Impact crater populations help us to understand solar system dynamics, planetary surface histories, and surface modification processes. A single previous effort to standardize how crater data are displayed in graphs, tables, and archives was in a 1978 NASA report by the Crater Analysis Techniques Working Group, published in 1979 in Icarus. The report had a significant lasting effect, but later decades brought major advances in statistical and computer sciences while the crater field has remained fairly stagnant. In this new work, we revisit the fundamental techniques for displaying and analyzing crater population data and demonstrate better statistical methods that can be used. Specifically, we address (1) how crater size‐frequency distributions (SFDs) are constructed, (2) how error bars are assigned to SFDs, and (3) how SFDs are fit to power‐laws and other models. We show how the new methods yield results similar to those of previous techniques in that the SFDs have familiar shapes but better account for multiple sources of uncertainty. We also recommend graphic, display, and archiving methods that reflect computers’ capabilities and fulfill NASA's current requirements for Data Management Plans.

One important, almost ubiquitous, tool for understanding the surfaces of solid bodies throughout the solar system is the study of impact craters. While measuring a distribution of crater diameters and locations is an important tool for a wide variety of studies, so too is measuring a crater's “depth.” Depth can inform numerous studies including the strength of a surface and modification rates in the local environment. There is, however, no standard data set, definition, or technique to perform this data‐gathering task, and the abundance of different definitions of “depth” and methods for estimating that quantity can lead to misunderstandings in and of the literature. In this review, we describe a wide variety of data sets and methods to analyze those data sets that have been, are currently, or could be used to derive different types of crater depth measurements. We also recommend certain nomenclature in doing so to help standardize practice in the field. We present a review section of all crater depths that have been published on different solar system bodies which shows how the field has evolved through time and how some common assumptions might not be wholly accurate. We conclude with several recommendations for researchers which could help different data sets to be more easily understood and compared.

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Revealing hidden patterns in astronomical data is often the path to fundamental scientific breakthroughs; meanwhile the complexity of scientific inquiry increases as more subtle relationships are sought. Contemporary data analysis problems often elude the capabilities of classical statistical techniques, suggesting the use of cutting edge statistical methods. In this light, astronomers have overlooked a whole family of statistical techniques for exploratory data analysis and robust regression, the so-called Generalized Linear Models (GLMs). In this paper -the first in a series aimed at illustrating the power of these methods in astronomical applications -we elucidate the potential of a particular class of GLMs for handling binary/binomial data, the so-called logit and probit regression techniques, from both a maximum likelihood and a Bayesian perspective. As a case in point, we present the use of these GLMs to explore the conditions of star formation activity and metal enrichment in primordial minihaloes from cosmological hydro-simulations including detailed chemistry, gas physics, and stellar feedback. We predict that for a dark mini-halo with metallicity ≈ 1.3 × 10 −4 Z , an increase of 1.2 × 10 −2 in the gas molecular fraction, increases the probability of star formation occurrence by a factor of 75%. Finally, we highlight the use of receiver operating characteristic curves as a diagnostic for binary classifiers, and ultimately we use these to demonstrate the competitive predictive performance of GLMs against the popular technique of artificial neural networks.

In this paper, the third in a series illustrating the power of generalized linear models (GLMs) for the astronomical community, we elucidate the potential of the class of GLMs which handles count data. The size of a galaxy's globular cluster population (N GC ) is a prolonged puzzle in the astronomical literature. It falls in the category of count data analysis, yet it is usually modelled as if it were a continuous response variable. We have developed a Bayesian negative binomial regression model to study the connection between N GC and the following galaxy properties: central black hole mass, dynamical bulge mass, bulge velocity dispersion, and absolute visual magnitude. The methodology introduced herein naturally accounts for heteroscedasticity, intrinsic scatter, errors in measurements in both axes (either discrete or continuous), and allows modelling the population of globular clusters on their natural scale as a non-negative integer variable. Prediction intervals of 99 per cent around the trend for expected N GC comfortably envelope the data, notably including the Milky Way, which has hitherto been considered a problematic outlier. Finally, we demonstrate how random intercept models can incorporate information of each particular galaxy morphological type. Bayesian variable selection methodology allows for automatically identifying galaxy types with different productions of GCs, suggesting that on average S0 galaxies have a GC population 35 per cent smaller than other types with similar brightness.