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Annual Review of +Statistics and Its Application, 9, 425–452. +https://doi.org/10.1146/annurev-statistics-040220-091910 + + + Automated parameter blocking for efficient +markov chain monte carlo sampling + Turek + Bayesian Analysis + 2 + 12 + 10.1214/16-BA1008 + 2017 + Turek, D., de Valpine, P., Paciorek, +C. J., & Anderson-Bergman, C. (2017). Automated parameter blocking +for efficient markov chain monte carlo sampling. Bayesian Analysis, +12(2), 465–490. +https://doi.org/10.1214/16-BA1008 + + + One size does not fit all: Customizing MCMC +methods for hierarchical models using NIMBLE + Ponisio + Ecology and evolution + 5 + 10 + 10.1002/ece3.6053 + 2020 + Ponisio, L. C., de Valpine, P., +Michaud, N., & Turek, D. (2020). One size does not fit all: +Customizing MCMC methods for hierarchical models using NIMBLE. Ecology +and Evolution, 10(5), 2385–2416. +https://doi.org/10.1002/ece3.6053 + + + Elliptical slice sampling + Murray + Proceedings of the thirteenth international +conference on artificial intelligence and statistics + 2010 + Murray, I., Adams, R., & MacKay, +D. (2010). Elliptical slice sampling. Proceedings of the Thirteenth +International Conference on Artificial Intelligence and Statistics, +541–548. + + + Automated factor slice +sampling + Tibbits + Journal of Computational and Graphical +Statistics + 2 + 23 + 10.1080/10618600.2013.791193 + 2014 + Tibbits, M. M., Groendyke, C., Haran, +M., & Liechty, J. C. (2014). Automated factor slice sampling. +Journal of Computational and Graphical Statistics, 23(2), 543–563. +https://doi.org/10.1080/10618600.2013.791193 + + + Mra: Mark-recapture analysis + McDonald + 2018 + McDonald, T. (2018). Mra: +Mark-recapture analysis. +https://CRAN.R-project.org/package=mra + + + Modeling survival and testing biological +hypotheses using marked animals: A unified approach with case +studies + Lebreton + Ecological monographs + 1 + 62 + 10.2307/2937171 + 1992 + Lebreton, J.-D., Burnham, K. P., +Clobert, J., & Anderson, D. R. (1992). Modeling survival and testing +biological hypotheses using marked animals: A unified approach with case +studies. Ecological Monographs, 62(1), 67–118. +https://doi.org/10.2307/2937171 + + + Efficient markov chain monte carlo sampling +for hierarchical hidden markov models + Turek + Environmental and ecological +statistics + 23 + 10.1007/s10651-016-0353-z + 2016 + Turek, D., de Valpine, P., & +Paciorek, C. J. (2016). Efficient markov chain monte carlo sampling for +hierarchical hidden markov models. Environmental and Ecological +Statistics, 23, 549–564. +https://doi.org/10.1007/s10651-016-0353-z + + + WinBUGS-a bayesian modelling framework: +Concepts, structure, and extensibility + Lunn + Statistics and computing + 10 + 10.1023/A:1008929526011 + 2000 + Lunn, D. J., Thomas, A., Best, N., +& Spiegelhalter, D. (2000). WinBUGS-a bayesian modelling framework: +Concepts, structure, and extensibility. Statistics and Computing, 10, +325–337. https://doi.org/10.1023/A:1008929526011 + + + Composable effects for flexible and +accelerated probabilistic programming in NumPyro + Phan + arXiv preprint +arXiv:1912.11554 + 10.48550/arXiv.1912.11554 + 2019 + Phan, D., Pradhan, N., & +Jankowiak, M. (2019). Composable effects for flexible and accelerated +probabilistic programming in NumPyro. arXiv Preprint arXiv:1912.11554. +https://doi.org/10.48550/arXiv.1912.11554 + + + Deep learning with tensorflow: A +review + Pang + Journal of Educational and Behavioral +Statistics + 2 + 45 + 10.3102/1076998619872761 + 2020 + Pang, B., Nijkamp, E., & Wu, Y. +N. (2020). Deep learning with tensorflow: A review. Journal of +Educational and Behavioral Statistics, 45(2), 227–248. +https://doi.org/10.3102/1076998619872761 + + + + + + From c76eb435939846604c5931f73167cad2e51c5f62 Mon Sep 17 00:00:00 2001 From: The Open Journals editorial robot <89919391+editorialbot@users.noreply.github.com> Date: Wed, 10 Jul 2024 21:18:07 +0100 Subject: [PATCH 3/4] Creating 10.21105.joss.06745.jats --- .../paper.jats/10.21105.joss.06745.jats | 769 ++++++++++++++++++ 1 file changed, 769 insertions(+) create mode 100644 joss.06745/paper.jats/10.21105.joss.06745.jats diff --git a/joss.06745/paper.jats/10.21105.joss.06745.jats b/joss.06745/paper.jats/10.21105.joss.06745.jats new file mode 100644 index 0000000000..cf6b8a1587 --- /dev/null +++ b/joss.06745/paper.jats/10.21105.joss.06745.jats @@ -0,0 +1,769 @@ + + +

