Writing
Preprints of my research work are posted on the arXiv as much as possible. Highlights include a long but comprehensive introduction to statistical computing and Hamiltonian Monte Carlo targeted at applied researches, and a more theoretical treatment of the geometric foundations of Hamiltonian Monte Carlo.
I am currently developing a book covering important concepts in probabilistic modeling with Stan. The ultimate goal is a reasonably self-contained treatment demonstrating how to build, evaluate, and utilize probabilistic models that capture domain expertise in applied analyses; the most important prerequisites are a familiarity with calculus and linear algebra.
While there is still much work to be done the currently available chapter drafts are listed below. Although relatively mature these resources are still very much dynamic and improving as I find better organizations of the material and receive feedback from readers. Please don’t hesitate to send comments through email or pull requests on the case study GitHub repositories linked below.
If this writing has been useful to you and you’d like the development of more then consider supporting me on Patreon.
Part I: Probability Theory
Updated Chapters
Chapter 1: Measure and Probability on Finite Sets HTML PDF
Chapter 2: Mathematical Spaces HTML PDF
Chapter 3: Product Spaces HTML PDF
Chapter 4: Measure and Probability on General Spaces HTML PDF
Chapter 5: Expectation Values HTML PDF
Chapter 6: Probability Density Functions HTML PDF
Chapter 7: Transforming Probability Spaces HTML PDF
Chapter 8: Conditional Probability Theory HTML PDF
Chapter 9: Probability Theory on Product Spaces (coming soon!)
Chapter 10: Useful Probability Density Functions (coming soon!)
Chapter 11: Sampling and Monte Carlo (coming soon!)
Older Chapters
Probability Theory on Product Spaces
Sampling and Monte Carlo
Common Families of Probabilty Densities
Probabilistic Computation
Markov Chain Monte Carlo
- More Comprehensive Markov chain Monte Carlo examples (Very Rough Draft!)
- arXiv manuscript
- Markov chain Monte Carlo diagnostic code
Hamiltonian Monte Carlo (coming soon!)
- arXiv manuscript
Part II: Modeling and Inference
Modeling and Inference
Generative Modeling
Prior Modeling
Introduction to Stan
Identifiability and Degeneracies
Principled Model Building Workflow
Part III: Modeling Techniques
Mixture Modeling HTML PDF
Hidden Markov Modeling HTML PDF
Pairwise Comparison Modeling HTML PDF
Hierarchical Modeling
Factor Modeling
Modeling Sparsity
Modeling Ordinal Outcomes HTML PDF
Survival Modeling
Modeling Consensus HTML PDF
Modeling Selection HTML PDF
Variate-Covariate Modeling
Modeling Functional Behavior I: Linearized Models
Modeling Functional Behavior II: General Linearized Models
Underdetermined Linearized Regression
The QR Decompostion for Linearized Regression
Modeling Functional Behavior III: Gaussian Processes
Modeling Functional Behavior IV: Stochastic Differential Equations
Modeling Functional Behavior V: The Brownian Bridge
A Short Note on The Exploded Logit Model HTML PDF
Case Studies
Inferring Customer Conversion HTML PDF
Inferring Gravity From Data
Modeling Tree Diameter Growth HTML PDF
Inferring Window Size In The Dark HTML PDF
Inferring and Deciding On Die Fairness HTML PDF
Modeling and Predicting Race Outcomes HTML PDF
Informing Movie Recommendations from Customer Reviews HTML PDF
Inferring Fertility HTML PDF
Miscellaneous
Voronoi Diagrams and Fortune’s Algorithm HTML PDF
Trying to Engineer a More Symmetric Prior Model For Positive Spaces HTML PDF
Some Ruminations on Containment Prior Modeling
Exploring a Cauchy Model
Underdetermined Linear Regression
The QR Parameterization For Linear Regression