Introduction

Surveying the Universe is the ultimate remote sensing problem. Inferring the intrinsic properties of the galaxy population, via analysis of survey-generated catalogues, is a major challenge for twenty-first century cosmology, but this challenge must be met without any prospect of measuring these properties in situ. Thus, for example, our knowledge of the intrinsic luminosity and spatial distribution of galaxies is filtered by imperfect distance information and by observational selection effects, issues which have come to be known generically in the literature as ‘Malmquist bias’. Figure 11.1 shows schematically how such effects may distort our inferences about the underlying population since, in general, these must be derived from a noisy, sparse and truncated sample of galaxies.

There is a long (and mostly honourable!) tradition in the astronomical literature of attempts to cast such remote surveying problems within a rigorous statistical framework. Indeed, it is interesting to note that seminal examples from the early twentieth century (Eddington 1913, 1940; Malmquist 1920, 1922) display, at least with hindsight, hints of a Bayesian formulation long before the recent renaissance of Bayesian methods in astronomy. Unfortunately, space does not permit us to review in detail that early literature, nor many of the more recent papers which evolved from it. A more thorough discussion of the literature on statistical analysis of survey data can be found in, e.g., Hendry and Simmons (1995), Strauss and Willick (1995), Teerikorpi (1997) and Loredo (2007).