The superposition of data sets with internal parametric self-similarity is a longstanding and widespread technique for the analysis of many types of experimental data across the physical sciences. Typically, this superposition is performed manually, or recently through the application of one of a few automated algorithms. However, these methods are often heuristic in nature, are prone to user bias via manual data shifting or parameterization, and lack a native framework for handling uncertainty in both the data and the resulting model of the superposed data. In this work, we develop a data-driven, nonparametric method for superposing experimental data with arbitrary coordinate transformations, which employs Gaussian process regression to learn statistical models that describe the data, and then uses maximum a posteriori estimation to optimally superpose the data sets. This statistical framework is robust to experimental noise and automatically produces uncertainty estimates for the learned coordinate transformations. Moreover, it is distinguished from black-box machine learning in its interpretability—specifically, it produces a model that may itself be interrogated to gain insight into the system under study. We demonstrate these salient features of our method through its application to four representative data sets characterizing the mechanics of soft materials. In every case, our method replicates results obtained using other approaches, but with reduced bias and the addition of uncertainty estimates. This method enables a standardized, statistical treatment of self-similar data across many fields, producing interpretable data-driven models that may inform applications such as materials classification, design, and discovery.

The Supernova Working Group was re-established at the IAU XXV General Assembly in Sydney, 21 July 2003, sponsored by Commissions 28 (Galaxies) and 47 (Cosmology). Here we report on some of its activities since 2005.

Background. Drop-out, often accompanied by treatment non-compliance, is common in psychiatric trials. Methodologists have criticized the use of a traditional intention-to-treat (ITT) approach in such cases, and have proposed alternative methods. We set out to describe and assess methods for estimation of a treatment effect when the trial is ‘broken’.

Method. We describe a stratified method of moments (SMOM) estimator that assesses treatment effects on subjects who are willing to comply with all the treatments under study. A simulation study and a re-analysis of data from an antipsychotics trial are used to compare SMOM to ITT, as-treated, and adequate estimators.

Results. The new estimator retains good statistical properties under different levels of non-compliance and drop-out mechanisms. The re-analysis indicates that SMOM yields more precise results.

Conclusions. Although the traditional ITT approach provides a valid method to estimate treatment effects, it can be biased in the presence of treatment non-compliance and drop-out. It is critical that researchers move beyond traditional approaches when trials are broken. A key first step is to consider non-compliance and drop-out as two independent phenomena, tracking and reporting rates separately.