Index: Research

Research

Routing Summary

This folder covers applied statistics, econometrics, causal inference, causal discovery, Bayesian experimental design, probabilistic numerics, physics, agent-based modeling, and market response models from textbooks and research papers. Contains 595 notes across 10 major topics (85 notes in 11 new clusters added 2026-09-18, including the new Machine Learning and AI topic).

• Need Bayesian inference, computation, or regression? → Bayesian Statistics
• Need the applied Bayesian workflow — priors, predictive checks, LOO, failure modes, or 16 worked case studies? → Bayesian Workflow, starting at Bayesian Workflow Book - Overview
• Need causal inference toolkit (IV, DiD, RD, synthetic control, GSC, DAGs)? → Econometrics
• Need causal structure learning / DAG discovery from data (NOTEARS, continuous optimization)? → Causal Discovery
• Need forking paths, power analysis, ad measurement, or longitudinal causal inference? → Research Methodology
• Need Bayesian experimental design / expected information gain (EIG estimators, gradient/ACE/PCE, deep adaptive design)? → Bayesian Experimental Design
• Need probabilistic numerics (Bayesian quadrature, probabilistic linear solvers, Bayesian optimisation, ODE filters — computation as inference)? → Probabilistic Numerics
• Need quantum mechanics, QFT, QED, renormalization, gauge theory, or the Standard Model? → Physics
• Need ABM methodology, consumer behavior simulation, WOM modeling, or ABM calibration (GA, HM+ABC, uncertainty quantification)? → Agent-Based Modeling
• Need market response models (functional forms, carryover, VAR, empirical elasticities)? → Market Response Models
• Need machine learning / AI (transformers, scaling laws, in-context learning, chain-of-thought, RAG, ReAct agents, RLHF, conformal prediction, probabilistic forecasting with DeepAR / Chronos / MinT)? → Machine Learning and AI
• Need ML for causal inference (DML, causal forests, R-learner)? → Causal Machine Learning; synthetic DiD / event studies / Honest DiD? → Synthetic Difference-in-Differences
• Need variational inference or neural simulation-based inference? → Variational Inference, Neural Simulation-Based Inference
• Need online A/B testing statistics (CUPED, always-valid inference, SRM, switchbacks)? → Online Experimentation; customer lifetime value (Pareto-NBD, BG-NBD)? → Customer Lifetime Value; LLM-powered simulated consumers? → LLM-Powered Agents
• Need user-level ad experiments (ghost ads, PSA/ITT designs, conversion lift, power economics, experimental benchmarks, identity fragmentation, user- vs geo-level)? → User-Level Ad Experiments
• Need a specific concept? Check the Concept Map below or use the .base files for database views

