Who this is for
- Practitioners who finished BayeZian I (or have equivalent Stan experience) and want the advanced, production-grade toolkit.
Not for you if
- You haven't built a Bayesian model before — start with BayeZian I
- You want a quick overview, not depth
- You don't work in R and Stan
- You want off-the-shelf models, not to build your own
What you leave with
- Mixture, survival, and ordinal models in Stan
- Gaussian processes and Hilbert-space approximations
- Physics-constrained and differential-equation models
- Production-level performance tuning — parallelization and GPU
The full curriculum
19 sections · 136 lessons. Every section is listed with its lesson count; click any section to see its lessons.
01Introduction3 lessons
1.1Welcome to the Course
1.2High-Level Review of First Course Topics
1.3Roadmap of this Course
02Workflow5 lessons
2.1Workflow Introduction
2.2Before Fitting a Model
2.3Fitting a Model and Working with Simulations
2.4Evaluating and Using the Fitted Model
2.5Understanding and Comparing Multiple Models
03Mixture Models9 lessons
3.1Mixture Models Introduction
3.2Overdispersion
3.3Exploring Baseball Scores as Poisson Distributed
3.4Negative Binomial as Mixture of Poisson Distributions
3.5Baseball Scores as Mixture of Poisson Distributions
3.6Zero-Inflation Processes and Hurdle Models
3.7Modeling Three Point Attempts with Poisson and NB Models
3.8Zero-Inflated Poisson
3.9Zero-Inflated Negative Binomial
04Rating and Ranking Models10 lessons
4.1Rating and Ranking Models Introduction
4.2Pairwise Comparisons
4.3Comparing Among Items in a Set
4.4Extended Ranking Models
4.5Fitting Plackett-Luce with stan
4.6Estimating Expectation of Position
4.7Ordinal Regression
4.8General Principles of Ordinal Regression
4.9Ordinal Regression in R and Stan
4.10Simulating Scout Scores in Stan
05(A Bit More) Advanced Hierarchical Models4 lessons
5.1Advanced Hierarchical Models Introduction
5.2Common Approach Omits Information
5.3Multi-level Structure Propagates Uncertainty
5.4Motivating Example
Career payoffSurvival and Gaussian-process models are what teams hire specialists for.
06Sufficient Statistics3 lessons
6.1Sufficient Statistics Introduction
6.2Understanding Sufficient Statistics in Sports Analytics
6.3Using Sufficient Statistics in Practice
07(More About) Correlation4 lessons
7.1(More About) Correlation Introudction
7.2Trivariate Reduction
7.3Marginal Plus Conditional
7.4Copulas
08QR Decomposition4 lessons
8.1QR Reparameterization
8.2Understanding the Problem of Correlated Covariates
8.3Mathematics of QR Decomposition
8.4Practical Implementation in Stan and R
09Autoregressive Processes6 lessons
9.1Autoregressive Processes Introduction
9.2AR Processes with Equal Time between Measures
9.3AR Processes with Irregular Times (Gaps) between Measures
9.4Coding the Model in Stan
9.5Fitting the Model with Data
9.6Multiple AR Processes with Interactions
10Survival Analysis16 lessons
10.1Survival Analysis Introduction
10.2Time-to-Events | Proportional to Power Law
10.3Simulate Time-to-Event Data
10.4General Hazard and Survivor Functions
10.5Weibull Survival Model without Covariates
10.6Weibull Model with Covariates
10.7Modifying the Priors for Baseball
10.8Fitting Model to Baseball Data
10.9Posterior Inference
10.10Interpreting the Coefficients
10.11Discretizing the Weibull Distribution
10.12Discrete Hazard Function
10.13Log-Hazard in Discrete Time
10.14Discrete Time Stan Model
10.15Estimate Parameters from Baseball Data
10.16Posterior Predictive Checks
Career payoffPhysics-constrained modeling is a rare differentiator few analysts can claim.
