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I presented my master’s project in October 2023. It was titled ‘Reliability Estimation in Series Systems: Maximum Likelihood Techniques for Right-Censored and Masked Failure Data’.
An R package where solvers are first-class functions that compose through chaining, racing, and restarts.
I've made my graduate coursework from SIUe's mathematics program available online, covering time series, regression, computational statistics, multivariate analysis, and statistical methods.
Introducing symlik - define statistical models symbolically and automatically derive score functions, Hessians, and Fisher information.
My R package for hypothesis testing, hypothesize, is now available on CRAN.
Extending masked failure data analysis when traditional C1-C2-C3 conditions are violated.
When can reliability engineers safely use simpler models? This paper provides sharp boundaries through likelihood ratio tests on Weibull series systems.
This paper provides complete analytical results for maximum likelihood estimation in series systems with masked failure data under exponential component lifetimes. Unlike numerical approaches, everything here has a closed form.
In series …
Maximum likelihood estimation of component reliability from masked failure data in series systems, with BCa bootstrap confidence intervals validated through extensive simulation studies.
A modern C++20 library for compositional online data reductions with numerically stable algorithms and algebraic composition.
I experiment with simple predictive / generative models to approximate Solomonoff induction for a relatively simple synthetic data-generating process.
I defended my mathematics thesis yesterday. It’s done.
Three years. Two degrees. Stage 3 cancer. And now: MS in Mathematics and Statistics from SIUE.
October 13, 2023: Defense complete.
Time for a post-mortem on what worked, what didn’t, …
I have a fairly broad interest in problem-solving, from problems in statistics to algorithms. Over the years, I’ve accumulated a collection of problem sets from graduate coursework and independent study. These represent solutions to challenging …
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 approaches to solving maximum likelihood estimation problems.
Most R packages hardcode specific likelihood models. likelihood.model provides a generic framework where likelihoods are first-class composable objects—designed to work seamlessly with algebraic.mle for maximum likelihood estimation.
The Weibull distribution models time-to-failure. In reliability engineering, that’s component lifetimes. In medicine, it’s survival times.
I’ve been studying Weibull distributions for my thesis on series system reliability. Then I …
R’s hypothesis testing functions are inconsistent—t.test() returns different structures than chisq.test(), making generic workflows painful. hypothesize provides a unified API so any test returns the same interface: p-value, test statistic, …
Problem sets for STAT 581 - Statistical Methods at SIUe, taught by Dr. Neath during Fall 2021.
An experiment is conducted to study the effect of fitness level on ego > strength. Random samples of college faculty members are selected from each
A randomized complete block design is used to study the effect of caliper on the measured diameters
An experiment is designed to investigate whether the time to drill holes in rock holes using wet or dry drilling.
A product developer is investigating the tensile strength of a new synthetic fiber that will be used to make cloth for men’s shirts.
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.
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
The insulating life of protective fluids at an accelerated load is being studied. The experiment has been performed for four types of fluids, with $n = 5$
A factorial experiment is used to develop a nitride etch process on a single wafer plasma etching tool.
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 %),
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
An experiment is designed to test for systematic differences in the hardness > measurements provided by two devices (fixed effect, factor $A$).
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.
This problem set covers the E-M algorithm for right-censored normal data with known variance.
In [1], the authors present a method for constructing a symbolic (nominal) representation for real-valued time series data. A symbolic representation is desirable because then it becomes possible to use many of the effective algorithms that require …
This problem set covers sampling from a Gamma distribution using Metropolis-Hastings and acceptance-rejection methods.
Bootstrap methods sit at a beautiful intersection: rigorous statistical theory implemented through brute-force computation.
The bootstrap is conceptually simple: if you don’t know the sampling distribution of a statistic, …
Most survival analysis forces you to pick from a catalog—Weibull, exponential, log-normal. dfr.dist flips this: you specify the hazard function directly, and it handles all the math.
Instead of choosing Weibull(shape, scale), you …
This problem set covers multicollinearity in regression analysis and the marginal and partial effects of predictor variables, among other topics.
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 …
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 …
An R package treating MLEs as first-class algebraic objects with composable statistical properties.
Discrete multivariate analysis exam covering log-linear models and categorical data analysis.
Final exam for discrete multivariate analysis.
Problem set 10 for discrete multivariate analysis.
Problem set 5 for discrete multivariate analysis.
Problem set 6 for discrete multivariate analysis.
Problem set 7 for discrete multivariate analysis.
Problem set 8 for discrete multivariate analysis.
Problem set 9 for discrete multivariate analysis.
Problem sets for STAT 478 - Time Series Analysis at SIUe, taught by Dr. Beidi during Spring 2021.
Problem sets for STAT 579 - Discrete Multivariate Analysis at SIUe, taught by Dr. Andrew Neath during Spring 2021.
Time series analysis exam covering ARMA processes and model identification.
Time series analysis coursework.
Final exam for time series analysis course.
Problem set 3 for time series analysis.
Problem set 4 for time series analysis.
Problem set 5 for time series analysis.
Problem set 6 for time series analysis.
Time series analysis project.
Most statistical software treats probability distributions as static parameter sets you pass to sampling or density functions. algebraic.dist takes a different approach: distributions are algebraic objects that compose, transform, and combine using …
One of the best parts of my mathematics degree is deepening my R skills—not just using R packages, but building them.
R has a unique position in statistics:
I’ve decided to pursue a second master’s degree—this time in Mathematics and Statistics at SIUE.
People ask: “You already have an MS in Computer Science. Why go back?”
Computer science gave me tools. …
One of the most interesting statistical problems I’ve encountered is reliability analysis with censored data—situations where you know something didn’t fail, but not when it will fail.
Imagine testing light bulbs. …