Related papers: Plotting the Differences Between Data and Expectat…
A very common task in data visualization is to plot many data points with some measured y-value as a function of fixed x-values. Uncertainties on the y-values are typically presented as vertical error bars that represent either a…
The increased use of cryptography to protect our personal information makes us want to understand the security of cryptosystems. The security of many cryptosystems relies on solving the discrete logarithm, which is thought to be relatively…
The exact expression is derived for the expected value, $< {p_i}> $, for the parameter for any bin $i$ of a histogram following a multinomial distribution derived by sorting $N$ observations into bins of $B$ classes, if $n_i$ of the…
The true process that generated data cannot be determined when multiple explanations are possible. Prediction requires a model of the probability that a process, chosen randomly from the set of candidate explanations, generates some future…
Statistical modeling is a powerful tool for developing and testing theories by way of causal explanation, prediction, and description. In many disciplines there is near-exclusive use of statistical modeling for causal explanation and the…
Two methods of data analysis are compared: spreadsheet software and a statistics software suite. Their use is compared analyzing data collected in three selected experiments taken from an introductory physics laboratory, which include a…
In 1977 John Tukey described how in exploratory data analysis, data analysts use tools, such as data visualizations, to separate their expectations from what they observe. In contrast to statistical theory, an underappreciated aspect of…
Large-scale datasets are increasingly being used to inform decision making. While this effort aims to ground policy in real-world evidence, challenges have arisen as selection bias and other forms of distribution shifts often plague…
Statistical estimation in many contemporary settings involves the acquisition, analysis, and aggregation of datasets from multiple sources, which can have significant differences in character and in value. Due to these variations, the…
In the classroom, we traditionally visualize inferential concepts using static graphics or interactive apps. For example, there is a long history of using apps to visualize sampling distributions. Recent developments in statistical graphics…
In this article we propose a method of performing arithmetic operations on varia-bles with unknown distribution. The approach to the evaluation results of arithme-tic operations can select probability intervals of the algebraic equations…
Current literature on posterior approximation for Bayesian inference offers many alternative methods. Does our chosen approximation scheme work well on the observed data? The best existing generic diagnostic tools treating this kind of…
When the difference between treatments in a clinical trial is estimated by a difference in means, then it is well known that randomization ensures unbiassed estimation, even if no account is taken of important baseline covariates. However,…
Science students must deal with the errors inherent to all physical measurements and be conscious of the need to expressvthem as a best estimate and a range of uncertainty. Errors are routinely classified as statistical or systematic.…
Conventional statistics begins with a model, and assigns a likelihood of obtaining any particular set of data. The opposite approach, beginning with the data and assigning a likelihood to any particular model, is explored here for the case…
We present sparse tree-based and list-based density estimation methods for binary/categorical data. Our density estimation models are higher dimensional analogies to variable bin width histograms. In each leaf of the tree (or list), the…
The distcomp command is introduced and illustrated. The command assesses whether or not two distributions differ at each possible value while controlling the probability of any false positive, even in finite samples. Syntax and the…
While conformal predictors reap the benefits of rigorous statistical guarantees on their error frequency, the size of their corresponding prediction sets is critical to their practical utility. Unfortunately, there is currently a lack of…
Firth-type logistic regression has become a standard approach for the analysis of binary outcomes with small samples. Whereas it reduces the bias in maximum likelihood estimates of coefficients, bias towards 1/2 is introduced in the…
In an attempt to provide an answer to the increasing criticism against p-values and to bridge the gap between statistical inference and prediction modelling, we introduce the probability of improved prediction (PIP). In general, the PIP is…