Residual Sum of Squares (RSS, SSR, SSE)
In statistics, the residual sum of squares (RSS) is the sum of squares of residuals. It is also known as the sum of squared residuals (SSR) or the sum of squared errors of prediction (SSE). It is a measure of the discrepancy between the data and an estimation model. A small RSS indicates a tight fit of the model to the data.
In general, total sum of squares = explained sum of squares + residual sum of squares. For a proof of this in the multivariate ordinary least squares (OLS) case, see partitioning in the general OLS model. …

Inferential Model (IM)
Probability is a useful tool for describing uncertainty, so it is natural to strive for a system of statistical inference based on probabilities for or against various hypotheses. But existing probabilistic inference methods struggle to provide a meaningful interpretation of the probabilities across experiments in sufficient generality. In this paper we further develop a promising new approach based on what are called inferential models (IMs). The fundamental idea behind IMs is that there is an unobservable auxiliary variable that itself describes the inherent uncertainty about the parameter of interest, and that posterior probabilistic inference can be accomplished by predicting this unobserved quantity. We describe a simple and intuitive threestep construction of a random set of candidate parameter values, each being consistent with the model, the observed data, and a auxiliary variable prediction. Then prior-free posterior summaries of the available statistical evidence for and against a hypothesis of interest are obtained by calculating the probability that this random set falls completely in and completely out of the hypothesis, respectively. We prove that these IM-based measures of evidence are calibrated in a frequentist sense, showing that IMs give easily-interpretable results both within and across experiments. …

Golomb Ruler Problem
The Golomb ruler problem is defined as follows: Given a positive integer n, locate n marks on a ruler such that the distance between any two distinct pair of marks are different from each other and the total length of the ruler is minimized. The Golomb ruler problem has applications in information theory, astronomy and communications, and it can be seen as a challenge for combinatorial optimization algorithms. Although constructing high quality rulers is well-studied, proving optimality is a far more challenging task. …

Origraph
Data wrangling is widely acknowledged to be a critical part of the data analysis pipeline. Nevertheless, there are currently no techniques to efficiently wrangle network datasets. Here we introduce a set of interaction techniques that enable analysts to carry out complex network wrangling operations. These operations include deriving attributes across connected classes, converting nodes to edges and vice-versa, and faceting nodes and edges based on attributes. We implement these operations in a web-based, open-source system, Origraph, which provides interfaces to execute the operations and investigate the results. Designed for wrangling, rather than analysis, Origraph can be used to load data in many forms, wrangle and transform the network, and export it in formats compatible with common network visualization tools. We demonstrate Origraph’s usefulness in a series of examples with different datasets from a variety of sources. …