diff --git a/joss.06424/10.21105.joss.06424.crossref.xml b/joss.06424/10.21105.joss.06424.crossref.xml new file mode 100644 index 0000000000..034ca08abf --- /dev/null +++ b/joss.06424/10.21105.joss.06424.crossref.xml @@ -0,0 +1,241 @@ + + + + 20240520T205043-75c2090e43f94eec4b0640f83c00912b8a1effb3 + 20240520205043 + + JOSS Admin + admin@theoj.org + + The Open Journal + + + + + Journal of Open Source Software + JOSS + 2475-9066 + + 10.21105/joss + https://joss.theoj.org + + + + + 05 + 2024 + + + 9 + + 97 + + + + Kirstine.jl: A Julia Package for Bayesian Optimal +Design of Experiments + + + + Ludger + Sandig + https://orcid.org/0000-0002-3174-3275 + + + + 05 + 20 + 2024 + + + 6424 + + + 10.21105/joss.06424 + + + http://creativecommons.org/licenses/by/4.0/ + http://creativecommons.org/licenses/by/4.0/ + http://creativecommons.org/licenses/by/4.0/ + + + + Software archive + 10.5281/zenodo.11185430 + + + GitHub review issue + https://github.com/openjournals/joss-reviews/issues/6424 + + + + 10.21105/joss.06424 + https://joss.theoj.org/papers/10.21105/joss.06424 + + + https://joss.theoj.org/papers/10.21105/joss.06424.pdf + + + + + + Julia: A fresh approach to numerical +computing + Bezanson + SIAM review + 1 + 59 + 10.1137/141000671 + 2017 + Bezanson, J., Edelman, A., Karpinski, +S., & Shah, V. B. (2017). Julia: A fresh approach to numerical +computing. SIAM Review, 59(1), 65–98. +https://doi.org/10.1137/141000671 + + + DoseFinding: Planning and analyzing dose +finding experiments + Bornkamp + 2023 + Bornkamp, B., Pinheiro, J., Bretz, +F., & Sandig, L. (2023). DoseFinding: Planning and analyzing dose +finding experiments. +https://CRAN.R-project.org/package=DoseFinding + + + Bayesian experimental design: A +review + Chaloner + Statistical Science + 3 + 10 + 10.1214/ss/1177009939 + 1995 + Chaloner, K., & Verdinelli, I. +(1995). Bayesian experimental design: A review. Statistical Science, +10(3), 273–304. +https://doi.org/10.1214/ss/1177009939 + + + Optimal design for nonlinear response +models + Fedorov + 10.1201/b15054 + 2013 + Fedorov, V. V., & Leonov, S. L. +(2013). Optimal design for nonlinear response models. CRC Press. +https://doi.org/10.1201/b15054 + + + POPED, a software for optimal experiment +design in population kinetics + Foracchia + Computer Methods and Programs in +Biomedicine + 74 + 10.1016/s0169-2607(03)00073-7 + 2004 + Foracchia, M., Hooker, A. C., Vicini, +P., & Ruggeri, A. (2004). POPED, a software for optimal experiment +design in population kinetics. Computer Methods and Programs in +Biomedicine, 74. +https://doi.org/10.1016/s0169-2607(03)00073-7 + + + ICAOD: Optimal designs for nonlinear +statistical models by imperialist competitive algorithm +(ICA) + Masoudi + 2020 + Masoudi, E., Holling, H., & Wong, +W. K. (2020). ICAOD: Optimal designs for nonlinear statistical models by +imperialist competitive algorithm (ICA). +https://CRAN.R-project.org/package=ICAOD + + + PopED: An extended, parallelized, nonlinear +mixed effects