Literature

The systems and papers foerster builds on.

Probabilistic programming systems

• Anglican — D. Tolpin, J.-W. van de Meent, H. Yang, F. Wood. Design and Implementation of Probabilistic Programming Language Anglican. IFL 2016. arXiv:1608.05263 · github.com/probprog/anglican
• Daphne — the probabilistic programming compiler of plai-group/daphne, following J.-W. van de Meent, B. Paige, H. Yang, F. Wood. An Introduction to Probabilistic Programming. arXiv:1809.10756.
• Gen — M. Cusumano-Towner, F. Saad, A. Lew, V. Mansinghka. Gen: A General-Purpose Probabilistic Programming System with Programmable Inference. PLDI 2019. gen.dev
• Church — N. Goodman, V. Mansinghka, D. Roy, K. Bonawitz, J. Tenenbaum. Church: a language for generative models. UAI 2008.
• WebPPL — N. D. Goodman, A. Stuhlmüller. The Design and Implementation of Probabilistic Programming Languages. 2014. dippl.org · webppl.org — JavaScript with sample, factor and Infer, implemented by CPS transformation. Its sources include an asynchronous particle filter (asyncpf) and particle MCMC (pmcmc): prior art for foerster's particle cascade and particle-MCMC methods.
• Stan — B. Carpenter, A. Gelman, M. D. Hoffman, D. Lee, B. Goodrich, M. Betancourt, M. Brubaker, J. Guo, P. Li, A. Riddell. Stan: A Probabilistic Programming Language. Journal of Statistical Software 76(1), 2017.
• PyMC — O. Abril-Pla, V. Andreani, C. Carroll, L. Dong, C. J. Fonnesbeck, M. Kochurov, R. Kumar, J. Lao, C. C. Luhmann, O. A. Martin, M. Osthege, R. Vieira, T. Wiecki, R. Zinkov. PyMC: a modern, and comprehensive probabilistic programming framework in Python. PeerJ Computer Science 9:e1516, 2023.
• Pyro — E. Bingham, J. P. Chen, M. Jankowiak, F. Obermeyer, N. Pradhan, T. Karaletsos, R. Singh, P. Szerlip, P. Horsfall, N. D. Goodman. Pyro: Deep Universal Probabilistic Programming. JMLR 20(28), 2019.
• NumPyro — D. Phan, N. Pradhan, M. Jankowiak. Composable Effects for Flexible and Accelerated Probabilistic Programming in NumPyro. 2019. arXiv:1912.11554
• Turing — H. Ge, K. Xu, Z. Ghahramani. Turing: A Language for Flexible Probabilistic Inference. AISTATS 2018.
• C. Weilbach. Structured Amortized Variational Inference. PhD thesis, University of British Columbia, 2025 — structured continuous normalizing flows, graphically structured diffusion models, and Daphne.

Inference algorithms

• SMC — A. Doucet, A. M. Johansen. A tutorial on particle filtering and smoothing: fifteen years later. 2009.
• Resampling schemes — R. Douc, O. Cappé, E. Moulines. Comparison of resampling schemes for particle filtering. ISPA 2005.
• Resample-move — W. R. Gilks, C. Berzuini. Following a moving target — Monte Carlo inference for dynamic Bayesian models. JRSS B 2001.
• IBIS — N. Chopin. A sequential particle filter method for static models. Biometrika 2002.
• SMC samplers (tempered SMC) — P. Del Moral, A. Doucet, A. Jasra. Sequential Monte Carlo samplers. JRSS B 2006.
• Adaptive tempering — Y. Zhou, A. M. Johansen, J. A. D. Aston. Toward automatic model comparison: an adaptive sequential Monte Carlo approach. JCGS 2016.
• Waste-free SMC — H.-D. Dau, N. Chopin. Waste-free sequential Monte Carlo. JRSS B 2022.
• SMCP3 — A. K. Lew, G. Matheos, T. Zhi-Xuan, M. Ghavamizadeh, N. Gothoskar, S. Russell, V. K. Mansinghka. SMCP3: Sequential Monte Carlo with Probabilistic Program Proposals. AISTATS 2023.
• Particle cascade — B. Paige, F. Wood, A. Doucet, Y. W. Teh. Asynchronous Anytime Sequential Monte Carlo. NeurIPS 2014. arXiv:1407.2864 — the stabilised branching rule (Eq. 14) foerster.cascade uses.
• Anytime Monte Carlo — L. M. Murray, S. S. Singh, A. Lee. Anytime Monte Carlo. Data-Centric Engineering 2021 — why a run must end by count, not by wall clock.
• Delayed sampling — L. M. Murray, D. Lundén, J. Kudlicka, D. Broman, T. B. Schön. Delayed Sampling and Automatic Rao-Blackwellization of Probabilistic Programs. AISTATS 2018.
• Particle MCMC (PIMH, PMMH, particle Gibbs) — C. Andrieu, A. Doucet, R. Holenstein. Particle Markov chain Monte Carlo methods. JRSS B 2010.
• SMC² — N. Chopin, P. E. Jacob, O. Papaspiliopoulos. SMC²: an efficient algorithm for sequential analysis of state space models. JRSS B 2013.
• PGAS — F. Lindsten, M. I. Jordan, T. B. Schön. Particle Gibbs with ancestor sampling. JMLR 2014.
• IPMCMC — T. Rainforth, C. A. Naesseth, F. Lindsten, B. Paige, J.-W. van de Meent, A. Doucet, F. Wood. Interacting Particle Markov Chain Monte Carlo. ICML 2016.
• Lightweight MH — D. Wingate, A. Stuhlmüller, N. Goodman. Lightweight implementations of probabilistic programming languages via transformational compilation. AISTATS 2011.
• Cycles and mixtures of kernels — L. Tierney. Markov chains for exploring posterior distributions. Annals of Statistics 1994.
• HMC — R. M. Neal. MCMC using Hamiltonian dynamics. Handbook of Markov Chain Monte Carlo, 2011.
• Involutive MCMC — M. Cusumano-Towner, A. K. Lew, V. Mansinghka. Automating Involutive MCMC using Probabilistic and Differentiable Programming. 2020. arXiv:2007.09871
• BBVI — R. Ranganath, S. Gerrish, D. Blei. Black Box Variational Inference. AISTATS 2014.

