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This paper aims mainly at introducing applied statisticians and econometricians to the current research methodology with non-Euclidean data sets. Specifically, it provides the basis and rationale for statistics in Wasserstein space, where the metric on probability measures is taken as a Wasserstein metric arising from optimal transport theory.

The authors spell out the basis and rationale for using Wasserstein metrics on the data space of (random) probability measures.

In elaborating the new statistical analysis of non-Euclidean data sets, the paper illustrates the generalization of traditional aspects of statistical inference following Frechet's program.

Besides the elaboration of research methodology for a new data analysis, the paper discusses the applications of Wasserstein metrics to the robustness of financial risk measures.

This paper aims to offer a tutorial/introduction to new statistics arising from the theory of optimal transport to empirical researchers in econometrics and machine learning.

Presenting in a tutorial/survey lecture style to help practitioners with the theoretical material.

The tutorial survey of some main statistical tools (arising from optimal transport theory) should help practitioners to understand the theoretical background in order to conduct empirical research meaningfully.

This study is an original presentation useful for new comers to the field.

This paper tests whether Bayesian A/B testing yields better decisions that traditional Neyman-Pearson hypothesis testing. It proposes a model and tests it using a large, multiyear Google Analytics (GA) dataset.

This paper is an empirical study. Competing A/B testing models were used to analyze a large, multiyear dataset of GA dataset for a firm that relies entirely on their website and online transactions for customer engagement and sales.

Bayesian A/B tests of the data not only yielded a clear delineation of the timing and impact of the intellectual property fraud, but calculated the loss of sales dollars, traffic and time on the firm’s website, with precise confidence limits. Frequentist A/B testing identified fraud in bounce rate at 5% significance, and bounces at 10% significance, but was unable to ascertain fraud at the standard significance cutoffs for scientific studies.

None within the scope of the research plan.

Bayesian A/B tests of the data not only yielded a clear delineation of the timing and impact of the IP fraud, but calculated the loss of sales dollars, traffic and time on the firm’s website, with precise confidence limits.

Bayesian A/B testing can derive economically meaningful statistics, whereas frequentist A/B testing only provide p-value’s whose meaning may be hard to grasp, and where misuse is widespread and has been a major topic in metascience. While misuse of p-values in scholarly articles may simply be grist for academic debate, the uncertainty surrounding the meaning of p-values in business analytics actually can cost firms money.

There is very little empirical research in e-commerce that uses Bayesian A/B testing. Almost all corporate testing is done via frequentist Neyman-Pearson methods.