models optimal design tool + Nyberg + Computer Methods and Programs in +Biomedicine + 108 + 10.1016/j.cmpb.2012.05.005 + 2012 + Nyberg, J., Ueckert, S., Stroemberg, +E. A., Hennig, S., Karlsson, M. O., & Hooker, A. C. (2012). PopED: +An extended, parallelized, nonlinear mixed effects models optimal design +tool. Computer Methods and Programs in Biomedicine, 108. +https://doi.org/10.1016/j.cmpb.2012.05.005 + + + acebayes: An R package for Bayesian optimal +design of experiments via approximate coordinate +exchange + Overstall + Journal of Statistical +Software + 13 + 95 + 10.18637/jss.v095.i13 + 2020 + Overstall, A. M., Woods, D. C., & +Adamou, M. (2020). acebayes: An R package for Bayesian optimal design of +experiments via approximate coordinate exchange. Journal of Statistical +Software, 95(13), 1–33. +https://doi.org/10.18637/jss.v095.i13 + + + A review of modern computational algorithms +for Bayesian optimal design + Ryan + International Statistical +Review + 1 + 84 + 10.1111/insr.12107 + 2015 + Ryan, E. G., Drovandi, C. C., McGree, +J. M., & Pettitt, A. N. (2015). A review of modern computational +algorithms for Bayesian optimal design. International Statistical +Review, 84(1), 128–154. +https://doi.org/10.1111/insr.12107 + + + On optimal designs for nonlinear models: A +general and efficient algorithm + Yang + Journal of the American Statistical +Association + 504 + 108 + 10.1080/01621459.2013.806268 + 2013 + Yang, M., Biedermann, S., & Tang, +E. (2013). On optimal designs for nonlinear models: A general and +efficient algorithm. Journal of the American Statistical Association, +108(504), 1411–1420. +https://doi.org/10.1080/01621459.2013.806268 + + + Particle swarm optimization + Kennedy + Proceedings of ICNN’95 - international +conference on neural networks + 4 + 10.1109/icnn.1995.488968 + 1995 + Kennedy, J., & Eberhart, R. +(1995). Particle swarm optimization. Proceedings of ICNN’95 - +International Conference on Neural Networks, 4, 1942–1948. +https://doi.org/10.1109/icnn.1995.488968 + + + + + + diff --git a/joss.06424/10.21105.joss.06424.pdf b/joss.06424/10.21105.joss.06424.pdf new file mode 100644 index 0000000000..9015ff9de6 Binary files /dev/null and b/joss.06424/10.21105.joss.06424.pdf differ diff --git a/joss.06424/paper.jats/10.21105.joss.06424.jats b/joss.06424/paper.jats/10.21105.joss.06424.jats new file mode 100644 index 0000000000..a0a32b96db --- /dev/null +++ b/joss.06424/paper.jats/10.21105.joss.06424.jats @@ -0,0 +1,486 @@ + + +
+ + + + +Journal of Open Source Software +JOSS + +2475-9066 + +Open Journals + + + +6424 +10.21105/joss.06424 + +Kirstine.jl: A Julia Package for Bayesian Optimal Design +of Experiments + + + +https://orcid.org/0000-0002-3174-3275 + +Sandig +Ludger + + + + + +Department of Statistics, TU Dortmund University, +Germany + + + + +8 +1 +2024 + +9 +97 +6424 + +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) + + + +Julia +design of experiments +Bayesian statistics + + + + + + Summary +

