Publication

Preprints / Technical Reports

[NEW!] T. Goda, One-dimensional quasi-uniform Kronecker sequences, Preprint. [arXiv]
[NEW!] T. Goda, A randomized lattice rule without component-by-component construction, Preprint. [arXiv]
T. Hironaka and T. Goda, Estimating nested expectations without inner conditional sampling and application to value of information analysis, Preprint. [arXiv]
T. Goda, Strong tractability for multivariate integration in a subspace of the Wiener algebra, Preprint. [arXiv]

Peer-Reviewed Articles

Accepted for publication

T. Goda, Y. Kazashi and K. Tanaka, How sharp are error bounds?---lower bounds on quadrature worst-case errors for analytic functions---, Accepted for publication in SIAM Journal on Numerical Analysis. [arXiv]

Published in 2024

T. Goda, The Sobol' sequence is not quasi-uniform in dimension 2, Proceedings of the American Mathematical Society, 152(8), 3209-3213 (2024). [doi] [arXiv]
T. Goda, Y. Kazashi and Y. Suzuki, Randomizing the trapezoidal rule gives the optimal RMSE rate in Gaussian Sobolev spaces, Mathematics of Computation, 93(348), 1655-1676 (2024). [doi] [arXiv]
T. Goda, K. Suzuki and M. Matsumoto, A universal median quasi-Monte Carlo integration, SIAM Journal on Numerical Analysis, 62(1), 533-566 (2024). [doi] [arXiv]

Published in 2023

T. Goda, Polynomial tractability for integration in an unweighted function space with absolutely convergent Fourier series, Proceedings of the American Mathematical Society, 151(9), 3925-3933 (2023). [doi] [arXiv]
T. Goda and W. Kitade, Constructing unbiased gradient estimators with finite variance for conditional stochastic optimization, Mathematics and Computers in Simulation, 204, 743-763 (2023). [doi] [arXiv]
T. Goda and K. Suzuki, Improved bounds on the gain coefficients for digital nets in prime power base, Journal of Complexity, 76, 101722 (2023). [doi] [arXiv]
T. Hironaka and T. Goda, An efficient estimation of nested expectations without conditional sampling, Journal of Computational and Applied Mathematics, 412, 114811 (2023). [doi] [arXiv]
Y. Kazashi, Y. Suzuki and T. Goda, Sub-optimality of Gauss-Hermite quadrature and optimality of the trapezoidal rule for functions with finite smoothness, SIAM Journal on Numerical Analysis, 61(3), 1426-1448 (2023). [doi] [arXiv]

Published in 2022

J. Dick, T. Goda and K. Suzuki, Component-by-component construction of randomized rank-1 lattice rules achieving almost the optimal randomized error rate, Mathematics of Computation, 91(338), 2771-2801 (2022). [doi] [arXiv]
T. Goda, A note on concatenation of quasi-Monte Carlo and plain Monte Carlo rules in high dimensions, Journal of Complexity, 72, 101647 (2022). [doi] [arXiv]
T. Goda, T. Hironaka, W. Kitade and A. Foster, Unbiased MLMC stochastic gradient-based optimization of Bayesian experimental designs, SIAM Journal on Scientific Computing, 44(1), A286-A311 (2022). [doi] [arXiv] [software]
T. Goda and P. L'Ecuyer, Construction-free median quasi-Monte Carlo rules for function spaces with unspecified smoothness and general weights, SIAM Journal on Scientific Computing, 44(4), A2765-A2788 (2022). [doi] [arXiv]

Published in 2021

J. Dick and T. Goda, Stability of lattice rules and polynomial lattice rules constructed by the component-by-component algorithm, Journal of Computational and Applied Mathematics, 382, 113062 (2021). [doi] [arXiv]
J. Dick, T. Goda and H. Murata, Toeplitz Monte Carlo, Statistics and Computing, 31, Article number 1 (2021). [doi] [arXiv] [software]
T. Goda, A simple algorithm for global sensitivity analysis with Shapley effects, Reliability Engineering and System Safety, 213, 107702 (2021). [doi] [arXiv]
T. Goda and Y. Yamada, Probabilistic threshold analysis by pairwise stochastic approximation for decision-making under uncertainty, Scientific Reports, 11, 19671 (2021). [doi]
K. Ishikawa and T. Goda, Efficient debiased evidence estimation by multilevel Monte Carlo sampling, Proceedings of the Thirty-Seventh Conference on Uncertainty in Artificial Intelligence, PMLR, 161:34-43. [link] [arXiv]
H. Kobayashi, R. Toyoda, H. Miyamoto, Y. Nakasugi, Y. Momoi, K. Nakamura, Q. Fu, H. Meada, T. Goda and K. Sato, Analysis of a methanogen and an actinobacterium dominating the thermophilic microbial community of an electromethanogenic biocathode, Archaea, 2021, Article ID 8865133 (2021). [doi]