Concept Map

Topic	Notes	Key Concepts
Bayesian Statistics	217	Bayes’ theorem, conjugate priors, hierarchical models, MCMC/HMC, GLMs, GPs, spatial, copulas, BART, Bayesian IPW, Bayesian causal inference, simulation-based calibration (SBC), and the full 2026 Bayesian Workflow textbook (79 notes: model building and priors, predictive checking, PSIS-LOO, computational failure modes, 16 case studies); variational inference (ELBO, CAVI, ADVI, VAEs, flows, PSIS/VSBC diagnostics) and neural simulation-based inference (NPE/NLE/NRE, amortized vs sequential, ABM calibration)
Bayesian Experimental Design	21	Lindley’s information measure (1956), expected information gain (EIG), nested Monte Carlo, variational EIG estimators (posterior/marginal/VNMC/implicit), unified stochastic-gradient design, adaptive & prior contrastive estimation (ACE/PCE), sequential/adaptive design, deep adaptive design (DAD) policies, EIG vs Fisher information
Probabilistic Numerics	36	Computation as Bayesian inference, the numerical agent, Gaussian algebra/GP regression, Gauss–Markov/SDE priors, Kalman filter & RTS smoother, Bayesian quadrature (kernel means, classical rules as posterior means), probabilistic linear solvers (CG = BayesCG), Bayesian optimisation (PI/EI/UCB/KG, entropy search), ODE filters & smoothers (EKF0/EKF1, convergence theory), uncertainty calibration
Econometrics	65	Selection bias, CEF, IV, LATE, DiD, RD, synthetic control, GSC, DAGs, Bayesian IPTW, quantile regression, discrete choice, SMM, Brock-Mirman structural estimation, staggered/multi-period DiD (group-time ATT, doubly-robust), factor copulas / high-dimensional tail dependence; synthetic DiD, event studies, pre-trend testing, Honest DiD, causal machine learning (DML, Neyman orthogonality, cross-fitting, causal forests / GRF, R-learner)
Causal Discovery	5	DAG / Bayesian-network structure learning, linear SEM, score-based learning, NOTEARS continuous optimization, smooth acyclicity $h(W)=\mathrm{tr}{e}^{W\circ W}-d$, augmented Lagrangian, vs FGS/GES/PC
Research Methodology	16+3+8	Forking paths, researcher degrees of freedom, activity bias, power analysis, FDR, survival analysis, Type S/M errors, Bayesian multiple comparisons, within/between-persons distinction (Rohrer & Murayama 2023), fixed-effects model, CLPM, dynamic panel model, estimands in longitudinal research, Table 2 Fallacy, regression adjustment logic, nuisance parameter bias simulation; online experimentation (CUPED, peeking, mSPRT / always-valid p-values, confidence sequences, SRM, marketplace interference, switchbacks)
Physics	14	Quantum mechanics (overview, formalism, phenomena, wave functions, Schrödinger equation, uncertainty, entanglement), QFT, canonical quantization, QED, renormalization, gauge theory, Yang–Mills, Standard Model (the former Theoretical Physics/ folder was merged in on 2026-09-18)
Agent-Based Modeling	42	ABM methodology, emergence, heterogeneity, consumer utility models, CUBES behavioral simulator, WOM, opinion leaders, network diffusion, GA calibration, validation, HM+ABC calibration (McCulloch et al. 2022), history matching, ABC, uncertainty quantification; LLM-powered agents (generative agents, silicon samples, homo silicus, persona-mixture calibration, validity threats)
Market Response Models	47	Functional forms (10), Koyck/ADL carryover, reaction functions, OLS/2SLS/Bayes estimation, ARIMA, transfer functions, VAR, cointegration, ECM, empirical generalizations (advertising ≈ 0.10, price ≈ −2.5), Bayesian MMM (adstock, Hill saturation, ROAS/mROAS, optimal media mix); customer lifetime value (Pareto-NBD, BG-NBD, Gamma-Gamma, RFM iso-value curves, shifted-beta-geometric retention); user-level ad experiments (ITT/PSA/ghost ads, ITT→ATT, Lewis–Rao power economics, conversion lift, Gordon et al. benchmarks, identity fragmentation, user- vs geo-level decision)
Machine Learning and AI	29	Transformers and LLM foundations (attention, architecture, pretraining, Kaplan and Chinchilla scaling laws, in-context learning), LLM reasoning, retrieval and agents (chain-of-thought, RAG, ReAct, tool-use loop, RLHF, reward modeling, evaluation), conformal prediction (split conformal, CQR, conditional coverage, covariate shift, counterfactual / ITE intervals), probabilistic forecasting (proper scoring rules, DeepAR, Chronos, local vs global models, MinT reconciliation, backtesting)

Cross-Cutting Themes

• ML meets inference (added 2026-09-18): Neyman Orthogonality → Cross-Fitting and Sample Splitting → Honest Trees and Causal Forests (ML for causal effects); Split Conformal Prediction and the Coverage Guarantee → Conformal Inference for Counterfactuals and ITEs (distribution-free uncertainty); The ELBO and KL Divergence Minimization → Reparameterization Trick and Variational Autoencoders → Neural Posterior Estimation (NPE) (neural Bayesian computation); Silicon Samples and Algorithmic Fidelity ↔ Poststratification (LLMs as simulated populations)

