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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’.
Maximum likelihood estimation of component reliability from masked failure data in series systems, with BCa bootstrap confidence intervals validated through extensive simulation studies.
I experiment with simple predictive / generative models to approximate Solomonoff induction for a relatively simple synthetic data-generating process.
Sometimes making stronger assumptions doesn’t limit you—it illuminates the problem. This paper, developed before my master’s thesis, shows what happens when you simplify both the distribution (exponential) and the masking model: you get …
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, …
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 …
Maximum likelihood estimators have rich mathematical structure—they’re consistent, asymptotically normal, efficient. algebraic.mle exposes this structure through an algebra where MLEs are objects you compose, transform, and query.
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. …