Published in 2020

T. Goda, Richardson extrapolation allows truncation of higher order digital nets and sequences, IMA Journal of Numerical Analysis, 40(3), 2052-2075 (2020). [doi] [arXiv]
T. Goda, T. Hironaka and T. Iwamoto, Multilevel Monte Carlo estimation of expected information gains, Stochastic Analysis and Applications, 38(4), 581-600 (2020). [doi] [arXiv]
T. Goda and K. Suzuki, Recent advances in higher order quasi-Monte Carlo methods, In: D. Bilyk, J. Dick and F. Pillichshammer (eds.), Discrepancy Theory, Radon Series on Computational and Applied Mathematics 26, pp. 69-102 (2020). [doi] [arXiv]
T. Hironaka, M. Giles, T. Goda and H. Thom, Multilevel Monte Carlo estimation of the expected value of sample information, SIAM/ASA Journal on Uncertainty Quantification, 8(3), 1236-1259 (2020). [doi] [arXiv]
鈴木航介, 合田隆. 準モンテカルロ法の最前線, 日本応用数理学会論文誌, 30(4), 320-374 (2020). [doi] [software]

Published in 2019

J. Dick, T. Goda and T. Yoshiki, Richardson extrapolation of polynomial lattice rules, SIAM Journal on Numerical Analysis, 57(1), 44-69 (2019). [doi] [arXiv]
M. Giles and T. Goda, Decision-making under uncertainty: using MLMC for efficient estimation of EVPPI, Statistics and Computing, 29(4), 739-751 (2019). [doi] [arXiv]
T. Goda, On the separability of multivariate functions, Mathematics and Computers in Simulation, 159, 210-219 (2019). [doi] [arXiv]
T. Goda, K. Suzuki and T. Yoshiki, Lattice rules in non-periodic subspaces of Sobolev spaces, Numerische Mathematik, 141(2), 399-427 (2019). [doi] [arXiv]

Published in 2018

T. Goda, D. Murakami, K. Tanaka and K. Sato, Decision-theoretic sensitivity analysis for reservoir development under uncertainty using multilevel quasi-Monte Carlo methods, Computational Geosciences, 22(4), 1009-1020 (2018). [doi]
T. Goda, K. Suzuki and T. Yoshiki, Optimal order quadrature error bounds for infinite-dimensional higher-order digital sequences, Foundations of Computational Mathematics, 18(2), 433-458 (2018). [doi] [arXiv]

Published in 2017

J. Dick, T. Goda, K. Suzuki and T. Yoshiki, Construction of interlaced polynomial lattice rules for infinitely differentiable functions, Numerische Mathematik, 137(2), 257-288 (2017). [doi] [arXiv]
T. Goda, Computing the variance of a conditional expectation via non-nested Monte Carlo, Operations Research Letters, 45(1), 63-67 (2017). [doi] [arXiv]
T. Goda, The b-adic symmetrization of digital nets for quasi-Monte Carlo integration, Uniform Distribution Theory, 12(1), 1-25 (2017). [doi] [arXiv]
T. Goda, K. Ohno and K. Sato, Value of information in optimizing reservoir development under geological uncertainty, Journal of the Japan Petroleum Institute, 60(1), 41-52 (2017). [doi]
T. Goda, K. Suzuki and T. Yoshiki, Optimal order quasi-Monte Carlo integration in weighted Sobolev spaces of arbitrary smoothness, IMA Journal of Numerical Analysis, 37(1), 505-518 (2017). [doi] [arXiv]
T. Goda, K. Suzuki and T. Yoshiki, Quasi-Monte Carlo integration for twice differentiable functions over a triangle, Journal of Mathematical Analysis and Applications, 454(1), 361-384 (2017). [doi] [arXiv]
田中啓, 合田隆, 佐藤光三, 尾串誠, 島野裕文, 藤澤英治, 友枝城太郎. 情報の価値分析ならびに大域的最適化手法の構築と貯留層評価への適用, 石油技術協会誌, 82(6), 415-422 (2017). [doi]