Good design of planned experiments increases the precision of + parameter estimates. In a dose-response study, for example, the + credible intervals for the response curve’s parameters are shorter + when the dose levels have been chosen carefully. The general + mathematical framework that guides the choice of values and weights + for the covariates in a regression model is called optimal design + theory. In the special case of nonlinear regression models, a + researcher must specify prior knowledge about the model parameters. + Accounting here for a full distribution of parameter values produces + designs that are more robust than designs for a single best guess. To + help compute such designs efficiently for general nonlinear regression + models, we propose the Julia + (Bezanson + et al., 2017) package Kirstine.jl.

+ + + Mathematical Background +

Consider a nonlinear regression model with mean function + + + μ:X×Θ→ℝm, + known covariance matrix + + Σ, + and compact design region + + + X⊂ℝd, + where we want to design an experiment for estimating the unknown + parameter + + θ. + In nonlinear optimal design theory + (Fedorov + & Leonov, 2013), we represent the design by a probability + measure + + ξ + on + + X. + For every such design measure we define the + normalized information matrix + + + M(ξ,θ)=∫(Dθμ(x,θ))′Σ−1(Dθμ(x,θ))ξ(dx), + where + + Dθμ + denotes the Jacobian matrix of + + μ + with respect to + + θ. + To obtain, on average, small confidence or posterior credible + intervals, we aim to construct a design + + ξ* + that maximizes a functional + + ϕ + of the normalized information matrix, with popular choices being the + D- or A-criterion + + + ϕD(M(ξ,θ))=logdet(M(ξ,θ)),ϕA(M(ξ,θ))=−tr(M(ξ,θ)−1). + Since + + M(ξ,θ) + still depends on the unknown + + θ, + we either plug in a best guess + + θ0 + and obtain a locally optimal design problem, or we + try to find a Bayesian optimal design that maximizes + the average of + + ϕ + with respect to a prior distribution with density + + + p:Θ→[0,∞) + (Chaloner + & Verdinelli, 1995). Having obtained a candidate design + + + ξ*, + we then apply an equivalence theorem from infinite-dimensional convex + analysis to verify that the design + + ξ* + is indeed optimal. The setup above can be generalized to designs that + are optimal for estimating a transformed + + + T(θ), + or to models where + + Σ + also depends on + + x.

+

To find a candidate design in practice, we must make three + simplifications. We first have to approximate the prior expectation, + since the integral is not tractable analytically. Monte-Carlo + (MC) integration + + ∫ϕ(M(ξ,θ))p(θ)dθ≈1S∑s=1Sϕ(M(ξ,θ(s))) + is a versatile method for that because we can use it with any + + + p + from which we can draw a sample + + θ(1),…,θ(S), + + + S∈ℕ. + Next, we reduce the search space from all probability measures on + + + X + to the subset of those that are discrete and have + + + K∈ℕ + design points. The optimal + + K* + is usually not known beforehand, but as long as we do not enforce + unique design points, we may guess at a + K^*]]> + K>K* + and will still be able to find the solution. Finally, we have to + choose one of the many proposed algorithms + (Ryan + et al., 2015) for maximizing the objective function + numerically.

+ + + Statement of Need +

Currently, most open-source experimental design software is + implemented in R. There is also a + Julia package that focuses on + factorial + design problems but does not address nonlinear regression. + Among the R packages + on + CRAN, only four deal with nonlinear regression models, and + all of them have to make a tradeoff between speed and flexibility. + With MC integration, thousands of information matrices, each built + from + + K + Jacobian matrices + + Dθμ, + have to be computed for one evaluation of the objective function. In + R, these matrix-valued functions are a + performance bottleneck since each call has to allocate new matrix + objects. To avoid the memory overhead, package authors can implement + internals in C and pass around pointers to + pre-allocated matrices. However, this requires the users to be + proficient in C in order to supply the Jacobian + matrices of their models. Consequently, packages either just accept + the slowdown + (Masoudi + et al., 2020), recommend using C++ + (Overstall + et al., 2020), or come with a small set of models pre-specified + (Bornkamp + et al., 2023; + Foracchia + et al., 2004; + Nyberg + et al., 2012). Hence a design package is needed where knowledge + of only one language is required for efficiently implementing + arbitrary nonlinear regression models.

