Statistics

Masked Failure Data: Looking Back, Looking Forward

A retrospective on three years of building R packages and writing papers for masked series system reliability, and what comes next.

Observation Functors: Composable Censoring for Series System Simulation

Observation functors in maskedcauses: composable functions that separate the data-generating process from the observation mechanism, enabling mixed-censoring simulation and verified Monte Carlo studies.

maskedcauses: Maximum Likelihood Estimation for Masked Series System Failures

The maskedcauses R package for MLE in series systems with masked component failures, built on composable likelihood contributions and validated through simulation.

All of Statistics

Bayesian Data Analysis

Notes

Applied Bayesian inference with computing methods. The standard Bayesian statistics reference.

compositional.mle: SICP-Inspired Optimization

An R package where optimization solvers are first-class functions that compose through chaining, racing, and restarts.

Introduction to Probability and Mathematical Statistics

Notes

Rigorous graduate-level probability + statistics; useful for inference and ML foundations.

Statistical Inference

Notes

Standard rigorous text on estimation, hypothesis testing, and asymptotic theory.

The Elements of Statistical Learning

Graduate Statistics Problem Sets

My graduate coursework from SIUe's math program is up: time series, regression, computational stats, multivariate analysis, and statistical methods.

symlik: Symbolic Likelihood Models in Python

Define statistical models symbolically and automatically derive score functions, Hessians, and Fisher information. No numerical approximation.

hypothesize: Now on CRAN

My R package for hypothesis testing, hypothesize, is now available on CRAN.

Likelihood Models for Series Systems with Masked Component Failure Data: An R Package for Maximum Likelihood Estimation

mdrelax: When Masking Conditions Don't Hold

Extending masked failure data analysis when the standard C1-C2-C3 masking conditions are violated.

Model Selection for Weibull Series Systems: When Simpler Models Suffice

When can reliability engineers safely use simpler models? Likelihood ratio tests on Weibull series systems give sharp boundaries.

Closed-Form Results for Masked Exponential Series Systems

Closed-form MLEs and Fisher information for exponential series systems with masked failure data. No numerical optimization required.

Statistical Inference for Series Systems from Masked Failure Time Data: The Exponential Case

Alea: A Modern C++ Library for Algebraic Random Elements

Fisher Flow: An Information-Geometric Framework for Sequential Estimation

Reliability Estimation in Series Systems: Maximum Likelihood Techniques for Right-Censored and Masked Failure Data

Maximum likelihood estimation of component reliability from masked failure data in series systems, with BCa bootstrap confidence intervals validated through extensive simulation studies.

Accumux: Compositional Online Statistical Reductions in C++

A C++20 library for composing online statistical accumulators with numerically stable algorithms and algebraic composition.

Approximations of Solomonoff Induction

I experiment with simple predictive / generative models to approximate Solomonoff induction for a relatively simple synthetic data-generating process.

Math Master's Done: Post-Mortem

I defended my mathematics thesis. Three years, stage 3 cancer, and a second master's degree. Here is what worked and what did not.

Model Selection for Reliability Estimation in Series Systems

Reliability Estimation in Series Systems Maximum Likelihood Techniques for Right-Censored and Masked Failure Data

Problem Set Solutions

Graduate problem set solutions in computational statistics and numerical methods from my math master's at SIUe. Implementing things from scratch teaches you what the libraries are hiding.

Model Selection in Weibull Series Systems

In my paper, Reliability Estimation in Series Systems, I discarded a lot of research that may be interesting to pursue further. This one is about using homogeneous shape parameters for the Weibull series system, which can greatly simplify the …

Numerical Methods for Maximum Likelihood Estimation

Numerical approaches to maximum likelihood estimation, covering the optimization methods and computational issues that come up in practice.

likelihood.model: Composable Likelihood Models in R

A generic R framework for composable likelihood models. Likelihoods are first-class objects that compose through independent contributions.

Weibull Distributions: From Reliability Theory to My Own Survival Curve

Weibull distributions model time-to-failure in reliability engineering and cancer survival. I study both professionally. One of them became personal.

hypothesize: A Consistent Interface for Statistical Tests

An R package that gives hypothesis tests a consistent interface. Every test returns the same structure. You can write generic code that works across all of them.

STAT 581 - Statistical Methods - SIUe - Fall 2021

Problem sets for STAT 581 - Statistical Methods at SIUe, taught by Dr. Neath during Fall 2021.

Statistical Methods - STAT 581 - Exam 1

An experiment is conducted to study the effect of fitness level on ego > strength. Random samples of college faculty members are selected from each

Statistical Methods - STAT 581 - Exam 2

A randomized complete block design is used to study the effect of caliper on the measured diameters

Statistical Methods - STAT 581 - Problem Set 1

An experiment is designed to investigate whether the time to drill holes in rock holes using wet or dry drilling.

Statistical Methods - STAT 581 - Problem Set 2

A product developer is investigating the tensile strength of a new synthetic fiber that will be used to make cloth for men’s shirts.

Statistical Methods - STAT 581 - Problem Set 3 a

An experiment is conducted to study the effect of drilling method on drilling time. Each method (dry drilling, wet drilling) is used on $n = 12$ rocks.

Statistical Methods - STAT 581 - Problem Set 3 b

An experiment to compare a new drug to a standard is in the planning stages. The response variable of interest is the clotting time (in minutes) of blood

Statistical Methods - STAT 581 - Problem Set 4

The insulating life of protective fluids at an accelerated load is being studied. The experiment has been performed for four types of fluids, with $n = 5$

Statistical Methods - STAT 581 - Problem Set 5

A factorial experiment is used to develop a nitride etch process on a single wafer plasma etching tool.

