He Yichen

He Yichen

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Understanding of Methodology for Fertility Rate Forecast Model

less than 1 minute read

Published:

Summary: This note records my understanding and supplementary proofs of Schmertmann et al. (2014)’s Bayesian fertility forecasting framework. It details notation, penalty structures for shape and time, covariance prior construction, and likelihood–prior integration. The write-up illustrates posterior fertility forecasts, using Singapore as an example, while emphasizing personal interpretation and derivations.

Ripley’s K and Besag’s L Function

13 minute read

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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

Published:

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.