arXiv subjects

Johanna Hardin

Publications and source records attributed to Johanna Hardin.

18 recordsLinked to original sources

arXiv2026

Measuring the Impact of Missingness in Traffic Stop Data

In this article we explore the data available through the Stanford Open Policing Project. The data consist of information on millions of traffic stops across close to 100 different cities and highway patrols. Using a variety of metrics, we identify that the data is not missing completely at random. Furthermore, we develop ways of quantifying and visualizing missingness trends for different variables across the data sets. Because of the way we have identified the missingness dependence on key variables, imputation is not possible and a sensitivity analysis is required. We perform a sensitivity analysis to extend work done on the outcome test as well as to extend work done on sharp bounds on the average treatment effect. We demonstrate that bias calculations can fundamentally shift depending on the assumptions made about the observations for which the race variable has not been recorded. We suggest ways that our missingness sensitivity analysis can be extended to myriad contexts.

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arXiv2025

Selecting ChIP-seq Normalization Methods from the Perspective of their Technical Conditions

Chromatin immunoprecipitation with high-throughput sequencing (ChIP-seq) provides insights into both the genomic location occupied by the protein of interest and the difference in DNA occupancy between experimental states. Given that ChIP-seq data is collected experimentally, an important step for determining regions with differential DNA occupancy between states is between-sample normalization. While between-sample normalization is crucial for downstream differential binding analysis, the technical conditions underlying between-sample normalization methods have yet to be examined for ChIP-seq. We identify three important technical conditions underlying ChIP-seq between-sample normalization methods: balanced differential DNA occupancy, equal total DNA occupancy, and equal background binding across states. To illustrate satisfying the selected normalization method's technical conditions for downstream differential binding analysis, we simulate ChIP-seq read count data where different combinations of the technical conditions are violated. We then externally verify our simulation results using experimental data. Based on our findings, we suggest that researchers use their understanding of the ChIP-seq experiment at hand to guide their choice of between-sample normalization method. Alternatively, researchers can use a high-confidence peakset, which is the intersection of the differentially bound peaksets obtained from using different between-sample normalization methods. In our two experimental analyses, roughly half of the called peaks were called as differentially bound for every normalization method. High-confidence peaks are less sensitive to choice of between-sample normalization method and could be a more robust basis for identifying genomic regions with differential DNA occupancy between experimental states when there is uncertainty about which technical conditions are satisfied.

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arXiv2025

A Mathematical Lens for Teaching Data Science

Using the National Academies report, {\em Data Science for Undergraduates: Opportunities and Options}, we connect data science curricula to the more familiar pedagogy used by many mathematical scientists. We use their list of ``data acumen" components to ground a discussion, which hopes to connect data science curricula to the more familiar pedagogy used by many mathematical scientists.

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arXiv2025

The Exchangeability Assumption for Permutation Tests of Multiple Regression Models: Implications for Statistics and Data Science Educators

Permutation tests are a powerful and flexible approach to inference via resampling. As computational methods become more ubiquitous in the statistics curriculum, use of permutation tests has become more tractable. At the heart of the permutation approach is the exchangeability assumption, which determines the appropriate null sampling distribution. We explore the exchangeability assumption in the context of permutation tests for multiple linear regression models, including settings where the assumption is not tenable. Various permutation schemes for the multiple linear regression setting have been proposed and assessed in the literature. As has been demonstrated previously, in most settings, the choice of how to permute a multiple linear regression model does not materially change inferential conclusions with respect to Type I errors. However, some violations (e.g., when clustering is not appropriately accounted for) lead to issues with Type I error rates. Regardless, we believe that understanding (1) exchangeability in the multiple linear regression setting and also (2) how it relates to the null hypothesis of interest is valuable. We close with pedagogical recommendations for instructors who want to bring multiple linear regression permutation inference into their classroom as a way to deepen student understanding of resampling-based inference.

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arXiv2024

Prediction Error Estimation in Random Forests

In this paper, error estimates of classification Random Forests are quantitatively assessed. Based on the initial theoretical framework built by Bates et al. (2023), the true error rate and expected error rate are theoretically and empirically investigated in the context of a variety of error estimation methods common to Random Forests. We show that in the classification case, Random Forests' estimates of prediction error is closer on average to the true error rate instead of the average prediction error. This is opposite the findings of Bates et al. (2023) which are given for logistic regression. We further show that our result holds across different error estimation strategies such as cross-validation, bagging, and data splitting.

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arXiv2024

Philosophy within Data Science Ethics Courses

There is wide agreement that ethical considerations are a valuable aspect of a data science curriculum, and to that end, many data science programs offer courses in data science ethics. There are not always, however, explicit connections between data science ethics and the centuries-old work on ethics within the discipline of philosophy. Here, we present a framework for bringing together key data science practices with ethics topics. The ethics topics were collated from sixteen data science ethics courses with public-facing syllabi and reading lists. We encourage individuals who are teaching data science ethics to engage with the philosophical literature and its connection to current data science practices, which are rife with potentially morally charged decision points.

