He Yichen

He Yichen

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Matrix-Structured Parameterization in MCMC for Accelerated Hypertension Prevalence Modeling

less than 1 minute read

Published:

Summary: This report presents a simpler way to format Bayesian hierarchical model for hypertension prevalence, using Singapore cohort data. It applies matrix-structured parameterization in MCMC to replace redundant intermediate variables from spline expansions, accelerating computation. This reduces runtime from 60 to 5 hours while maintaining convergence and accuracy, enabling efficient large-scale hypertension prevalence modeling.

Ripley’s K and Besag’s L Function

13 minute read

Published:

Summary: This note introduces Ripley’s $K$ and Besag’s $L$ functions for analyzing spatial point patterns. It explains CSR as the null model, defines and estimates $K(r)$ with edge corrections, variance-stabilization via $L(r)$, and the need for Monte Carlo envelopes. Redwood data illustrate clustering versus intensity-driven inhomogeneity.

Understanding of Logistic Regression

1 minute read

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Summary: This note explains why logistic regression is suited for classification. Unlike linear regression, probabilities must remain between 0 and 1. The logistic function enforces this constraint, mapping linear predictors into valid probabilities. Its log-odds formulation ensures interpretability, making logistic regression a well-defined, probabilistic approach for binary classification tasks.

Shell File Descriptor and Redirection Reference

6 minute read

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Summary: This note explains shell file descriptors and redirection. It covers stdin, stdout, stderr, and how to redirect or merge them with operators like >, 2>, and 2>&1. It shows differences between & in redirection and background execution, common command flags, pitfalls, examples, and best practices for HPC logging.

Difference between Standard Deviation and Standard Error

2 minute read

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Summary: This note clarifies the distinction between standard deviation and standard error. Standard deviation measures variability within a dataset, serving as a descriptive statistic, while standard error measures variability of sample means across repeated samples, serving as an inferential statistic. Derivations include Bessel’s correction for unbiased variance estimation and the SE formula.