From Classical Inference to Bayesian Methods: A Comprehensive Practical Guide to Statistical Modeling

This article introduces an open-source statistical modeling project maintained by Archecyn, integrating three major paradigms: classical inference, Bayesian reasoning, and probabilistic modeling. It provides dual-language implementations in Python/R and reproducible Jupyter Notebook tutorials to help learners compare the application scenarios, advantages, and disadvantages of different methods.

Statistical modeling is a core foundational skill in the field of data science, but many learners are confused about choosing between classical frequentist and Bayesian methods. As an end-to-end reference resource library, this project's uniqueness lies in integrating the three major statistical paradigms under a unified framework, providing dual-language implementations considering community language preference differences, and encapsulating all examples in reproducible Notebooks.

Classical inference constructs confidence intervals and hypothesis tests based on the idea of repeated sampling, covering parameter estimation, hypothesis testing, analysis of variance (ANOVA), and regression diagnostics. The project uses visualization and Monte Carlo simulations to help understand p-values, sampling distributions, standard errors, and confidence intervals, intuitively showing the distribution patterns of statistics under repeated sampling.

The Bayesian method treats parameters as random variables, combining prior distributions with likelihood functions to obtain posterior distributions. The content progresses step by step: from conjugate prior cases to techniques like MCMC sampling and variational inference, with PyMC3/Stan modeling examples. It specifically compares the two modeling approaches on the same dataset, clearly showing the differences in result interpretation (Bayesian as probability statements, frequentist as long-term frequency statements).

Probabilistic modeling connects statistical theory with practical applications, focusing on advanced topics such as mixture models, hierarchical models, and latent variable models. Hierarchical models are suitable for nested structure data (e.g., student-school, patient-hospital), and through education/medical cases, they demonstrate the setting of random effects and the interpretation of cross-level variations; latent variable models cover factor analysis and structural equation models, providing a complete workflow from setup to fitting evaluation.

The project emphasizes reproducibility. Each Notebook includes environment configuration instructions, dependency package version information, and random seed settings to ensure result reproducibility. In addition, it introduces the Docker containerization environment method to solve the "it works on my machine" problem and reduce the communication cost of team collaboration.

Suggested systematic learning path: first master the basics of classical inference, then transition to the Bayesian framework to build probabilistic thinking, and finally learn probabilistic modeling to integrate the two. Notebooks are graded by difficulty; beginners start with basic descriptive statistics, and it is recommended to apply the methods to their own datasets after completing the modules to consolidate knowledge through transfer application.

This project provides comprehensive resources for data science learners, suitable for students who want to solidify their foundations and practitioners who want to review advanced methods. The project code and documentation are open-sourced on GitHub, following the MIT license, allowing free use and modification. It is recommended to bookmark it as a long-term reference.