TATTER (Two-sAmple TesT EstimatoR) performs two-sample hypothesis test. The two-sample hypothesis test is concerned with whether distributions p(x) and q(x) are different on the basis of finite samples drawn from each of them. This ubiquitous problem appears in a legion of applications, ranging from data mining to data analysis and inference. This implementation can perform the Kolmogorov-Smirnov test (for one-dimensional data only), Kullback-Leibler divergence, and Maximum Mean Discrepancy (MMD) test. The module performs a bootstrap algorithm to estimate the null distribution and compute p-value.

PoPE (Population Profile Estimator) analyzes spatial distribution or internal spatial structure problems of samples of astronomical systems. This population-based Bayesian inference model uses the conditional statistics of spatial profile of multiple observables assuming the individual observations are measured with errors of varying magnitude. Assuming the conditional statistics of the observables can be described with a multivariate normal distribution, the model reduces to the conditional average profile and conditional covariance between all observables. The method consists of two steps: (1) reconstructing the average profile using non-parametric regression with Gaussian Processes and (2) estimating the property profiles covariance given a set of independent variable. PoPE is computationally efficient and capable of inferring average profiles of a population from noisy measurements without stacking and binning nor parameterizing the shape of the average profile.

KLLR (Kernel Localized Linear Regression) generates estimates of conditional statistics in terms of the local slope, normalization, and covariance. This method provides a more nuanced description of population statistics appropriate for very large samples with non-linear trends. The code uses a bootstrap re-sampling technique to estimate the uncertainties and also provides tools to seamlessly generate visualizations of the model parameters.