Search Results for "probability"

...The code emphasizes Bayesian data analysis using R, the rethinking package, and Stan models. It includes lecture code files, example datasets, and structured exercises that parallel the topics covered in the lectures (probability, regression, model comparison, Bayesian updating). The repo functions as a direct hands-on reference for students following the 2022 recorded lecture series. There are 10 weeks of instruction. Links to lecture recordings will appear in this table. Weekly problem sets are assigned on Fridays and due the next Friday, when we discuss the solutions in the weekly online meeting.

...The key insight illustrated is that over sufficiently long holding periods (e.g. 40 years), the stock market stabilizes and nearly always yields positive returns, even accounting for extreme market crashes and recessions. The visualizations show “return curves” for different starting years and durations, and also illustrate the probability of losses over various time horizons. The project is centered on transparency in finance and encourages users to examine the data themselves; the code is shared in R and uses ggplot2 for plotting.

RStan is the R interface to Stan, a C++ library for statistical modeling and high-performance statistical computation. It lets users specify models in the Stan modeling language (for Bayesian inference), compile them, and perform inference from R. Key inference approaches include full Bayesian inference via Hamiltonian Monte Carlo (specifically the No-U-Turn Sampler, NUTS), approximate Bayesian inference via variational methods, and optimization (penalized likelihood). RStan integrates with...