+ + + + +Journal of Open Source Software +JOSS + +2475-9066 + +Open Journals + + + +6745 +10.21105/joss.06745 + +nimbleHMC: An R package for Hamiltonian Monte Carlo +sampling in nimble + + + +https://orcid.org/0000-0002-1453-1908 + +Turek +Daniel + + +* + + +https://orcid.org/0000-0002-8329-6796 + +de Valpine +Perry + + + + + +Paciorek +Christopher J. + + + + + +Lafayette College, USA + + + + +University of California, USA + + + + +* E-mail: + + +5 +7 +2024 + +9 +99 +6745 + +Authors of papers retain copyright and release the +work under a Creative Commons Attribution 4.0 International License (CC +BY 4.0) +2022 +The article authors + +Authors of papers retain copyright and release the work under +a Creative Commons Attribution 4.0 International License (CC BY +4.0) + + + +R +hierarchical model +Markov chain Monte Carlo +Hamiltonian Monte Carlo +nimble + + + + + + Summary +

Markov chain Monte Carlo (MCMC) algorithms are widely used for + fitting hierarchical models to data. MCMC is the predominant tool used + in Bayesian analyses to generate samples from the posterior + distribution of model parameters conditional on observed data. MCMC is + not a single algorithm, but rather a framework in which various + sampling methods (samplers) are assigned to operate on subsets of + unobserved parameters. There exists a vast set of valid samplers to + draw upon, which differ in complexity, autocorrelation of samples + produced, and applicability.

+

Hamiltonian Monte Carlo [HMC; Radford M. Neal + (2011)] + sampling is one such technique, applicable to continuous-valued + parameters, which uses gradients to generate large transitions in + parameter space. The resulting samples have low autocorrelation, and + therefore have high information content, relative for example to an + equal-length sequence of highly autocorrelated samples. The No-U-Turn + (NUTS) variety of HMC sampling [HMC-NUTS; Hoffman & Gelman + (2014)] + greatly increases the usability of HMC by introducing a recursive tree + of numerical integration steps that makes it unnecessary to + pre-specify a fixed number of steps. Hoffman & Gelman + (2014) + also introduce a self-tuning scheme for the step size, resulting in a + fully automated HMC sampler with no need for manual tuning.

+

Many software packages offer implementations of MCMC, such as + nimble + (de + Valpine et al., 2017), WinBUGS + (Lunn + et al., 2000), JAGS + (Plummer, + 2003), PyMC + (Fonnesbeck + et al., 2015), NumPyro + (Phan + et al., 2019), TensorFlow Probability + (Pang + et al., 2020), and Stan + (Carpenter + et al., 2017), among others. These packages differ, however, in + their approaches to sampler assignments. As sampling techniques vary + in computation and quality of the samples, the effectiveness of the + MCMC algorithms will vary depending on the software and model.

+

A key design feature of nimble’s MCMC is to + allow easy customization of sampler assignments from a high-level + interface. Users may assign any valid samplers to each parameter or + group of parameters, selecting from samplers provided with + nimble or samplers they have written in + nimble’s algorithm programming system. Samplers + provided with nimble include random walk + Metropolis-Hastings sampling + (Robert + & Casella, 1999), slice sampling + (Radford + M. Neal, 2003), elliptical slice sampling + (Murray + et al., 2010), automated factor slice sampling + (Tibbits + et al., 2014), conjugate sampling + (George + et al., 1993), and others.

