Statistics

Fine-Tuning Tiny LLMs for ElasticSearch DSL

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

Approximations of Solomonoff Induction

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

When Simplicity Unlocks Insight: Closed-Form Fisher Information for Masked Exponential Data

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 …

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: MLEs as First-Class Algebraic Objects

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.

The Core Idea …

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 …