• Experimentation stack for marketing measurement: CUPED and Regression-Adjusted Variance Reduction / Always-Valid p-values and the mSPRT (user-level A/B) → Interference and Marketplace Experiments / Switchback Experiment Design and Analysis → User-Level Ad Experiments - Overview / User-Level vs Geo-Level Experiments - When to Use Which → Geo-Experiment Methodology - Overview → SDID for Geo Experiments and Marketing Panels → Bayesian Media Mix Modeling - Overview; value metric from Customer Lifetime Value - Overview

• Bayesian vs. Frequentist: Asymptotics and Frequentist Connections, Forking Paths and Bayesian Approaches

• Causal Inference: The Experimental Ideal, Activity Bias in Advertising, Data Collection Models, Counterfactual Inference, Nonparametric Causal Inference, Directed Acyclic Graphs, Synthetic Control, Bayesian Inverse Probability Weighting, DAGs and Causal Identification, Bayesian Inverse Probability Weighting, Table 2 Fallacy, Logic of Regression Adjustment

• Staggered Difference-in-Differences (Callaway & Sant’Anna): Difference-in-Differences with Multiple Time Periods - Overview → Group-Time Average Treatment Effects → Identifying Assumptions for Staggered DiD → Doubly-Robust Estimands for ATT(g,t) → Aggregating Group-Time Effects → Simultaneous Inference via Multiplier Bootstrap

• High-Dimensional Dependence (Factor Copulas): Factor Copulas - Overview → Factor Copula Construction → Tail Dependence in Factor Copulas / Multi-Factor and Block Dependence Structures → SMM Estimation of Factor Copulas → Factor Copula Application - S&P 100 and Systemic Risk

• Simulation-Based Calibration (SBC): Simulation-Based Calibration - Overview → Data-Averaged Posterior Self-Consistency → Rank Statistics and Uniformity → The SBC Algorithm → Interpreting SBC Histograms → SBC Case Studies

• Bayesian Media Mix Modeling: Carryover (Adstock) Functional Forms + Shape (Saturation) Effects → Bayesian Media Mix Modeling - Overview → Bayesian Estimation and Priors for MMM → ROAS, mROAS, and Optimal Media Mix → MMM Model Selection and Application

• Causal Discovery (structure learning): NOTEARS - Overview, DAG Structure Learning Problem, Smooth Characterization of Acyclicity, NOTEARS Algorithm, NOTEARS Experiments

• Bayesian Experimental Design (EIG): Lindley’s Information Measure → Expected Information Gain → Nested Estimation and Nested Monte Carlo → Variational BOED - Overview → Unified SGD BOED - Overview (Adaptive Contrastive Estimation (ACE) / Prior Contrastive Estimation (PCE)) → Modern Bayesian Experimental Design - Overview → From Designs to Policies (Deep Adaptive Design)

• Probabilistic Numerics (computation as inference): Computation as Probabilistic Inference / The Numerical Agent → Gaussian Distributions and Algebra → {Gaussian Process Regression, Gauss-Markov Processes and SDEs → Bayesian Filtering and Smoothing} → application branches: Bayesian Quadrature → Classical Quadrature as Inference; Probabilistic Linear Solvers - Algorithmic Scaffold → Conjugate Gradients as Probabilistic Inference; Bayesian Optimisation → Acquisition Functions; ODE Filters and Smoothers → Theory of ODE Filters and Smoothers

• Model Building: Bayesian Workflow Book - Overview → From Inference to Data Analysis to Workflow → Choosing an Initial Model → Prior Predictive Checking → Posterior Predictive Checking → Cross Validation Checking → Model Expansion - Predictive Consistency and Coherence; also Bayesian Workflow - Overview, Model Checking, Model Comparison, Overfitting and Information Criteria