+

The nimbleHMC package provides + implementations of two versions of HMC-NUTS sampling for use within + nimble, both written in + nimble’s algorithm programming system within R. + Specifically, nimbleHMC provides the original + (“classic”) HMC-NUTS algorithm as developed in Hoffman & Gelman + (2014), + and a modern version of HMC-NUTS sampling matching the HMC sampler + available in version 2.32.2 of Stan + (Stan + Development Team, 2023). The samplers provided in + nimbleHMC can be assigned to any + continuous-valued parameters, and may be used in combination with + other samplers provided with nimble.

+
+ + Example +

The following example demonstrates fitting a hierarchical model to + data using nimbleHMC. We use the European + Dipper (Cinclus cinclus) dataset drawn from + ecological capture-recapture (e.g., + Lebreton + et al., 1992; + Turek + et al., 2016). Modelling includes both continuous parameters to + undergo HMC sampling and discrete parameters that cannot be sampled + via HMC.

+

Individual birds are captured, tagged, and potentially recaptured + on subsequent sighting occasions. Data is a + + + 255×7 + binary-valued array of capture histories of 255 uniquely tagged birds + over 7 years. Model parameters are detection probability + ( + + p), + and annual survival rates on non-flood years + ( + + ϕ1) + and flood years ( + + ϕ2). + Data is provided in the R package mra + (McDonald, + 2018), and individuals which are first sighted on the final + (7 + + th) + sighting occasion do not contribute to inference, and are removed from + the sighting histories.

+ library(mra) +data(dipper.data) +dipper <- dipper.data[,1:7] +y <- dipper[apply(dipper, 1, which.max) < 7, ] +

We specify the hierarchical model using uniform priors on the + interval + + [0,1] + for all parameters. Binary-valued latent states + + + xi,t + represent the true alive (1) or dead (0) state of individual + + + i + on year + + t. + Doing so allows the survival process to be modelled as + + + xi,t+1Bernoulli(ϕftxi,t) + where + + ft + indicates the flood/non-flood history of year + + + t. + The model structure conditions on the first observation of each + individual, where + + firsti + is the first observation period of individual + + + i, + and + + xi,firsti + is assigned the value one. Observations are modelled as + + + yi,tBernoulli(pxi,t).

+ library(nimbleHMC) + +code <- nimbleCode({ + phi[1] ~ dunif(0, 1) + phi[2] ~ dunif(0, 1) + p ~ dunif(0, 1) + for(i in 1:N) { + x[i,first[i]] <- 1 + for(t in (first[i]+1):T) { + x[i,t] ~ dbern(phi[f[t]] * x[i,t-1]) + y[i,t] ~ dbern(p * x[i,t]) + } + } +}) +

A nimble model object is now built. The + argument buildDerivs = TRUE results in + under-the-hood support for obtaining derivatives from model + calculations, as necessary for derivative-based HMC sampling.

+ Rmodel <- nimbleModel( + code, + constants = list(N = nrow(y), T = ncol(y), f = c(1,2,2,1,1,1,1), + first = apply(y, 1, which.max)), + data = list(y = y), + inits = list(phi = c(0.5, 0.5), p = 0.5, x = array(1, dim(y))), + buildDerivs = TRUE) +

Next we create an MCMC configuration object, which specifies the + sampling algorithm to be applied to each parameter. By default, + configureMCMC uses + nimble’s default sampler assignments of + adaptive random walk Metropolis-Hastings [RW + sampler; Robert & Casella + (1999)] + for each parameter, and a binary Gibbs sampler + for each + + xi,t + latent state.

+ conf <- configureMCMC(Rmodel) + +## RW sampler (3) +## - phi[] (2 elements) +## - p +## binary sampler (848) +## - x[] (848 elements) +

Now we customize the MCMC configuration object to use HMC sampling + for the model parameters. replaceSamplers + replaces the samplers operating on + + ϕ1, + + + ϕ2 + and + + p + with the modern HMC-NUTS sampler (called the + NUTS sampler) provided in + nimbleHMC. The classic version of the HMC-NUTS + sampler could be assigned by specifying + type = "NUTS_classic".

+ conf$replaceSamplers(target = c("phi", "p"), type = "NUTS") +conf$printSamplers(byType = TRUE) + +## NUTS sampler (1) +## - phi, p +## binary sampler (848) +## - x[] (848 elements) +

Alternatively, the convenience function + configureHMC could be used to create an + identical MCMC configuration, applying HMC-NUTS sampling to + + + ϕ1, + + + ϕ2 + and + + p, + and default binary samplers for discrete parameters.

