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 1375 notes across 13 major topics (85 notes in 11 new clusters added 2026-09-18, including the new Machine Learning and AI topic; 229 notes added 2026-10-13, including the new Model Validation and Interpretability topic; 190 notes added 2026-11-08 in the new Evidence Synthesis, Generalization and Privacy topic and 361 in the new Applied Bayesian Model Families 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 model validation and interpretability: false discovery and overfitting, RF/SHAP importance bias and stability, explanations vs causal effects, Goodhart, time-series CV, known-truth simulation (ADEMP/AMSS), SR 11-7 / NIST AI RMF? → Model Validation and Interpretability, starting at Model Validation and Interpretability - Overview
  • Need meta-analysis (random effects, HKSJ, bayesmeta, publication bias, Meager hierarchical pooling), benchmark development (ImageNet, GLUE, HELM, Datasheets, Benchmark Lottery, ACIC 2016), causal transportability (selection diagrams, transport formulas, trial-to-target estimators, site-selection bias) or differential privacy (Laplace/Gaussian mechanisms, composition, RDP, GDP, DP-SGD, Census TopDown)? → Evidence Synthesis, Generalization and Privacy
  • Need a model family used in applied PyMC work — causal sensitivity and mediation, Dirichlet/Pitman-Yor/IBP and topic models, ChEES/MEADS and HMMs, value of information and decision curves, Bradley-Terry/IRT/annotation models, occupancy and capture-recapture, nowcasting/Fay-Herriot/poll aggregation, GAMLSS/compositional/circular/extremes, Hawkes/LGCP/BYM2/graph learning, ODE likelihoods/BNNs/BART/popPK, drift diffusion/radiocarbon/Lee-Carter/threshold test? → Applied Bayesian Model Families
  • Need a specific concept? Check the Concept Map below or use the .base files for database views

Concept Map

TopicNotesKey Concepts
Bayesian Statistics217Bayes’ 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 Design21Lindley’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 Numerics36Computation 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
Econometrics65Selection 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 Discovery5DAG / Bayesian-network structure learning, linear SEM, score-based learning, NOTEARS continuous optimization, smooth acyclicity , augmented Lagrangian, vs FGS/GES/PC
Research Methodology42Forking 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)
Physics14Quantum 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 Modeling42ABM 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 Models86Functional 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; Blake et al. 2015 eBay paid-search experiment; full paper maps of Gordon et al. 2019 and Lewis & Rao 2015)
Machine Learning and AI29Transformers 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)
Model Validation and Interpretability186False discovery and overfitting (Ioannidis PPV, Simmons et al. researcher degrees of freedom, Breiman two cultures / Rashomon, Riley sample size for prediction models), feature importance and stability (Strobl RF importance bias and conditional importance, Hooker permute-and-predict extrapolation, Fisher model class reliance, Meinshausen-Bühlmann stability selection), explanations, causality and proxies (Kumar Shapley critique, Janzing interventional SHAP, Dillon SHAP vs causal effects, Goodhart variants), time-series validation (Granger spurious regression and cointegration, Bergmeir K-fold CV for AR models), simulation-based validation (ADEMP, AMSS, Chan & Perry MMM challenges), model risk governance (SR 11-7, NIST AI RMF 1.0)
Evidence Synthesis, Generalization and Privacy190Meta-analysis (DerSimonian-Laird, REML, , HKSJ, bayesmeta priors, Egger/funnel asymmetry, Andrews-Kasy publication-bias correction, Meager hierarchical pooling of RCTs), benchmark development (ImageNet, GLUE, HELM, Datasheets for Datasets, Benchmark Lottery, ACIC 2016 causal-inference competition), causal transportability (Pearl-Bareinboim selection diagrams and S-admissibility, data fusion, Degtiar-Rose review, Dahabreh trial-to-target doubly robust estimators, Allcott site-selection bias), differential privacy (Laplace mechanism, Dwork-Roth toolbox and composition, Wasserman-Zhou rates, Rényi DP, Gaussian DP/f-DP, DP-SGD moments accountant, 2020 Census TopDown)
Applied Bayesian Model Families361Gap-fill against the 117 PyMC worked examples: causal sensitivity and mediation (Cinelli-Hazlett robustness values, Imai mediation, Franks sensitivity, Rosenman shrinkage), Bayesian nonparametrics (DP, Pitman-Yor/Gibbs-type, IBP, LDA, anchor words), advanced MCMC (ChEES-HMC, MEADS, funnels, HMMs), decisions and VOI (EVPPI, decision curves, sensor placement, quantile dotplots, HOPs), latent traits (Bradley-Terry, Glicko/TrueSkill, Dawid-Skene, IRT, market structure), population estimation (occupancy, N-mixture, MSE), nowcasting (NobBS, Rt, Fay-Herriot, Linzer, Bańbura nowcasting), distributional outcomes (GAMLSS, CoDA, directional, BQR, extreme-event attribution), spatial/point processes (Hawkes/ETAS, LGCP, BYM2, latent space, order-MCMC, graphical horseshoe), mechanistic models (BART, neural ODEs, BNN posteriors, popPK), applied latent models (HDDM, radiocarbon, Lee-Carter, threshold test, JMbayes)

Cross-Cutting Themes

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)
  • Ioannidis 2005, Simmons, Nelson & Simonsohn 2011, Breiman 2001, Riley et al. 2020 — overfitting and false discovery (2026-10-13)
  • Strobl et al. 2007, Strobl et al. 2008, Hooker, Mentch & Zhou 2021, Fisher, Rudin & Dominici 2019, Meinshausen & Bühlmann 2010 — feature importance and stability (2026-10-13)
  • Kumar et al. 2020, Janzing et al. 2020, Dillon et al., Manheim & Garrabrant 2018 — explanations, causality and proxies (2026-10-13)
  • Granger 2003, Bergmeir, Hyndman & Koo 2018 — time-series validation (2026-10-13)
  • Morris, White & Crowther 2019, Zhang & Vaver 2017, Chan & Perry 2017 — simulation-based method validation (2026-10-13)
  • SR 11-7 (2011), NIST AI RMF 1.0 (2023) — model risk governance (2026-10-13)
  • Viechtbauer 2010, Pearl & Bareinboim 2014, Liang et al. 2022, Dwork & Roth 2014 and 20 more — meta-analysis, benchmarks, causal transportability, differential privacy (2026-11-08); full list in Evidence Synthesis, Generalization and Privacy
  • Cinelli & Hazlett 2020, Teh 2010, Rabiner 1989, Chipman et al. 2010 and 49 more — applied Bayesian model families (2026-11-08); full list in Applied Bayesian Model Families
  • Blake, Nosko & Tadelis 2015 — eBay paid-search field experiment (Econometrica 83(1); NBER WP 20171) (2026-10-13)

See Also

  • Clippings — Web articles and saved content