• Multiple Comparisons: Multiple Comparisons - Bayesian Perspective, Multiple Testing Corrections, Type S and Type M Errors, Partial Pooling as Multiple Comparisons Correction

• Missing Data: Missing Data Models, Missing Data - Statistical Rethinking, Data Collection Models

• Regression: Bayesian Linear Regression, Regression and the CEF, Hierarchical Linear Models, Generalized Linear Models

• Physics Chain (survey): Quantum Mechanics - Overview → Quantum Mechanics - Mathematical Formalism → Quantum Field Theory - Overview → QED and Renormalization → Gauge Theory - Overview → Standard Model and Gauge Groups

• Physics Chain (concepts): Wave Function and Hilbert Space → Schrödinger Equation and Time Evolution → Uncertainty Principle → Quantum Entanglement → Canonical Quantization of Fields → Renormalization → Yang-Mills Theory and Gauge Fields

• ABM Calibration Chain: ABM Calibration Overview → Genetic Algorithm Calibration for ABM → HM-ABC Calibration Framework → History Matching for ABMs → Approximate Bayesian Computation for ABMs (with Uncertainty Quantification for ABM Calibration feeding both HM and ABC)

• Longitudinal Causal Inference: Within-Between Persons Distinction - Overview → Within-Between Persons Causal Inference → Fixed-Effects Model / Cross-Lagged and Dynamic Panel Models (guided by Estimands in Longitudinal Research)