+

Now we build and compile the MCMC algorithm.

+ Rmcmc <- buildMCMC(conf) +Cmodel <- compileNimble(Rmodel) +Cmcmc <- compileNimble(Rmcmc, project = Rmodel) +

We execute the MCMC for 20,000 iterations, and discard the initial + 10,000 samples as burn-in.

+ set.seed(0) +samples <- runMCMC(Cmcmc, niter = 20000, nburnin = 10000) +

Finally, posterior summary statistics are calculated for the model + parameters.

+ samplesSummary(samples, round = 2) + +## Mean Median St.Dev. 95%CI_low 95%CI_upp +## p 0.90 0.90 0.03 0.84 0.95 +## phi[1] 0.58 0.58 0.03 0.52 0.63 +## phi[2] 0.50 0.50 0.06 0.39 0.61 +

Traceplots and posterior density plots are generated using the + samplesPlot function from the + basicMCMCplots package.

+ basicMCMCplots::samplesPlot(samples, legend.location = "topleft") + +
+ + Statement of need +

HMC is recognized as a state-of-the-art MCMC sampling algorithm. As + testimony to this, software packages such as + Stan exclusively employ HMC sampling. + Consequently, such software cannot operate on models containing + discrete parameters (upon which HMC cannot operate), or would require + marginalization of the likelihood to remove these discrete dimensions + from the sampling problem. Models with discrete parameters arise in a + range of statistical motifs including hidden Markov models, finite + mixture models, and generally in the presence of unobserved + categorical data + (Bartolucci + et al., 2022). In contrast, other mainstream MCMC packages + (WinBUGS, OpenBUGS and + JAGS) can sample discrete parameters, but + provide no facilities for HMC sampling. This leaves the use case of + HMC sampling of hierarchical models that also contain discrete + parameters.

+

nimbleHMC accomplishes this, by providing + two HMC samplers that operate inside nimble’s + MCMC engine. The base nimble package provides a + variety of MCMC sampling algorithms, as well as the ability to + customize MCMC sampler assignments. nimbleHMC + augments the set of sampling algorithms provided in + nimble with two options for HMC sampling, which + can be used alongside any other samplers. The example presented here + demonstrates precisely that: HMC sampling operating alongside discrete + samplers, which is not possible without the use of + nimbleHMC.

+

Which combination of samplers will optimize MCMC efficiency for any + particular problem is an open question. One metric of comparison is + the effective sample size of the samples generated per unit runtime of + the algorithm, which quantifies how quickly an MCMC algorithm + generates information about parameter posteriors. This metric is + studied in Turek et al. + (2017) + and Ponisio et al. + (2020), + with the conclusion that the best sampling strategy is + problem-specific rather than universal. For that reason, the ability + to mix-and-match samplers from a large pool of candidates is important + from both practical and theoretical standpoints. Indeed, packages such + as compareMCMCs + (de + Valpine et al., 2022) exist specifically to compare the + relative performance of MCMC algorithms. The addition of HMC sampling + provided by nimbleHMC supports new practical + combinations for applied MCMC, as well as facilitates a deeper study + of Bayesian modelling.

