Lecture 6 Monte-Carlo Integration R, Distribution Background (Hazard, survival, reparameterization) скачать в хорошем качестве

Lecture 6 Monte-Carlo Integration R, Distribution Background (Hazard, survival, reparameterization)

📘 Lecture 6: Bayesian Inference — Distribution Background (Hazard, Survival & Reparameterization) and Monte Carlo Integration in R In this lecture we connect distribution theory with Bayesian computation. We cover the hazard and survival functions, practical reparameterization strategies for Bayesian models, and hands-on Monte Carlo integration (with R code) to approximate posterior summaries and predictive quantities. You will learn: ✔️ Definitions & intuition: survival function, hazard function, and their relationships ✔️ Why and when to reparameterize (stability, interpretability, and better MCMC mixing) ✔️ Common reparameterizations for lifetime models (Weibull, Gamma, Log-Normal, etc.) ✔️ How the hazard/survival perspective changes model formulation and priors ✔️ Monte Carlo integration: basics, importance sampling, and simple Monte Carlo estimators ✔️ Practical R implementations: sampling, estimating posterior expectations, MC standard error, and simple importance sampling examples ✔️ Diagnostics and practical tips for reliable Monte Carlo estimation ✔️ Example applications in reliability, survival analysis, and risk modelling By the end of this lecture you will be able to: Interpret hazard and survival functions and use them to build Bayesian models. Choose and apply useful reparameterizations to improve inference. Implement Monte Carlo integration and importance sampling in R to compute posterior summaries and predictive probabilities. Check Monte Carlo error and basic diagnostic checks for sampling-based estimates. 📚 Who is this for? Students and researchers in Statistics, Biostatistics, Reliability Engineering, Data Science, and anyone using Bayesian methods with lifetime or survival data. 🔧 Includes: R code snippets, worked examples, and practical recommendations. 🔔 If you found this helpful, please like, share, and subscribe for the rest of the Bayesian lecture series. Comment below any questions or topics you want covered in future lectures! 📩 For academic queries or collaborations — feel free to reach out. #BayesianInference #SurvivalAnalysis #HazardFunction #Reparameterization #MonteCarlo #ImportanceSampling #Rstats #Reliability #StatisticsLecture