Becoming a BayeZian II | Advanced Bayesian Analysis with Stan | AthlyticZ
Advanced • Becoming a BayeZian II

Master Advanced Stan Programming

Go beyond foundations into production-ready Bayesian modeling: mixture models, survival analysis, Gaussian Processes, physics-constrained likelihoods, and performance engineering - all in Stan with a Columbia professor.

Mixture & Zero-Inflated Survival Analysis Gaussian Processes Physics-Constrained HSGP Approximations
19 Modules 136 Lessons 30+ Stan Files Cloud VMs Included
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Every student gets access to enterprise cloud virtual machines with Stan pre-configured, directly through the AthlyticZ Academy LMS.

Prerequisites

Build on Strong Foundations

This advanced course assumes mastery of foundational Bayesian concepts and R/Tidyverse fluency.

Becoming a BayeZian I

Priors, likelihoods, posteriors, GLMs, hierarchical models, cmdstanr basics.

View Course →
BreeZing Through the Tidyverse

Data wrangling, visualization, and functional programming in R.

View Course →
Why Advanced Bayesian?

The Gap Between Mid-Level and Principal

Overdispersion breaks simple models

Poisson assumes mean equals variance. Real count data doesn’t. Excess zeros, heavy tails, and overdispersion need mixture approaches.

NB, ZIP, ZINB & hurdle models

Principled mixture models that handle overdispersion and excess zeros. The right tool for every count distribution.

Smooth functions need hand-tuning

Polynomial fits oscillate. Arbitrary smoothing parameters have no principled basis. Small changes wreck predictions.

GPs, HSGP & splines in Stan

Gaussian Processes with full posterior uncertainty. Scalable HSGP approximations. B-splines and tensor products for flexible xG models.

Stan models too slow for production

Sampling takes hours. No parallelization strategy. Models that work on toy data fail on real-scale datasets.

Performance engineering for Stan

Vectorization, within-chain parallelization, GPU acceleration, QR reparameterization, and memory management. Make Stan fly.

Scott Spencer
Your Instructor

Scott Spencer

Columbia University • Stan Language Collaborator • Fortune 500 Advisor
“The techniques in this course - GPs, survival models, physics-constrained likelihoods - are what separate academic Bayesian from production Bayesian. These are the patterns I use when advising Fortune 500 companies and sports franchises.”

Scott Spencer is one of the world’s foremost experts in applied Bayesian analysis. As a Columbia professor and Stan collaborator, his methods power decisions at Amazon, Johnson & Johnson, Vevo, and leading sports franchises. In this advanced course, Scott shares the production-ready patterns and performance optimizations that distinguish academic exercises from real-world Bayesian systems.

Columbia University Stan Collaborator Fortune 500 Advisor Sports Analytics
The Full Curriculum

19 Advanced Modules

19 modules. 136 lessons. 30+ Stan files. Click any module to see every lesson.

I
Phase I • Workflow & Mixture Models
From Rigorous Workflow to Overdispersion
3 modules • 17 lessons

Establish a repeatable Bayesian workflow, then tackle overdispersion and excess zeros with NB, ZIP, ZINB, and hurdle models using baseball and basketball data.

01
Introduction
3 lessons
Welcome to the Course
High-Level Review of First Course Topics
Roadmap of this Course
02
Workflow
5 lessonsFree Preview
Workflow Introduction
Before Fitting a Model
Fitting a Model and Working with Simulations
Evaluating and Using the Fitted Model
Understanding and Comparing Multiple Models
03
Mixture Models
9 lessonsFree Preview
Mixture Models Introduction
Overdispersion
Exploring Baseball Scores as Poisson
Negative Binomial as Mixture of Poisson
Baseball Scores as Mixture of Poisson
Zero-Inflation Processes and Hurdle Models
Three Point Attempts with Poisson and NB
Zero-Inflated Poisson
Zero-Inflated Negative Binomial
The Foundation

Rigorous Workflow Before Fancy Models

Advanced models are worthless without rigorous workflow. Scott starts with the end-to-end process - prior predictive checks, diagnostics, posterior validation, model comparison - before touching any advanced technique. This discipline is what separates production Bayesian from academic Bayesian.

II
Phase II • Ranking, Structure & Computation
Advanced Hierarchical Models & Computational Tricks
6 modules • 31 lessons

Rating and ranking models, advanced hierarchical structures, sufficient statistics, correlation modeling, QR decomposition, and autoregressive processes.