Published in 2016

T. Goda, Quasi-Monte Carlo integration using digital nets with antithetics, Journal of Computational and Applied Mathematics, 304, 26-42 (2016). [doi] [arXiv]
T. Goda, R. Ohori, K. Suzuki and T. Yoshiki, The mean square quasi-Monte Carlo error for digitally shifted digital nets, In: R. Cools and D. Nuyens (eds.), Monte Carlo and Quasi-Monte Carlo Methods, Springer Proceedings in Mathematics & Statistics 163, pp. 331-350 (2016). [doi] [arXiv]
T. Goda, K. Suzuki and T. Yoshiki, An explicit construction of optimal order quasi-Monte Carlo rules for smooth integrands, SIAM Journal on Numerical Analysis, 54(4), 2664-2683 (2016). [doi] [arXiv]
T. Goda, K. Suzuki and T. Yoshiki, Digital nets with infinite digit expansions and construction of folded digital nets for quasi-Monte Carlo integration, Journal of Complexity, 33, 30-54 (2016). [doi] [arXiv]
M. Nakayasu, T. Goda, K. Tanaka and K. Sato, Evaluating the value of single-point data in heterogeneous reservoirs with the expectation-maximization algorithm, SPE Economics & Management, 8(1), 1-10 (2016). [doi]

Published in 2015

T. Goda, Constructing good higher order polynomial lattice rules with modulus of reduced degree, Journal of Complexity, 31(2), 237-259 (2015). [doi] [arXiv]
T. Goda, Fast construction of higher order digital nets for numerical integration in weighted Sobolev spaces, Numerical Algorithms, 69(2), 357-396 (2015). [doi] [arXiv]
T. Goda, Good interlaced polynomial lattice rules for numerical integration in weighted Walsh spaces, Journal of Computational and Applied Mathematics, 285, 279-294 (2015). [doi] [arXiv]
T. Goda and J. Dick, Construction of interlaced scrambled polynomial lattice rules of arbitrary high order, Foundations of Computational Mathematics, 15(5), 1245-1278 (2015). [doi] [arXiv]
T. Goda, M. Nakayasu, D. Murakami and K. Sato, Effects of likelihood functions on value of information analysis in resource development, Journal of the Japan Petroleum Institute, 58(6), 376-383 (2015). [doi]
T. Goda, K. Suzuki and T. Yoshiki, The b-adic tent transformation for quasi-Monte Carlo integration using digital nets, Journal of Approximation Theory, 194, 62-86 (2015). [doi] [arXiv]

Published in 2014 or earlier

T. Goda, Construction of scrambled polynomial lattice rules over F2 with small mean square weighted L2 discrepancy, BIT Numerical Mathematics, 54(2), 401-423 (2014). [doi] [arXiv]
T. Goda, On the Lp discrepancy of two-dimensional folded Hammersley point sets, Archiv der Mathematik, 103(4), 389-398 (2014). [doi] [arXiv]
T. Goda and K. Sato, History matching with iterative Latin hypercube samplings and parameterization of reservoir heterogeneity, Journal of Petroleum Science and Engineering, 114, 61-73 (2014). [doi]
T. Goda and K. Sato, Gravity currents of carbon dioxide with residual gas trapping in a two-layered porous medium, Journal of Fluid Mechanics, 673, 60-79 (2011). [doi]
合田隆, 佐藤光三. 繰り返しラテン超方格法を用いたCO2地中貯留における坑井配置の大局的最適化, 石油技術協会誌, 76(3), 233-243 (2011). [doi]
合田隆, 佐藤光三. アンサンブルカルマンフィルターを用いたトレーサー試験データの逐次同化によるフラクチャーの同定, Journal of the Japan Petroleum Institute, 52(5), 275-282 (2009). [doi]
合田隆, 佐藤光三. CIP法適用による多孔質媒体内2相流動シミュレーション, Journal of the Japan Petroleum Institute, 52(5), 257-264 (2009). [doi]
合田隆, 佐藤光三. 関数変換を用いたアンサンブルカルマンフィルターによる相対浸透率の推定, Journal of the Japan Petroleum Institute, 52(5), 248-256 (2009). [doi]