Sources

• BDA3 — Bayesian Data Analysis, 3rd Edition (Gelman et al., 2013/2025)
• BayesWorkflow — Bayesian Workflow (Gelman, Vehtari, Simpson et al., 2020)
• StatRethink-Bayes — Statistical Rethinking: A Bayesian Course (McElreath, 2015)
• p_hacking — The Garden of Forking Paths (Gelman & Loken, 2013)
• ssrn-2080235 — Here, There, and Everywhere (Lewis, Rao, & Reiley, 2011)
• Mostly Harmless Econometrics — Mostly Harmless Econometrics (Angrist & Pischke, 2008)
• Discrete Choice and Random Utility Models — PyMC tutorial: Bayesian discrete choice / random utility models (2026-04-08)
• Factor analysis — PyMC tutorial: factor analysis and probabilistic PCA (2026-04-08)
• Baby Births Modelling with HSGPs — PyMC tutorial: Hilbert Space Gaussian Processes for time series (2026-04-09)
• Bayesian Non-parametric Causal Inference — PyMC tutorial: BART + propensity scores for causal ATE/ATT estimation (2026-04-09)
• Bayesian copula estimation Describing correlated joint distributions — PyMC tutorial: Gaussian copula for joint distributions (2026-04-09)
• Missing Data — PyMC / Statistical Rethinking Lecture 18: DAG-based missing data analysis (2026-04-09)
• Counterfactual inference calculating excess deaths due to COVID-19 — PyMC tutorial: Bayesian counterfactual inference, COVID excess deaths (2026-04-09)
• Confirmatory Factor Analysis and Structural Equation Models in Psychometrics — PyMC case study: CFA and SEM for psychometrics (2026-04-09)
• The Besag-York-Mollie Model for Spatial Data — PyMC tutorial: BYM spatial model on NYC traffic data (2026-04-09)
• Difference in differences — PyMC tutorial: Bayesian DiD with counterfactual prediction (2026-04-09)
• Social Networks — PyMC / Statistical Rethinking Lecture 15: dyadic social network models (2026-04-09)
• Bayesian moderation analysis — PyMC tutorial: moderation analysis with interaction terms (2026-04-09)
• multiple2f — “Why we (usually) don’t have to worry about multiple comparisons” (Gelman, Hill & Yajima, 2009)
• 15 - Synthetic Control — Causal Inference for the Brave and True — Causal Inference for the Brave and True, Ch. 15: synthetic control with Python (Matheu Facure, 2023)
• Unlock the Secrets of Causal Inference with a Master Class in Directed Acyclic Graphs — Graham Harrison, Towards Data Science (2023-04-06): DAGs, confounders, backdoor adjustment, d-separation
• How to use Bayesian propensity scores and inverse probability weights — Andrew Heiss (2021-12-18): Liao-Zigler Bayesian IPW in R/brms
• Quantum mechanics — Wikipedia: quantum mechanics, Hilbert space formalism, Schrödinger equation, entanglement, Bell’s theorem (2026-04-11)
• Quantum field theory — Wikipedia: quantum field theory, canonical quantization, Fock space, path integrals, Feynman diagrams (2026-04-11)
• Gauge theory — Wikipedia: gauge theory, local symmetry, Yang-Mills, Standard Model gauge groups (2026-04-11)
• Market Response Models Econometric and Time Series Analysis — Hanssens, Parsons & Schultz (2001), 2nd Ed.: functional forms, Koyck/ADL lags, OLS/2SLS/Bayes, ARIMA, transfer functions, VAR/cointegration/ECM, advertising/price empirical generalizations
• abm_word_of_mouth — Bonabeau (2002), ABM methods and techniques for simulating human systems (PNAS)
• abm_consumer — Karakaya, Badur & Aytekin (2011), marketing strategies with WOM using ABM
• abm_human_behaviour — Ben Said, Bouron & Drogoul (2002), CUBES consumer behavior simulator
• calibration_ABM — McCulloch et al. (2022), Calibrating ABMs using Uncertainty Quantification Methods (JASSS 25(2))
• rohrer-murayama-2023 — Rohrer & Murayama (2023), These Are Not the Effects You Are Looking For: Causality and the Within/Between-Persons Distinction (AMPPS 6(1))
• These Are Not the Effects You Are Looking For — A. Jordan Nafa (2022), Table 2 Fallacy, logic of statistical control/mutual adjustment, simulation (R/Python/Stan) demonstrating nuisance parameter bias (2026-06-26)
• 19 — Evans (2024), Computational Methods for Economists, Ch. 19: SMM theory, Python implementation, Brock-Mirman structural macro exercise (2026-04-12)
• NOTEARS — Zheng, Aragam, Ravikumar & Xing (2018), DAGs with NO TEARS: Continuous Optimization for Structure Learning (NeurIPS), arXiv:1803.01422 (2026-06-17)
• Callaway & Sant’Anna - DiD with Multiple Time Periods — Callaway & Sant’Anna (2020), staggered difference-in-differences: group-time ATT, doubly-robust estimands, aggregation, multiplier-bootstrap inference (2026-06-17)
• Oh & Patton - Factor Copulas — Oh & Patton (2012), high-dimensional factor copulas, EVT tail dependence, rank-based SMM, S&P 100 systemic risk (2026-06-17)
• Talts et al. - Simulation-Based Calibration — Talts, Betancourt, Simpson, Vehtari & Gelman (2018), validating Bayesian inference algorithms via rank-statistic SBC (2026-06-17)
• Jin et al. - Bayesian Media Mix Modeling — Jin, Wang, Sun, Chan & Koehler (Google, 2017), Bayesian MMM with adstock carryover and Hill shape effects, ROAS/mROAS, optimal media mix (2026-06-17)
• Hennig, Osborne & Kersting - Probabilistic Numerics — Hennig, Osborne & Kersting (2022), Probabilistic Numerics: Computation as Machine Learning (Cambridge University Press): computation as Bayesian inference, Bayesian quadrature, probabilistic linear solvers, Bayesian optimisation, ODE filters/smoothers (2026-07-01)

See Also

• Clippings — Web articles and saved content