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arXiv2023

Long-term Averages of the Stochastic Logistic Map

The logistic map is a nonlinear difference equation well studied in the literature, used to model self-limiting growth in certain populations. It is known that, under certain regularity conditions, the stochastic logistic map, where the parameter is varied according to a specified distribution, has a unique invariant distribution. In these cases we can compare the long-term behavior of the stochastic system with that of the deterministic system evaluated at the average parameter value. Here we examine the relationship between the mean of the stochastic logistic equation and the mean of orbits of the deterministic logistic equation at the expected value of the parameter. We formally prove that, in some cases, the addition of noise is beneficial to the populations, in the sense that it increases the mean, while for other ranges of parameters it is detrimental. A conjecture based on numerical evidence is presented at the end.

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arXiv2022

Community, Collaboration, and Climate

The Department of Mathematics & Statistics at Pomona College has long worked to create an inclusive and welcoming space for all individuals to study mathematics. Many years ago, our approach to the lack of diversity we saw in our majors was remediation through programming which sought to ameliorate student deficits. More recently, however, we have taken an anti-deficit approach with focus on changes to the department itself. The programs we have implemented are described below as enhancing community, collaboration, and climate within our department.

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arXiv2022

An educator's perspective of the tidyverse

Computing makes up a large and growing component of data science and statistics courses. Many of those courses, especially when taught by faculty who are statisticians by training, teach R as the programming language. A number of instructors have opted to build much of their teaching around use of the tidyverse. The tidyverse, in the words of its developers, "is a collection of R packages that share a high-level design philosophy and low-level grammar and data structures, so that learning one package makes it easier to learn the next". These shared principles have led to the widespread adoption of the tidyverse ecosystem. A large part of this usage is because the tidyverse tools have been intentionally designed to ease the learning process and make it easier for users to learn new functions as they engage with additional pieces of the larger ecosystem. Moreover, the functionality offered by the packages within the tidyverse spans the entire data science cycle, which includes data import, visualisation, wrangling, modeling, and communication. We believe the tidyverse provides an effective and efficient pathway for undergraduate students at all levels and majors to gain computational skills and thinking needed throughout the data science cycle. In this paper, we introduce the tidyverse from an educator's perspective. We provide a brief introduction to the tidyverse, demonstrate how foundational statistics and data science tasks are accomplished with the tidyverse, and discuss the strengths of the tidyverse, particularly in the context of teaching and learning.

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arXiv2021

A Unified Framework for Random Forest Prediction Error Estimation

We introduce a unified framework for random forest prediction error estimation based on a novel estimator of the conditional prediction error distribution function. Our framework enables simple plug-in estimation of key prediction uncertainty metrics, including conditional mean squared prediction errors, conditional biases, and conditional quantiles, for random forests and many variants. Our approach is especially well-adapted for prediction interval estimation; we show via simulations that our proposed prediction intervals are competitive with, and in some settings outperform, existing methods. To establish theoretical grounding for our framework, we prove pointwise uniform consistency of a more stringent version of our estimator of the conditional prediction error distribution function. The estimators introduced here are implemented in the R package forestError.

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arXiv2020

"Playing the whole game": A data collection and analysis exercise with Google Calendar

We provide a computational exercise suitable for early introduction in an undergraduate statistics or data science course that allows students to 'play the whole game' of data science: performing both data collection and data analysis. While many teaching resources exist for data analysis, such resources are not as abundant for data collection given the inherent difficulty of the task. Our proposed exercise centers around student use of Google Calendar to collect data with the goal of answering the question 'How do I spend my time?' On the one hand, the exercise involves answering a question with near universal appeal, but on the other hand, the data collection mechanism is not beyond the reach of a typical undergraduate student. A further benefit of the exercise is that it provides an opportunity for discussions on ethical questions and considerations that data providers and data analysts face in today's age of large-scale internet-based data collection.

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arXiv2018

Dynamic Data in the Statistics Classroom

The call for using real data in the classroom has long meant using datasets which are culled, cleaned, and wrangled prior to any student working with the observations. However, an important part of teaching statistics should include actually retrieving data from the Internet. Nowadays, there are many different sources of data that are continually updated by the organization hosting the data website. The R tools to download such dynamic data have improved in such a way to make accessing the data possible even in an introductory statistics class. We provide five full analyses on dynamic data as well as an additional nine sources of dynamic data that can be brought into the classroom. The goal of our work is to demonstrate that using dynamic data can have a short learning curve, even for introductory students or faculty unfamiliar with the landscape. The examples provided are unlikely to create expert data scrapers, but they should help motivate students and faculty toward more engaged use of online data sources.