Others

[Plenary talk] T. Goda, Randomized lattice rules for high-dimensional integration, 16th International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing (MCQMC 2024), Waterloo, Canada, August 2024. (To be presented)
T. Goda, Polynomial tractability for integrating functions with slowly decaying Fourier series, 10th International Congress on Industrial and Applied Mathematics (ICIAM 2023), Tokyo, Japan, August 2023.
T. Goda, A universal numerical integration by digital nets, Foundations of Computational Mathematics 2023 conference (FoCM 2023), Paris, France, June 2023.
T. Goda, Construction-free median lattice rules (joint with P. L'Ecuyer), 15th International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing (MCQMC 2022), Linz, Austria, July 2022.
合田隆, 入れ子型期待値: マルチレベルモンテカルロ法による効率的推定と諸問題への応用, 第11回東京大学数理情報学談話会, 2022年6月. [link]
T. Goda, Multilevel Monte Carlo methods for estimating the expected value of information (joint with M. Giles, T. Hironaka and H. Thom), SIAM Conference on Uncertainty Quantification (UQ22), hybrid (Atlanta, Georgia, US and online), April 2022.
合田隆, 情報の期待価値とは -定義から効率的推定まで-, 計測自動制御学会制御部門「データ駆動型社会を支える適応学習制御調査研究会」第2回講演会, 2021年12月.
T. Goda, Multilevel Monte Carlo methods for efficient nested simulations (joint with M. Giles, T. Hironaka and H. Thom), Satellite Bayesian/Monte Carlo workshop on Statistical modeling for stochastic processes and related fields, online, September 2021. [link]
K. Ishikawa and T. Goda, Efficient debiased evidence estimation by multilevel Monte Carlo sampling, 37th Conference on Uncertainty in Artificial Intelligence (UAI2021), online, July 2021.
合田隆, 佐藤光三, 中島崇裕, Recent advances in value of information analysis and application to geological CO2 storage, Japan Geoscience Union Meeting 2021 (JpGU 2021), online, June 2021.
T. Hironaka and T. Goda, Two applications of multilevel Monte Carlo methods to Bayesian experimental designs, 14th International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing (MCQMC 2020), online, August 2020.
合田隆, 高次準モンテカルロ法へのリチャードソン補外の応用, RIMS共同研究（公開型）「諸科学を結ぶ基礎学問としての数値解析学」, 京都, 2019年11月. [link]
合田隆, 高次収束準モンテカルロ法とリチャードソン補外, 第1回「乱数・準乱数の数学」研究集会, 東京, 2019年10月. [link]
T. Goda, Multilevel Monte Carlo methods for estimating the expected value of information (joint with M. Giles, T. Hironaka and H. Thom), Dagstuhl Seminer on "Algorithms and Complexity for Continuous Problems", Dagstuhl, Germany, August 2019. [link]
[Plenary talk] T. Goda, Richardson extrapolation and higher order QMC, International Conference on Monte Carlo Methods and applications (MCM 2019), Sydney, Australia, July 2019. [slides]
合田隆, マルチレベルモンテカルロ法とEVPPI推定への応用, 数値解析セミナー, 東京, 2018年12月. [link]
T. Goda, Optimal order digital nets and sequences (joint with K. Suzuki and T. Yoshiki), Discrepancy workshop in RICAM Special Semester "Multivariate Algorithms and their Foundations in Number Theory", Linz, Austria, November 2018. [slides]
T. Goda, Quasi-Monte Carlo integration over a triangle (joint with K. Suzuki and T. Yoshiki), 13th International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing (MCQMC 2018), Rennes, France, July 2018. [slides]
合田隆, 高次準モンテカルロ法へのリチャードソン加速の応用, 乱数・準乱数とその周辺, 愛媛, 2018年6月. [link]
H. Thom, W. Fang, Z. Wang, N. Welton, T. Goda and M. Giles, Advanced Monte-Carlo sampling schemes for value of information estimation, ISPOR 20th Annual European Congress, Glasgow, Scotland, November 2017. Published from Value in Health, 20(9), A772 (2017). [link]
T. Goda, Richardson extrapolation of polynomial lattice rules for smooth functions (joint with J. Dick and T. Yoshiki), ESI Program on Tractability of High Dimensional Problems & Discrepancy, Vienna, Austria, September-October 2017. [link]
合田隆, 準モンテカルロ法の基礎から工学的応用の可能性まで, 日本OR学会2017年度中部支部シンポジウム, 愛知, 2017年9月. [link]
T. Goda, Optimal order quasi-Monte Carlo integration for smooth functions (joint with K. Suzuki and T. Yoshiki), International Conference on Monte Carlo Methods and Applications (MCM 2017), Montreal, Canada, July 2017.
