing the marginalized likelihood over the intrinsic space.