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arXiv2016

Selecting between-sample RNA-Seq normalization methods from the perspective of their assumptions

RNA-Seq is a widely-used method for studying the behavior of genes under different biological conditions. An essential step in an RNA-Seq study is normalization, in which raw data are adjusted to account for factors that prevent direct comparison of expression measures. Errors in normalization can have a significant impact on downstream analysis, such as inflated false positives in differential expression analysis. An under-emphasized feature of normalization is the assumptions upon which the methods rely and how the validity of these assumptions can have a substantial impact on the performance of the methods. In this paper, we explain how assumptions provide the link between raw RNA-Seq read counts and meaningful measures of gene expression. We examine normalization methods from the perspective of their assumptions, as an understanding of methodological assumptions is necessary for choosing methods appropriate for the data at hand. Furthermore, we discuss why normalization methods perform poorly when their assumptions are violated and how this causes problems in subsequent analysis. To analyze a biological experiment, researchers must select a normalization method with assumptions that are met and that produces a meaningful measure of expression for the given experiment.

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arXiv2015

Resistant Multiple Sparse Canonical Correlation

Canonical Correlation Analysis (CCA) is a multivariate technique that takes two datasets and forms the most highly correlated possible pairs of linear combinations between them. Each subsequent pair of linear combinations is orthogonal to the preceding pair, meaning that new information is gleaned from each pair. By looking at the magnitude of coefficient values, we can find out which variables can be grouped together, thus better understanding multiple interactions that are otherwise difficult to compute or grasp intuitively. CCA appears to have quite powerful applications to high throughput data, as we can use it to discover, for example, relationships between gene expression and gene copy number variation. One of the biggest problems of CCA is that the number of variables (often upwards of 10,000) makes biological interpretation of linear combinations nearly impossible. To limit variable output, we have employed a method known as Sparse Canonical Correlation Analysis (SCCA), while adding estimation which is resistant to extreme observations or other types of deviant data. In this paper, we have demonstrated the success of resistant estimation in variable selection using SCCA. Additionally, we have used SCCA to find multiple canonical pairs for extended knowledge about the datasets at hand. Again, using resistant estimators provided more accurate estimates than standard estimators in the multiple canonical correlation setting. R code is available and documented at https://github.com/hardin47/rmscca.

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arXiv2015

Network Analysis with the Enron Email Corpus

We use the Enron email corpus to study relationships in a network by applying six different measures of centrality. Our results came out of an in-semester undergraduate research seminar. The Enron corpus is well suited to statistical analyses at all levels of undergraduate education. Through this note's focus on centrality, students can explore the dependence of statistical models on initial assumptions and the interplay between centrality measures and hierarchical ranking, and they can use completed studies as springboards for future research. The Enron corpus also presents opportunities for research into many other areas of analysis, including social networks, clustering, and natural language processing.

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arXiv2015

Data Science in Statistics Curricula: Preparing Students to "Think with Data"

A growing number of students are completing undergraduate degrees in statistics and entering the workforce as data analysts. In these positions, they are expected to understand how to utilize databases and other data warehouses, scrape data from Internet sources, program solutions to complex problems in multiple languages, and think algorithmically as well as statistically. These data science topics have not traditionally been a major component of undergraduate programs in statistics. Consequently, a curricular shift is needed to address additional learning outcomes. The goal of this paper is to motivate the importance of data science proficiency and to provide examples and resources for instructors to implement data science in their own statistics curricula. We provide case studies from seven institutions. These varied approaches to teaching data science demonstrate curricular innovations to address new needs. Also included here are examples of assignments designed for courses that foster engagement of undergraduates with data and data science.

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arXiv2014

Differential expression analysis for multiple conditions

As high-throughput sequencing has become common practice, the cost of sequencing large amounts of genetic data has been drastically reduced, leading to much larger data sets for analysis. One important task is to identify biological conditions that lead to unusually high or low expression of a particular gene. Packages such as DESeq implement a simple method for testing differential signal when exactly two biological conditions are possible. For more than two conditions, pairwise testing is typically used. Here the DESeq method is extended so that three or more biological conditions can be assessed simultaneously. Because the computation time grows exponentially in the number of conditions, a Monte Carlo approach provides a fast way to approximate the $p$-values for the new test. The approach is studied on both simulated data and a data set of {\em C. jejuni}, the bacteria responsible for most food poisoning in the United States.

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arXiv2013

A method for generating realistic correlation matrices

Simulating sample correlation matrices is important in many areas of statistics. Approaches such as generating Gaussian data and finding their sample correlation matrix or generating random uniform $[-1,1]$ deviates as pairwise correlations both have drawbacks. We develop an algorithm for adding noise, in a highly controlled manner, to general correlation matrices. In many instances, our method yields results which are superior to those obtained by simply simulating Gaussian data. Moreover, we demonstrate how our general algorithm can be tailored to a number of different correlation models. Using our results with a few different applications, we show that simulating correlation matrices can help assess statistical methodology.

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