Steering and twisted SMC

• Twisted particle filters — N. Whiteley, A. Lee. Twisted particle filters. Annals of Statistics 2014.
• Twisted SMC for language models — S. Zhao, R. Brekelmans, A. Makhzani, R. Grosse. Probabilistic Inference in Language Models via Twisted Sequential Monte Carlo. ICML 2024. arXiv:2404.17546
• SMC steering — A. K. Lew, T. Zhi-Xuan, G. Grand, V. K. Mansinghka. Sequential Monte Carlo Steering of Large Language Models using Probabilistic Programs. 2023. arXiv:2306.03081
• Controlled generation by SMC (genlm) — J. Loula, B. LeBrun, L. Du, B. Lipkin, C. Pasti, G. Grand, T. Liu, Y. Emara, M. Freedman, J. Eisner, R. Cotterell, V. Mansinghka, A. K. Lew, T. Vieira, T. J. O'Donnell. Syntactic and Semantic Control of Large Language Models via Sequential Monte Carlo. ICLR 2025. arXiv:2504.13139 · genlm-control
• The reward as a tilt — T. Korbak, E. Perez, C. L. Buckley. RL with KL penalties is better viewed as Bayesian inference. Findings of EMNLP 2022.

Causality

• J. Pearl. Causality: Models, Reasoning, and Inference. 2nd ed., 2009 — interventions, the three-step counterfactual (abduction, action, prediction), the probability of necessity.

Checking models and samplers

• Bayesian workflow — A. Gelman, A. Vehtari, D. Simpson, C. C. Margossian, B. Carpenter, Y. Yao, L. Kennedy, J. Gabry, P.-C. Bürkner, M. Modrák. Bayesian Workflow. 2020. arXiv:2011.01808 — the outline of the workflow guide.
• R-hat, ESS, MCSE — A. Vehtari, A. Gelman, D. Simpson, B. Carpenter, P.-C. Bürkner. Rank-normalization, folding, and localization: an improved R̂ for assessing convergence of MCMC. Bayesian Analysis 16(2), 2021 — the diagnostics foerster.diagnostics computes.
• PSIS-LOO and WAIC — A. Vehtari, A. Gelman, J. Gabry. Practical Bayesian model evaluation using leave-one-out cross-validation and WAIC. Statistics and Computing 27, 2017 — what pointwise-log-likelihood is the input of.
• Simulation-based calibration — S. Talts, M. Betancourt, D. Simpson, A. Vehtari, A. Gelman. Validating Bayesian Inference Algorithms with Simulation-Based Calibration. 2018. arXiv:1804.06788

Monte Carlo, and the name

• N. Metropolis, S. Ulam. The Monte Carlo Method. JASA 1949.
• N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, E. Teller. Equation of State Calculations by Fast Computing Machines. J. Chem. Phys. 1953.
• G. Dyson. Turing's Cathedral. 2012 — the ENIAC and the Monte Carlo runs Klára Dán von Neumann programmed.
• H. von Foerster. Understanding Understanding: Essays on Cybernetics and Cognition. 2003.
• G. Bateson. Steps to an Ecology of Mind. 1972.