+

Kirstine.jl attempts to fill this gap in the + design software ecosystem. The package achieves modeling flexibility + through Julia’s multiple dispatch mechanism, + and performs matrix operations efficiently by passing object + references to BLAS and + LAPACK routines. It currently implements the D- + and A-criterion, vector-valued measurements, posterior transformations + of + + θ + via the Delta method, box-shaped design regions of arbitrary + dimension, particle swarm optimization + (Kennedy + & Eberhart, 1995), and a variant of Fedorov’s coordinate + exchange algorithm + (Yang + et al., 2013). Plotting functions for checking the equivalence + theorem are also provided. Locally optimal design is supported + implicitly. Since user-defined Julia code does + not inherently incur performance penalties, specific regression models + are not supplied. Instead, users should first define subtypes of + NonlinearRegression, + Covariate, Parameter, + and CovariateParameterization, and then add + methods for a few functions that dispatch on them. Optionally, one of + Julia’s automatic differentiation packages can + be used. Kirstine.jl has a modular and readable + code base, which enables users to extend the package’s functionality + with drop-in replacements for new criteria, design regions, or even + custom optimization algorithms. Thanks to multiple dispatch, no + changes are required in the package internals. This way, + Kirstine.jl provides an additional level of + flexibility without sacrificing efficiency.

+ + + Acknowledgments +

This work has been supported by the Research Training Group + Biostatistical Methods for High-Dimensional Data in + Toxicology (RTG 2624, Project P2), funded by the Deutsche + Forschungsgemeinschaft (DFG, German Research Foundation – Project + Number 427806116).

+ + + + + + + + BezansonJeff + EdelmanAlan + KarpinskiStefan + ShahViral B + + Julia: A fresh approach to numerical computing + SIAM review + SIAM + 2017 + 59 + 1 + 10.1137/141000671 + 65 + 98 + + + + + + BornkampBjoern + PinheiroJose + BretzFrank + SandigLudger + + DoseFinding: Planning and analyzing dose finding experiments + 2023 + https://CRAN.R-project.org/package=DoseFinding + + + + + + ChalonerKathryn + VerdinelliIsabella + + Bayesian experimental design: A review + Statistical Science + 1995 + 10 + 3 + 10.1214/ss/1177009939 + 273 + 304 + + + + + + FedorovValerii V. + LeonovSergei L. + + Optimal design for nonlinear response models + CRC Press + 2013 + 10.1201/b15054 + + + + + + ForacchiaMarco + HookerAndrew C + ViciniPaolo + RuggeriA + + POPED, a software for optimal experiment design in population kinetics + Computer Methods and Programs in Biomedicine + 2004 + 74 + 10.1016/s0169-2607(03)00073-7 + + + + + + MasoudiEhsan + HollingHeinz + WongWeng Kee + + ICAOD: Optimal designs for nonlinear statistical models by imperialist competitive algorithm (ICA) + 2020 + https://CRAN.R-project.org/package=ICAOD + + + + + + NybergJoakim + UeckertSebastian + StroembergEric A + HennigStefanie + KarlssonMats O + HookerAndrew C + + PopED: An extended, parallelized, nonlinear mixed effects models optimal design tool + Computer Methods and Programs in Biomedicine + 2012 + 108 + https://CRAN.R-project.org/package=PopED + 10.1016/j.cmpb.2012.05.005 + + + + + + OverstallAntony M. + WoodsDavid C. + AdamouMaria + + acebayes: An R package for Bayesian optimal design of experiments via approximate coordinate exchange + Journal of Statistical Software + 2020 + 95 + 13 + https://CRAN.R-project.org/package=acebayes + 10.18637/jss.v095.i13 + 1 + 33 + + + + + + RyanElizabeth G. + DrovandiChristopher C. + McGreeJames M. + PettittAnthony N. + + A review of modern computational algorithms for Bayesian optimal design + International Statistical Review + 2015 + 84 + 1 + 10.1111/insr.12107 + 128 + 154 + + + + + + YangMin + BiedermannStefanie + TangElina + + On optimal designs for nonlinear models: A general and efficient algorithm + Journal of the American Statistical Association + 201312 + 108 + 504 + 10.1080/01621459.2013.806268 + 1411 + 1420 + + + + + + KennedyJames + EberhartRussell + + Particle swarm optimization + Proceedings of ICNN’95 - international conference on neural networks + IEEE + 1995 + 4 + 10.1109/icnn.1995.488968 + 1942 + 1948 + + + + +