A few statistical principles for data science

Abstract

In any other circumstance, it might make sense to define the extent of the terrain (Data Science) first, and then locate and describe the landmarks (Principles). But this data revolution we are experiencing defies a cadastral survey. Areas are continually being annexed into Data Science. For example, biometrics was traditionally statistics for agriculture in all its forms but now, in Data Science, it means the study of characteristics that can be used to identify an individual. Examples of non-intrusive measurements include height, weight, fingerprints, retina scan, voice, photograph/video (facial landmarks and facial expressions) and gait. A multivariate analysis of such data would be a complex project for a statistician, but a software engineer might appear to have no trouble with it at all. In any appliedstatistics project, the statistician worries about uncertainty and quantifies it by modelling data as realisations generated from a probability space. Another approach to uncertainty quantification is to find similar data sets, and then use the variability of results between these data sets to capture the uncertainty. Both approaches allow 'error bars' to be put on estimates obtained from the original data set, although the interpretations are different. A third approach, that concentrates on giving a single answer and gives up on uncertainty quantification, could be considered as Data Engineering, although it has staked a claim in the Data Science terrain. This article presents a few (actually nine) statistical principles for data scientists that have helped me, and continue to help me, when I work on complex interdisciplinary projects.

Decisions, decisions, decisions in an uncertain environment

“…Inefficiency of a decision can be defined, for example, via the working/true expected posterior losses. Inefficiencies also arise when a “working” probability model for $$$ Y $$$ and $$$ z $$$ are used instead of the “true” probability model; see Cressie (2021).…”

“…What should one do if none of the models is correct? The models are capturing the “known unknowns,” but the correct model may be one of the “unknown unknowns.” One way to fill this gap is to include an extra, maximum‐entropy model (e.g., Cressie, 2021). Indeed, Le and Zidek (2006, Chapter 11) proposed using only a maximum‐entropy model for design and analysis because, in the design stage, the totality of questions that will be asked of the data is never known.…”

A Festschrift for Adrian Baddeley

“…The special issue concludes with a pair of delightful articles that promote ideas of which I am sure Adrian will approve: the central role of statistical principles in data analysis, and the importance of clear thinking in the face of deceptively complex probability problems. Cressie (2021) offers some advice to data scientists seeking statistical principles, while Gill (2021) wrestles with the classic 'Two Envelope Problem' in a characteristically entertaining manner.…”