04
Rating and Ranking Models
10 lessonsFree Preview
Rating and Ranking Models Introduction
Pairwise Comparisons
Comparing Among Items in a Set
Extended Ranking Models
Fitting Plackett-Luce with Stan
Estimating Expectation of Position
Ordinal Regression
General Principles of Ordinal Regression
Ordinal Regression in R and Stan
Simulating Scout Scores in Stan
05
Advanced Hierarchical Models
4 lessonsFree Preview
Advanced Hierarchical Models Introduction
Common Approach Omits Information
Multi-level Structure Propagates Uncertainty
Motivating Example
06
Sufficient Statistics
3 lessonsFree Preview
Sufficient Statistics Introduction
Understanding Sufficient Statistics in Sports
Using Sufficient Statistics in Practice
07
Correlation
4 lessonsFree Preview
Correlation Introduction
Trivariate Reduction
Marginal Plus Conditional
Copulas
08
QR Decomposition
4 lessonsFree Preview
QR Reparameterization
Problem of Correlated Covariates
Mathematics of QR Decomposition
Practical Implementation in Stan and R
09
Autoregressive Processes
6 lessonsFree Preview
Autoregressive Processes Introduction
AR with Equal Time between Measures
AR with Irregular Times
Coding the Model in Stan
Fitting the Model with Data
Multiple AR Processes with Interactions
The Toolkit

Computational Tricks That Make Stan Practical

QR decomposition fights collinearity. Sufficient statistics compress data without losing information. Copulas model flexible dependence structures. These are the computational tricks that turn slow, unstable Stan models into fast, reliable production systems.

III
Phase III • Survival, GPs & Splines
The Advanced Modeling Techniques
6 modules • 63 lessons

The core of the advanced curriculum: survival analysis, differential and difference equations, B-splines, full Gaussian Processes, and scalable HSGP approximations.

10
Survival Analysis
16 lessonsFree Preview
Survival Analysis Introduction
Time-to-Events | Proportional to Power Law
Simulate Time-to-Event Data
General Hazard and Survivor Functions
Weibull Survival Model without Covariates
Weibull Model with Covariates
Modifying the Priors for Baseball
Fitting Model to Baseball Data
Posterior Inference
Interpreting the Coefficients
Discretizing the Weibull Distribution
Discrete Hazard Function
Log-Hazard in Discrete Time
Discrete Time Stan Model
Estimate Parameters from Baseball Data
Posterior Predictive Checks
11
Differential Equations
5 lessonsFree Preview
Differential Equations Introduction
Usain Bolt’s World Record Sprint
Joint Model of Sprinter World Champions
Using the Model
Refactoring for Parallelizing the Likelihood
12
Difference Equations
5 lessonsFree Preview
Difference Equations Introduction
Bannister’s Impulse-Response Model
Cycling Power Data for Training
Coding the Model in Stan
Using the Model
13
Splines
15 lessonsFree Preview
Splines Introduction
Expected Goals Data
Simulating Data for Splines
Model Overview
B-Spline Construction for a Single Variable
Regression on B-Spline using Stan
Counterfactual Data and Use of Model
Speeding up the Spline
Tensor Product of Spline Bases
Two-Dimensional Splines
Implementing the Tensor Product in Stan
Regression and Kronecker Product
Prediction for New Data
Model Comparison
Implications
14
Gaussian Processes
10 lessonsFree Preview
Gaussian Processes Introduction
Likelihood
GP Prior for Latent Function
Understanding the Cholesky Decomposition
Using the Cholesky Decomposition
Hyperparameters and Priors
Estimates at New or Counterfactual x
Stan Code for N-Dimensional GPs
Testing the Code in One Dimension
Testing the Code in Two Dimensions
15
Hilbert-Space Approximate GPs
12 lessonsFree Preview
HSGP Introduction
Fourier Transforms Refresher
HSGP Basis Functions Generally
Frequencies in Basis Functions
Spectral Densities
Basis Functions
Weighted Basis Function to Sum Model
Likelihood for Observed Data
Priors for Parameters
Full Model Specification
Visual Walkthrough in R
Implementation of N-Dimensional HSGP in Stan
The Deep End

Survival. GPs. Splines. The Skills That Command $250K+

These six modules cover the techniques that separate a $120K data scientist from a $250K+ principal. Pfizer uses survival models for drug approval. Citadel uses GPs for risk pricing. Amazon uses HSGP for personalization at billion-user scale. Every technique here maps to a real hiring signal.

