astronomical source detection, separation, and photometry

*now with an inferential basis!*

It took one hell of a long time, but I felt so
probabilistically righteous.

— J. J. User

The *Tractor* is a new project (by Lang & Hogg) to
generate probabilistically justified astronomical catalogs from
multi-pass, multi-band imaging.
Instead of simply measuring

star and galaxy properties, the
*Tractor* optimizes a likelihood for the catalog properties given
the data and an informative noise model. In this sense, it treats the
catalog as the *parameters* of a flexible model—a model
with variable complexity. In principle the *Tractor* can even
*sample* in catalog space and marginalize out uninteresting
catalog properties.

Traditionally, sources are detected in astronomical imaging with single-point estimates of significance and then measured and then characterized with single-point estimates of their properties. There are several significant issues with this approach. One is that the single-point estimates are rarely (though sometimes) maximum-likelihood estimates. Another is that the code must make hard decisions about the existence of souces or whether to analyze a source as a star or a galaxy, and these are rarely justified in terms of probabilistic utility. Another is that sources can overlap, and naive single-point estimates cannot account for the mixture of influences on the image pixels. Another is that single-point estimates cannot be combined with non-trivial priors to produce more probable solutions when informative prior or external data exist.

All of these issues can be ameliorated if we see catalog generation
or measurement as the optimization of a justified scalar objective
function. To be justified, this function must have both probabilistic
content (the likelihood or the probability of the data given the
model) *and* utility content (so that models of differing
complexity can be compared). The *Tractor* is a first-in-class
implementation of these ideas
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