I have been accumulating problem set solutions from graduate coursework and independent study. Computational statistics, numerical methods, algorithm design. I am posting them here because working through these problems taught me more about how statistical methods actually work than any amount of calling library functions.
STAT 575: Computational Statistics
This was a valuable course taught by Dr. Qiang Beidi during Summer 2021. The problem sets covered:
Numerical Methods:
- Newton-Raphson for root finding
- Secant method and convergence analysis
- Multivariate optimization
- Numerical derivatives (Jacobian and Hessian computation)
Statistical Computing:
- Poisson regression with hand-coded Newton-Raphson
- Maximum likelihood estimation
- Comparison with built-in GLM implementations
Sampling and Simulation:
- Inverse transform method for logistic and Cauchy distributions
- Acceptance-rejection sampling for custom distributions
- Generating from geometric distributions via Bernoulli trials
- Sampling from bimodal and half-normal distributions
Everything had to be implemented from scratch in R. Fitting a Poisson regression model by hand-coding Newton-Raphson, computing gradients and Hessians numerically, teaches you things that calling glm() never will. You learn why starting values matter. You learn what convergence failure looks like from the inside. You develop the kind of debugging intuition that lets you figure out why a built-in function is giving you garbage.
STAT 482: Additional Topics
Complementary material in statistical methods and applications. More problem sets, more implementation.
Why I Post These
There is real value in implementing statistical methods from scratch. When you need to extend existing methods or develop new ones, understanding the computational substrate is not optional. After hand-coding these algorithms, you also gain a healthy respect for what well-optimized statistical software is actually doing for you.
During cancer treatment, working through these problems was a way to stay engaged with concrete, well-defined work when larger research questions felt overwhelming. A problem set with a clear answer is good for the brain when everything else is uncertain.
Accessing the Problem Sets
They are organized by course at /probsets. Each includes detailed solutions with R implementations. Full working: mathematical derivations, implementation details, and verification against built-in functions. Written for someone who wants to understand not just what works but why it works.
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