Ben Lambert’s “A Student’s Guide to Bayesian Statistics” is a valuable resource for anyone venturing into the world of Bayesian statistical methods. Now available on Amazon, this book provides a comprehensive introduction to the subject. The problem set questions and answers for the book are available here, and the data for the problem questions is available here. An errata is also available here, highlighting areas for improvement in the first edition.
One particularly useful tool created by Ben Lambert is the “Distribution Zoo” Shiny app. This application allows users to dynamically explore various probability distributions and understand the impact of their parameters.
Exploring the Distribution Zoo
The ‘The distribution zoo‘ app is designed to help students visualize and understand different distributions. Here are some of its key features:
- Dynamic Parameter Adjustment: The app allows users to change the parameters of 24 different distributions. These range from common distributions like the normal and Poisson to more complex examples like the LKJ correlation distribution. By adjusting these parameters, users can observe how they affect the distribution’s properties.
- Visualizations: The app provides plots of the probability density function (PDF) or probability mass function (PMF) for each distribution. In cases where PDFs are difficult to visualize, histograms of the sampling distribution are provided. Cumulative distribution functions (CDFs) are also available.
Alt text: A screenshot of the Distribution Zoo Shiny app interface, showcasing the dynamic parameter adjustment sliders and the probability density function plot for a selected distribution.
- Code Snippets in Multiple Languages: The app generates dynamic code snippets in R, Python, Matlab, Mathematica, and Stan. These snippets reflect the current parameter values, enabling users to see how the distributions can be implemented in different programming languages. This is especially helpful because different languages often use different parameterizations, which can make translating code challenging.
Alt text: Example of dynamic code snippets generated within the Distribution Zoo app, demonstrating the implementation of a chosen distribution in R, Python, Matlab, Mathematica, and Stan, with parameters adjusted via the app interface.
- Detailed Formulae: The app provides detailed and vetted formulae for each distribution, including useful properties. These formulae are also available in LaTeX format, simplifying their use in reports, articles, and other documents.
Accessibility and Usage
Because it is deployed on the web, the Distribution Zoo is accessible from any device. Whether you are using a laptop, tablet, or smartphone, you can explore the world of distributions.
Bug Reporting
The code is new, so errors may occur. If you encounter any issues, please report them on the Github repo here.
Conclusion
Ben Lambert’s “A Student’s Guide to Bayesian Statistics,” accompanied by the interactive “Distribution Zoo” app, provides students with a powerful set of tools for learning and understanding Bayesian statistics. The book offers a comprehensive introduction to the theoretical concepts, while the app allows for hands-on exploration and visualization of different probability distributions. By utilizing these resources, students can gain a deeper understanding of Bayesian methods and their applications. Consider checking out the book and the Distribution Zoo to enhance your understanding of Bayesian statistics.
