Worked examples of treating selection effects, including via sampling over non-detections in Stan. See Mandel, Farr & Gair (2018). Contents:
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A simple worked example of a flux-limited survey of standard candles in Euclidean space illustrating that the commonly-used modification of the population distribution to incorporate the selection function generates biased inferences over population parameters. The correct solution is briefly discussed and demonstrated to be correct.
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Three different ways of hierarchically modelling a flux-limited survey of a population of objects with a log-normal luminosity function, with known photometric uncertainty in each observation. In this case the selection function can be computed analytically; methods that using sampling to account for the selection function are derived and validated by comparison to the analytic model. See
Gaussian.ipynb. -
A more realistic worked example of inferring the parameters of a Schechter luminosity function from a hypothetical flux-limited galaxy survey in the nearby universe, again incorporating photometic uncertainties. In this case, the selection function is not analytically tractible, so must be treated numerically. See
Schechter.ipynb.