  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.
