Hierarchical probabilistic inference of cosmic shear

TL;DR

This paper introduces a hierarchical probabilistic framework for cosmic shear inference that improves accuracy over traditional point estimators by marginalizing over galaxy properties and using importance sampling for computational efficiency.

Contribution

The authors develop a novel probabilistic forward modeling approach with hierarchical inference and importance sampling, addressing biases and computational challenges in cosmic shear measurement.

Findings

Improved accuracy in shear inference demonstrated with numerical examples.

Hierarchical inference effectively models diverse galaxy populations.

Importance sampling enhances computational efficiency for large surveys.

Abstract

Point estimators for the shearing of galaxy images induced by gravitational lensing involve a complex inverse problem in the presence of noise, pixelization, and model uncertainties. We present a probabilistic forward modeling approach to gravitational lensing inference that has the potential to mitigate the biased inferences in most common point estimators and is practical for upcoming lensing surveys. The first part of our statistical framework requires specification of a likelihood function for the pixel data in an imaging survey given parameterized models for the galaxies in the images. We derive the lensing shear posterior by marginalizing over all intrinsic galaxy properties that contribute to the pixel data (i.e., not limited to galaxy ellipticities) and learn the distributions for the intrinsic galaxy properties via hierarchical inference with a suitably flexible conditional probabilitiy distribution specification. We use importance sampling to separate the modeling of small imaging areas from the global shear inference, thereby rendering our algorithm computationally tractable for large surveys. With simple numerical examples we demonstrate the improvements in accuracy from our importance sampling approach, as well as the significance of the conditional distribution specification for the intrinsic galaxy properties when the data are generated from an unknown number of distinct galaxy populations with different morphological characteristics.