+
+ + + + + + + + NealRadford M. + + Handbook of markov chain monte carlo + Chapman; Hall/CRC + 2011 + 113 + 162 + + + + + + de ValpinePerry + PaganinSally + TurekDaniel + + compareMCMCs: An R package for studying MCMC efficiency + Journal of Open Source Software + 2022 + 7 + 69 + 10.21105/joss.03844 + 3844 + + + + + + + de ValpinePerry + TurekDaniel + PaciorekChristopher J + Anderson-BergmanClifford + LangDuncan Temple + BodikRastislav + + Programming with models: Writing statistical algorithms for general model structures with NIMBLE + Journal of Computational and Graphical Statistics + Taylor & Francis + 2017 + 26 + 2 + 10.1080/10618600.2016.1172487 + 403 + 413 + + + + + + PlummerMartyn + + JAGS: A program for analysis of bayesian graphical models using gibbs sampling + Proceedings of the 3rd international workshop on distributed statistical computing + Vienna, Austria. + 2003 + 124 + 1 + 10 + + + + + + FonnesbeckChris + PatilAnand + HuardDavid + SalvatierJohn + + PyMC: Bayesian stochastic modelling in python + Astrophysics Source Code Library + 2015 + ascl + 1506 + + + + + + CarpenterBob + GelmanAndrew + HoffmanMatthew D + LeeDaniel + GoodrichBen + BetancourtMichael + BrubakerMarcus + GuoJiqiang + LiPeter + RiddellAllen + + Stan: A probabilistic programming language + Journal of statistical software + Columbia Univ., New York, NY (United States); Harvard Univ., Cambridge, MA + 2017 + 76 + 1 + 10.18637/jss.v076.i01 + + + + + + Stan Development Team + + Stan modeling language users guide and reference manual, version 2.32.2 + 2023 + https://mc-stan.org + + + + + + RobertChristian P + CasellaGeorge + + The metropolis—hastings algorithm + Monte carlo statistical methods + Springer + 1999 + 231 + 283 + + + + + + NealRadford M + + Slice sampling + The annals of statistics + Institute of Mathematical Statistics + 2003 + 31 + 3 + 10.1214/aos/1056562461 + 705 + 767 + + + + + + GeorgeEdward I + MakovUE + SmithAFM + + Conjugate likelihood distributions + Scandinavian Journal of Statistics + JSTOR + 1993 + 147 + 156 + + + + + + HoffmanMatthew D + GelmanAndrew + + The no-u-turn sampler: Adaptively setting path lengths in hamiltonian monte carlo. + J. Mach. Learn. Res. + 2014 + 15 + 1 + 1593 + 1623 + + + + + + BartolucciFrancesco + PandolfiSilvia + PennoniFulvia + + Discrete latent variable models + Annual Review of Statistics and Its Application + Annual Reviews + 2022 + 9 + 10.1146/annurev-statistics-040220-091910 + 425 + 452 + + + + + + TurekDaniel + de ValpinePerry + PaciorekChristopher J + Anderson-BergmanClifford + + Automated parameter blocking for efficient markov chain monte carlo sampling + Bayesian Analysis + International Society for Bayesian Analysis + 2017 + 12 + 2 + 10.1214/16-BA1008 + 465 + 490 + + + + + + PonisioLauren C + de ValpinePerry + MichaudNicholas + TurekDaniel + + One size does not fit all: Customizing MCMC methods for hierarchical models using NIMBLE + Ecology and evolution + Wiley Online Library + 2020 + 10 + 5 + 10.1002/ece3.6053 + 2385 + 2416 + + + + + + MurrayIain + AdamsRyan + MacKayDavid + + Elliptical slice sampling + Proceedings of the thirteenth international conference on artificial intelligence and statistics + JMLR Workshop; Conference Proceedings + 2010 + 541 + 548 + + + + + + TibbitsMatthew M + GroendykeChris + HaranMurali + LiechtyJohn C + + Automated factor slice sampling + Journal of Computational and Graphical Statistics + Taylor & Francis + 2014 + 23 + 2 + 10.1080/10618600.2013.791193 + 543 + 563 + + + + + + McDonaldTrent + + Mra: Mark-recapture analysis + 2018 + https://CRAN.R-project.org/package=mra + + + + + + LebretonJean-Dominique + BurnhamKenneth P + ClobertJean + AndersonDavid R + + Modeling survival and testing biological hypotheses using marked animals: A unified approach with case studies + Ecological monographs + Wiley Online Library + 1992 + 62 + 1 + 10.2307/2937171 + 67 + 118 + + + + + + TurekDaniel + de ValpinePerry + PaciorekChristopher J + + Efficient markov chain monte carlo sampling for hierarchical hidden markov models + Environmental and ecological statistics + Springer + 2016 + 23 + 10.1007/s10651-016-0353-z + 549 + 564 + + + + + + LunnDavid J + ThomasAndrew + BestNicky + SpiegelhalterDavid + + WinBUGS-a bayesian modelling framework: Concepts, structure, and extensibility + Statistics and computing + Springer + 2000 + 10 + 10.1023/A:1008929526011 + 325 + 337 + + + + + + PhanDu + PradhanNeeraj + JankowiakMartin + + Composable effects for flexible and accelerated probabilistic programming in NumPyro + arXiv preprint arXiv:1912.11554 + 2019 + 10.48550/arXiv.1912.11554 + + + + + + PangBo + NijkampErik + WuYing Nian + + Deep learning with tensorflow: A review + Journal of Educational and Behavioral Statistics + SAGE Publications Sage CA: Los Angeles, CA + 2020 + 45 + 2 + 10.3102/1076998619872761 + 227 + 248 + + + + +
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