11Differential Equations5 lessons
11.1Differential Equations Introduction
11.2Example: Usain Bolt's World Record Sprint
11.3Example: Joint Model of Sprinter World Champions
11.4Using the Model
11.5Refactoring the Model for Parallelizing the Likelihood
12Difference Equations5 lessons
12.1Difference Equations Introduction
12.2Modeling Performance: Bannister's Impulse-Response Model
12.3Cycling Power Data for Training
12.4Coding the Model in Stan
12.5Using the Model
13Splines15 lessons
13.1Splines Introduction
13.2Expected Goals Data
13.3Simulating Data for Splines
13.4Model Overview
13.5B-Spline Construction for a Single Variable
13.6Regression on B-Spline using Stan
13.7Counterfactual Data and use of Model
13.8Speeding up the Spline
13.9Tensor Product of Spline Bases
13.10Two-Dimensional Splines
13.11Implementing the Tensor Product in Stan and R
13.12Regression and Kroenecker Product
13.13Prediction for New Data
13.14Model Comparison
13.15Implications
14Gaussian Processes10 lessons
14.1Gaussian Processes Introduction
14.2Likelihood
14.3Gaussian Process Prior for Latent Function
14.4Understanding the Cholesky Decomposition in Gaussian Processes
14.5Using the Cholesky Decomposition
14.6Hyperparameters and Priors
14.7Estimates at New or Counterfactual x
14.8Stan Code for N-Dimensional Gaussian Processes
14.9Testing the Code in One Dimension
14.10Testing the Code in Two Dimensions
Career payoffProduction performance — parallelization and GPU — is what ships models in production.
15Hilbert-Space Approximate GPs12 lessons
15.1Hilbert-Space Approximate GPs Introduction
15.2Math Refresher, Fourier Transforms
15.3HSGP Basis Functions Generally
15.4Frequencies in Basis Functions
15.5More Math, Spectral Densities
15.6Basis Functions
15.7Weighted Basis Function to Sum Model
15.8Likelihood for Observed Data
15.9Priors for Parameters
15.10Full Model Specification
15.11Visual Walkthrough in r
15.12Implementation of N-Dimensional HSGP in Stan
16Physics-Constrained Models9 lessons
16.1Physics-Constrained Models Introduction
16.2Sail GP Racing
16.3Load and Explore the Data
16.4Physics of Sailing
16.5Coding the Physics in Stan
16.6Checking and Reviewing the Posterior
16.7Golf Putting
16.8Base Running
16.9Umpire Called Strikes
17Common Issues10 lessons
17.1Common Issues Introduction
17.2Outliers and Robustness
17.3Missing Data Imputation
17.4Hit Tracking System Data in Baseball
17.5Constraints in the Measurement Systems
17.6Mathematical Model
17.7Implementation in Stan
17.8Estimating Missing Values with the Model
17.9Censoring and Truncation
17.10Parameter Space Transformations
18Computational Performance5 lessons
18.1Computational Performance Introduction
18.2Coding Optimizations
18.3Within Chain Parallelization
18.4GPU
18.5Memory
19Next Steps1 lesson
19.1Next Steps
What's included
- Lifetime accessEvery module and lesson, yours to keep and revisit, forever.
- Posit cloud workspaceA provisioned enterprise IDE and compute. Nothing to install.
- Project files and codeEvery notebook, dataset, and finished build, to keep and adapt.
- All future updatesNew lessons and refreshes as the tools move, at no extra cost.
- Self-pacedStart today, go at your own pace, no cohort to wait for.
- Free with MembershipOr get this course and the full catalog with Membership.
Your instructor
Scott Spencer, PhD
Applied Analytics Professor, Columbia University | Consultant, Nottingham Forest
Known for Consultant, Nottingham Forest
Scott teaches Bayesian statistics at Columbia University and has trained analysts across professional sports, pharma, and tech. His approach emphasizes building intuition through real data before touching any formula, then immediately translating that intuition into working Stan code. His teaching method is distinctive: every concept is grounded in sports examples (Olympic sprints, basketball free throws, soccer expected goals) before being generalized to the broader statistical framework. Students leave with both deep understanding and production-ready skills. He believes Bayesian modeling is a superpower for anyone working with data, giving a principled framework to combine domain knowledge with evidence, with Stan as the engine that makes it practical.
Questions
Is this included with Membership?
Yes. AthlyticZ Membership ($2,999/yr) includes this and the entire course catalog, plus the live Masterclass. If you plan to take more than a couple of courses, Membership is the better math.
Is it self-paced?
Yes. Start today and go at your own pace, with lifetime access to every lesson and all future updates.
Do I need to install anything?
No. You work on the provisioned Posit platform in the browser, on the same enterprise tools professional teams use.