Pith. sign in

REVIEW 1 major objections 6 minor 102 references

Calibration of Quantum Devices via Robust Statistical Methods

T0 review · 1 major / 6 minor · reviewed 2026-08-06 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read Upgrading the numerical engine of Bayesian inference—from a moment-preserving particle filter to Markov-chain and tempered samplers—is what makes quantum-device calibration data-efficient, cutting dephasing-time uncertainty by 10x on real…

desk verdict Useful sampler benchmark for quantum calibration, but the hardware claims are confounded by device drift and the 10x/3x factors are swapped in the abstract. read the letter →

arxiv 2507.06941 v1 pith:AK7LYLZK submitted 2025-07-09 quant-ph

Alexandra Ramôa , Raffaele Santagati , Nathan Wiebe This is my paper · ORCID
classification quant-ph
keywords BayesianinferencequantumcharacterizationsequentialMonteCarloHamiltoniantemperedlikelihoodestimationmultimodalposteriorqubitcalibrationdatasubsampling
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Quantum-device calibration is a statistical estimation problem, and this paper argues that the representation of the Bayesian posterior is the bottleneck. It replaces the widely used Gaussian-shrinkage particle filter—which preserves only mean and variance and fails on multimodal or high-dimensional posteriors—with sequential Monte Carlo using Markov-chain moves, Hamiltonian Monte Carlo, tempered likelihood estimation, and subsampling. In simulations of phase estimation and precession dynamics, these samplers handle multimodality and high dimensions where the standard filter fails. On real cloud superconducting qubits, the same inference machinery estimates dephasing and relaxation times and detuning frequencies with markedly better uncertainty per measurement than the platform's default curve-fitting tools: a ten-fold reduction in Hahn echo dephasing-time uncertainty and three-fold in Ramsey experiments at equal data, and equal quality with up to about 99.5% fewer measurements. The paper also shows that data ordering, adaptivity heuristics, and the choice of resampling kernel materially change learning speed.

What carries the argument

The central mechanism is the particle representation of the posterior inside sequential Monte Carlo (SMC): a weighted cloud of parameter samples that is updated data-point by data-point and periodically moved by a Markov kernel. The paper's upgrade is the choice of that kernel—random-walk accept/reject steps and gradient-guided Hamiltonian Monte Carlo moves, optionally embedded in tempered likelihood estimation (annealing the posterior through increasing powers) and accelerated by data subsampling with control variates and block pseudo-marginal index updates. This machinery is what handles multimodality and high dimensionality, and it is the same machinery applied to the hardware calibration likelihoods: exponential decay for coherence times and a damped cosinusoid for detuning frequencies.

What would settle it

Monitor a single qubit's backend-reported dephasing time before and after every data collection window, and interleave the Bayesian sampler and the default fitter on exactly matched datasets and timespans. If the factor-of-10 Hahn echo and factor-of-3 Ramsey advantages appear only when the backend's own estimate drifts between windows, or disappear on a qubit whose parameters are stable to within a few percent, the hardware advantage claim would be shown to be drift rather than algorithmic gain.

Watch

Extended reading notes

Core claim

On the paper's own terms, the discovery is that the practical power of Bayesian quantum characterization is decided less by the Bayesian update itself than by how the posterior is represented numerically. The authors show that replacing the widely used Gaussian-shrinkage resampling filter—which preserves only the mean and variance of the particle cloud—with Markov-chain moves (random-walk proposals and gradient-guided Hamiltonian Monte Carlo) inside a sequential Monte Carlo scheme preserves the full posterior and therefore stays correct when the likelihood is multimodal or high-dimensional. Tempered likelihood estimation, in which the posterior is raised through increasing powers before the final target, adds further robustness: in the paper's four-dimensional, 24-mode test it raises correct-mode coverage from 50% to 100%. On cloud superconducting hardware, this machinery estimates dephasing time, energy relaxation time, and detuning frequency with less uncertainty per measurement than the platform's default fitting tools—a ten-fold reduction in Hahn echo dephasing-time uncertainty and three-fold in Ramsey experiments at equal data, and equal accuracy with up to 99.5% fewer measurements. The reported Ramsey detuning learning rate, roughly $\mathcal{O}(CPT^{-0.75})$, lies between the classical and quantum metrology limits, i.e., below the standard quantum limit.

Load-bearing premise

The hardware comparison assumes the qubit's true parameters stay effectively constant while the different methods collect their data, so that the gap in estimation error reflects method quality rather than device drift; the paper itself notes up to 50% variation between consecutive backend calibrations.

