Inferactive data analysis

Abstract

We describe inferactive data analysis, so-named to denote an interactive approach to data analysis with an emphasis on inference after data analysis. Our approach is a compromise between Tukey's exploratory (roughly speaking "model free") and confirmatory data analysis (roughly speaking classical and "model based"), also allowing for Bayesian data analysis. We view this approach as close in spirit to current practice of applied statisticians and data scientists while allowing frequentist guarantees for results to be reported in the scientific literature, or Bayesian results where the data scientist may choose the statistical model (and hence the prior) after some initial exploratory analysis. While this approach to data analysis does not cover every scenario, and every possible algorithm data scientists may use, we see this as a useful step in concrete providing tools (with frequentist statistical guarantees) for current data scientists. The basis of inference we use is selective inference [Lee et al., 2016, Fithian et al., 2014], in particular its randomized form [Tian and Taylor, 2015a]. The randomized framework, besides providing additional power and shorter confidence intervals, also provides explicit forms for relevant reference distributions (up to normalization) through the {\em selective sampler} of Tian et al. [2016]. The reference distributions are constructed from a particular conditional distribution formed from what we call a DAG-DAG -- a Data Analysis Generative DAG. As sampling conditional distributions in DAGs is generally complex, the selective sampler is crucial to any practical implementation of inferactive data analysis. Our principal goal is in reviewing the recent developments in selective inference as well as describing the general philosophy of selective inference.