IV
Phase IV • Physics, Robustness & Performance
Production-Ready Advanced Stan
4 modules • 25 lessons

Embed mechanics into likelihoods for sailing, golf, and baseball. Handle missing data, censoring, and outliers. Then make Stan fly with vectorization, parallelization, and GPU acceleration.

16
Physics-Constrained Models
9 lessonsFree Preview
Physics-Constrained Models Introduction
Sail GP Racing
Load and Explore the Data
Physics of Sailing
Coding the Physics in Stan
Checking and Reviewing the Posterior
Golf Putting
Base Running
Umpire Called Strikes
17
Common Issues
10 lessonsFree Preview
Common Issues Introduction
Outliers and Robustness
Missing Data Imputation
Hit Tracking System Data in Baseball
Constraints in the Measurement Systems
Mathematical Model
Implementation in Stan
Estimating Missing Values with the Model
Censoring and Truncation
Parameter Space Transformations
18
Computational Performance
5 lessons
Computational Performance Introduction
Coding Optimizations
Within Chain Parallelization
GPU
Memory
19
Next Steps
1 lesson
Next Steps
The Finish Line

Physics in the Likelihood. Production at Scale.

By the end of this course, you can embed sailing mechanics into a Stan model, impute missing tracking data, handle censored observations, and make your models fast enough for production with GPU acceleration and within-chain parallelization. This is the full advanced Bayesian toolkit.

Industry Endorsements

Trusted by Analytics Leaders

Michael S. Czahor, PhD
Michael S. Czahor, PhD
President, AthlyticZ

“Scott Spencer brings Bayesian modeling alive. He not only explains the math, but shows how to implement models in Stan that are clear, scalable, and ready for research or production.”

Bill Geivett
Bill Geivett, M.Ed.
Former Sr. VP, Colorado Rockies

“AthlyticZ has completely transformed the learning approach to data science through the use of sports-based problems. The instructors are the best of the best.”

Invest in Advanced Bayesian

Enroll in Becoming a BayeZian II

Advanced Course

Becoming a BayeZian II

$1,449
Lifetime Access • Cloud VMs Included
  • 19 modules, 136 lessons
  • 30+ advanced Stan model files
  • GPs, HSGP, survival, splines, physics models
  • Performance engineering: GPU, parallelization
  • Taught by Columbia professor Scott Spencer
  • Certificate of completion
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Stan pre-configured via AthlyticZ Academy LMS
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Save With the Bundle

Get Both Bayesian Courses Together

Combine Becoming a BayeZian I (foundations) + Becoming a BayeZian II (advanced) into one bundle for a complete Bayesian education - from priors to physics-constrained models.

AthlyticZ Membership

Members Pay $1,159 for This Course

Plus unlimited cloud VM access, 10+ live sessions per month, the full replay library, and 20% off every course in the catalog.

Frequently Asked Questions

Yes. This course assumes mastery of foundational Bayesian concepts covered in BayeZian I: priors, likelihoods, posteriors, GLMs, hierarchical models, and cmdstanr basics. You should also be comfortable with R and the Tidyverse.
BayeZian I covers foundations through hierarchical models and a soccer xG capstone. BayeZian II covers advanced topics: mixture models, survival analysis, Gaussian Processes, HSGP, physics-constrained models, splines, differential equations, and computational performance engineering. Consider the BayeZian Bundle to get both.
Real sports data throughout: baseball survival models, basketball mixture models, sailing physics, golf putting geometry, Usain Bolt’s sprint dynamics, cycling training load, soccer expected goals with splines and GPs, and umpire strike zone modeling. Every advanced technique is taught through a concrete application.
Cloud virtual machine access is included with your enrollment. You will code in enterprise-grade cloud environments directly through the AthlyticZ Academy LMS - no local installation required. Stan and all dependencies are pre-configured.
You may drop within 3 days of commencement for a full refund. No refunds after day 3 or if you have completed 25% or more of the course.
Becoming a BayeZian II

Join the Elite Analysts Who
Build What Others Can’t

19 modules. 136 lessons. 30+ Stan files. GPs, survival, physics-constrained models. Cloud virtual machines included.

$1,449
Lifetime Access
Members pay $1,159
3-day money-back guarantee • Lifetime updates • Certificate of completion
$1,449
Members $1,159 • Cloud VMs Included
Enroll Now