Statistical Methods - STAT 581 - Problem Set 6

A soft drink bottler is interested in studying the effects on a filling process. A factorial experiment is run using three factors: percent carbonation (in %),

Statistical Methods - STAT 581 - Problem Set 7

A paired comparisons design is used to study the effect of machine operator on > the measured running time (in secs.) of a fuse. A sample of $n = 10$ fuses is

Statistical Methods - STAT 581 - Problem Set 8

An experiment is designed to test for systematic differences in the hardness > measurements provided by two devices (fixed effect, factor $A$).

Statistical Methods - STAT 581 - Problem Set 9

The surface finish of metal parts made on $a=4$ machines is under > investigation. > Each machine can be run by one of $b=3$ operators.

Computational Statistics - SIUe - STAT 575 - Problem Set 2

This problem set covers the E-M algorithm for right-censored normal data with known variance.

Review: A Symbolic Representation of Time Series, with Implications for Streaming Algorithms

A review of SAX (Symbolic Aggregate approXimation), a method for converting real-valued time series into symbolic representations with guaranteed distance lower bounds.

SIUe - Computational Statistics (STAT 575) - Problem Set 4

This problem set covers sampling from a Gamma distribution using Metropolis-Hastings and acceptance-rejection methods.

Bootstrap Methods: When Theory Meets Computation

Bootstrap resampling trades mathematical complexity for computational burden. When you can't derive the variance analytically, you resample. For my thesis work on masked failure data, that trade is essential.

flexhaz: Specify the Hazard Function Directly

An R package for specifying hazard functions directly instead of picking from a catalog of named distributions. You write the hazard. It handles the rest.

Regression Analysis - SIUe - STAT 482 - Probem Set 8

This problem set covers multicollinearity in regression analysis and the marginal and partial effects of predictor variables, among other topics.

STAT 482 - Regression Analysis - SIUe - Fall 2022

This is a problem set for STAT 482 - Regression Analysis at SIUe. These problem sets were given by Dr. Andrew Neath, a professor in the Department of Mathematics and Statistics at Southern Illinois University Edwardsville (SIUe) during the Fall 2022 …

STAT 575 - Computational Statistics - SIUe - Summer 2021

This is a problem set for STAT 575 - Computational Statistics at SIUe. These problem sets were given by Dr. Qiang Beidi, a professor in the Department of Mathematics and Statistics at Southern Illinois University Edwardsville (SIUe) during the Summer …

algebraic.mle: MLEs as Algebraic Objects

An R package that treats MLEs as algebraic objects. They carry Fisher information, compose through independent likelihoods, and propagate uncertainty correctly.

Discrete Multivariate Analysis - STAT 579 - Exam 2

Discrete multivariate analysis exam covering log-linear models and categorical data analysis.

Discrete Multivariate Analysis - STAT 579 - Final Exam

Final exam for discrete multivariate analysis.

Discrete Multivariate Analysis - STAT 579 - Problem Set 10

Problem set 10 for discrete multivariate analysis.

Discrete Multivariate Analysis - STAT 579 - Problem Set 5

Problem set 5 for discrete multivariate analysis.

Discrete Multivariate Analysis - STAT 579 - Problem Set 6

Problem set 6 for discrete multivariate analysis.

Discrete Multivariate Analysis - STAT 579 - Problem Set 7

Problem set 7 for discrete multivariate analysis.

Discrete Multivariate Analysis - STAT 579 - Problem Set 8

Problem set 8 for discrete multivariate analysis.

Discrete Multivariate Analysis - STAT 579 - Problem Set 9

Problem set 9 for discrete multivariate analysis.

STAT 478 - Time Series Analysis - SIUe - Spring 2021

Problem sets for STAT 478 - Time Series Analysis at SIUe, taught by Dr. Beidi during Spring 2021.

STAT 579 - Discrete Multivariate Analysis - SIUe - Spring 2021

Problem sets for STAT 579 - Discrete Multivariate Analysis at SIUe, taught by Dr. Andrew Neath during Spring 2021.

Time Series Analysis - STAT 478 - Exam 1

Time series analysis exam covering ARMA processes and model identification.

Time Series Analysis - STAT 478 - Exam 2

Time series analysis coursework.

Time Series Analysis - STAT 478 - Final Exam

Final exam for time series analysis course.

Time Series Analysis - STAT 478 - Problem Set 3

Problem set 3 for time series analysis.

Time Series Analysis - STAT 478 - Problem Set 4

Problem set 4 for time series analysis.

Time Series Analysis - STAT 478 - Problem Set 5

Problem set 5 for time series analysis.

Time Series Analysis - STAT 478 - Problem Set 6

Problem set 6 for time series analysis.

Time Series Analysis - STAT 478 - Project

Time series analysis project.

algebraic.dist: Distributions as Algebraic Objects in R

An R package that treats probability distributions as algebraic objects. They compose through standard operations. The algebra preserves distributional structure.

hypothesize: API for Hypothesis Testing

Likelihood Model

Algebra over distribution (random elements) objects

Algebraic Maximum Likelihood Estimators

Building R Packages for Statistical Inference

I'm building R packages for reliability analysis, not just using other people's. R's strengths for statistical computing are real, and building packages forces you to understand the theory.

Going Back for a Second Master's, This Time in Math

I already have an MS in Computer Science. Now I'm going back for Mathematics and Statistics, because I kept hitting walls where I could use methods but not derive them.

Dynamic failure rate (DFR) distributions

Reliability Analysis and the Problem of Censored Data

Introduction to reliability analysis with censored data, where observations are incomplete but statistically informative.