T. Goda, Optimal order quadrature error bounds for higher order digital nets and sequences (joint with K. Suzuki and T. Yoshiki), 7th Workshop on High-Dimensional Approximation (HDA 2017), Sydney, Australia, February 2017.
K. Tanaka, T. Goda and K. Sato, Estimation of geological data using assisted history matching in the pilot-scale CO2 injection site, Iwanohara, Japan, 13th International Conference on Greenhouse Gas Control Technologies (GHGT13), Lausanne, Switzerland, November 2016. Published from Energy Procedia, 114, 5847-5854 (2017). [link]
T. Goda, Antithetic sampling for quasi-Monte Carlo integration using digital nets, 12th International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing (MCQMC 2016), Stanford, USA, August 2016.
合田隆, 不偏推定量を構成する汎用的手法としてのマルチレベル（＋ランダム化準）モンテカルロ法, 乱数と超一様性集会, 東京, 2016年6月. [link]
T. Goda, The b-adic tent transformation for digital nets (joint with K. Suzuki and T. Yoshiki), 10th IMACS Seminar on Monte Carlo Methods (MCM 2015), Linz, Austria, July 2015.
T. Goda, Construction of interlaced polynomial lattice rules achieving accelerating convergence for a class of infinitely smooth functions (joint with J. Dick, K. Suzuki and T. Yoshiki), Information-Based Complexity, Bedlewo, Poland, April 2015.
合田隆, 重み付きWAFOMの小さなinterlaced polynomial lattice点集合の構成アルゴリズム, 広島モンテカルロ法・準モンテカルロ法セミナー, 広島, 2015年2月. [link]
合田隆, 多次元数値積分の実用的アルゴリズムとしての準モンテカルロ法, 愛媛大学代数セミナー, 愛媛, 2014年10月. [link]
T. Goda, Constructing good higher order digital nets in reduced construction costs (joint with K. Suzuki and T. Yoshiki), 11th International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing (MCQMC 2014), KU Leuven, Belgium, April 2014. [link]
T. Goda, Construction of interlaced scrambled polynomial lattice rules (joint with J. Dick), Oberwolfach Workshop on Uniform Distribution Theory and Applications, Oberwolfach, Germany, September-October 2013. Published from Oberwolfach Reports, 10(4), 2854-2856 (2013). [link]
合田隆, 被積分関数の滑らかさに応じた準モンテカルロ法, 日本応用数理学会2013年度年会, 福岡, 2013年9月.
合田隆, シドニー滞在記(グローバル・アイ), 人工知能学会誌, 28(3), 502-503 (2013).
T. Goda and K. Sato, Global optimization of injection well placement toward higher safety of CO2 geological storage, 11th International Conference on Greenhouse Gas Control Technologies (GHGT11), Kyoto, Japan, November 2012. Published from Energy Procedia, 37, 4583-4590 (2013). [link]
合田隆，佐藤光三, ラテン超方格サンプリングを用いた大域的最適化手法の開発, 第1回進化計算学会研究会/第7回進化計算フロンティア研究会合同研究会, 東京, 2011年9月.
合田隆，佐藤光三, 新規大局的最適化手法の開発とCO2地中貯留における坑井配置最適化への適用, 平成23年度石油技術協会春季講演会, 東京, 2011年6月.
田代浩樹, 合田隆, 佐藤光三. 地中貯留CO2のトラッピングメカニズムに対する貯留層不均質性の影響, 平成23年度石油技術協会春季講演会, 東京, 2011年6月.
T. Goda and K. Sato, Optimization of well placement for geological sequestration of carbon dioxide using adaptive evolutionary Monte Carlo algorithm, 10th International Conference on Greenhouse Gas Control Technologies (GHGT10), Amsterdam, Netherlands, September 2010. Published from Energy Procedia, 4, 4275-4282 (2011). [link]
T. Goda and K. Sato, Accurate fluid interface tracking of interwell tracer flow by the constrained interpolation profile method, 130728-MS, 2010 International Oil & Gas Conference and Exhibition in China (IOGCEC), Beijing, China, June 2010. [link]
T. Goda and K. Sato, Gravity-driven flows of carbon dioxide sequestered in a two-layered porous medium, 2nd GMSI International Symposium, Tokyo, Japan, April 2010.
T. Goda and K. Sato, Numerical simulation of interwell tracer flow and effluent behavior using constrained interpolation profile (CIP) method, The 15th Formation Evaluation Symposium of Japan, Chiba, Japan, October 2009.
合田隆, 佐藤光三, 関数変換を用いたアンサンブルカルマンフィルターによる相対浸透率の推定, 平成21年度石油技術協会春季講演会, 東京, 2009年6月.
田代浩樹, 合田隆, 佐藤光三. アンサンブルカルマンフィルターを用いた貯留層特性解析におけるパラメータの選定とデータ取得に関する研究, 平成21年度石油技術協会春季講演会, 東京, 2009年6月.
合田隆, 佐藤光三, Ensemble Kalman Filterを用いたトレーサー試験最適化分析によるフラクチャーの同定, 平成20年度石油技術協会春季講演会, 新潟, 2008年6月.
合田隆, 佐藤光三, ストリームラインに沿ったCIP法適用による流動シミュレーションに関する研究, 平成19年度石油技術協会春季講演会, 東京, 2007年6月.