Statistics

Fine-Tuning Tiny LLMs for ElasticSearch DSL

I am creating a tiny LLM for ElasticSearch DSL as a proof of concept.

compositional.mle: SICP-Inspired Optimization

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

Graduate Statistics Problem Sets Now Available

I've made my graduate coursework from SIUe's mathematics program available online, covering time series, regression, computational statistics, multivariate analysis, and statistical methods.

symlik: Symbolic Likelihood Models in Python

Introducing symlik - define statistical models symbolically and automatically derive score functions, Hessians, and Fisher information.

mdrelax: When Masking Conditions Don't Hold

Extending masked failure data analysis when traditional C1-C2-C3 conditions are violated.

Model Selection for Weibull Series Systems: When Simpler Models Suffice

When can reliability engineers safely use simpler models? This paper provides sharp boundaries through likelihood ratio tests on Weibull series systems.

Closed-Form Results for Masked Exponential 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.

The Problem

In series …

Approximations of Solomonoff Induction

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

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 …

likelihood.model: Composable Statistical Inference in R

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 Core Concept …

hypothesize: A Consistent API for Statistical Tests in R

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, …

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

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 …

dfr.dist: Specify the Hazard Function Directly

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.

The Core Insight

Instead of choosing Weibull(shape, scale), you …

algebraic.mle: The Foundation of a Statistical Inference Ecosystem

An R package treating MLEs as first-class algebraic objects with composable statistical properties.

algebraic.dist: Treating Distributions as First-Class Algebraic Objects in R

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 …