Editorial extensions

If this is right

  • Calibration on current superconducting hardware can trade classical computation for experimental data: the same uncertainty is reached with far fewer measurements.
  • Multimodal and high-dimensional posteriors, which arise naturally from symmetric or redundant likelihoods, are no longer a failure mode for Bayesian quantum learning if the resampling kernel is Markov-chain based.
  • Tempered likelihood estimation recovers modes that plain sequential Monte Carlo misses, raising correct-mode coverage from 50% to 100% in the paper's four-dimensional test.
  • Subsampled likelihoods with control variates and block pseudo-marginal index updates preserve posterior accuracy while cutting likelihood evaluations by roughly 60%.
  • Data ordering matters: for exponential-decay likelihoods, feeding the longest evolution times first prevents particle collapse and gives steadier learning.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A controlled drift audit, interleaving Bayesian and default fits on one qubit while monitoring backend-reported parameters, would separate method quality from device drift; the paper itself reports up to 50% variation between consecutive backend calibrations.
  • The same sampler stack is a natural candidate for learning Lindblad dissipators in open quantum systems, where the paper expects multimodal, high-dimensional posteriors but does not demonstrate the learning itself.
  • The reported $O(CPT^{-0.75})$ scaling suggests the residual gap to the Heisenberg limit might be a classical statistical inefficiency; combining the robust samplers with fully optimized adaptive controls could test whether the exponent moves toward 1.
  • Because data ordering and heuristics change results, published calibration comparisons should report these details; otherwise apparent algorithmic gains may be confounded by unobserved experimental-design choices.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

1 major / 6 minor

Summary. The paper studies numerical representations for Bayesian inference in quantum characterization, comparing sequential importance resampling with Liu-West filtering, Markov chain Monte Carlo variants (random walk Metropolis, Hamiltonian Monte Carlo, stochastic-gradient and subsampling variants), tempered likelihood estimation, block pseudo-marginal methods, and Gaussian rejection filtering. It applies these methods to simulated iterative phase estimation, precession dynamics, and multimodal sum-of-cosines models, then to IBMQ hardware experiments for Hahn echo (T2), T1, Ramsey (T2* and detuning), and echoed Ramsey estimation. The central advertised claims are that the Bayesian methods are more robust to multimodality and high dimensionality than standard SMC-Liu-West, and that on IBMQ hardware they outperform Qiskit's default fitters by factors of 10 and 3 in uncertainty at equal data, or match Qiskit with up to 99.5% less data. The paper also proposes an adaptive occupation-rate heuristic (Eq. 6) and discusses dataset ordering and adaptive design, with pseudocode and a public code repository.

Significance. The paper addresses a real and practically relevant problem: choosing and tuning the numerical representation of Bayesian posteriors for quantum device calibration. Its strengths are the breadth of the method comparison, the explicit treatment of multimodality (Eq. 5) and high dimensionality, the pseudocode for the main algorithms, and the publicly available code. The simulated results, especially the SMC-with-MCMC behavior on multimodal targets and the occupation-rate heuristic in Table 1, are useful contributions. The hardware comparisons are the main advertised result, but as presented they are not yet reliable: the comparisons are not protected against backend drift, and the headline numbers are internally inconsistent between the abstract, the discussion, and the tables. If the drift issue is addressed and the numbers are reconciled, the paper could make a practically important claim about sample-efficient calibration of superconducting devices; at present that claim is not established.

major comments (1)
  1. [Abstract, §5, Tables 2 and 3] The quantity called 'number of measurements' is used inconsistently, which makes the data-saving claims unverifiable. Table 3 reports 150 measurements for both Bayesian inference and the curve fit, but the text says the curve fit used 512 shots per time point and Bayesian inference used 2 shots per time point, so the fair shot counts are 38,400 versus 150 (a 99.6% saving by shots). In Table 2, the 'Qiskit fitter' low-data row has 2,535 measurements versus Bayesian's 2,524, so there is no data saving in that row, while the high-data row's 38,400/2,524 is a factor of about 15.2, not 11 as stated in the table note. Please define the metric (shots versus data points) and recompute all quoted savings ('93.4%', '99.5%', '99.6%', '11 times') from that metric.
minor comments (6)
  1. [§3.3, Figure 5 caption, §5] Figure 5 says '4-dimensional estimation (24 modes)', and for dim=4 with Eq. (5) the number of modes is dim! = 24; Section 5 says 'a model with 4 dimensions and 16 modes'. The latter appears to be a typo and should be corrected.
  2. [§3.2, Figure 3 caption] Panel (b) of Figure 3 is labeled 'Gaussian rejection filtering' but the text describes sequential Monte Carlo with the Liu-West filter; the caption should match the method actually used.
  3. [§4.2] The sentence 'The final standard deviation was 2.9' is incomplete: it should state the units (microseconds) and preferably give the corresponding estimate of T1 as well.
  4. [§4.4, Table 4] The column header 'Precision(σ2CPT)' uses CPT without definition, while the text defines precision as σ²Δt_acc; the notation should be harmonized and the abbreviation defined.
  5. [Abstract, §4.3, Figure 14] The abstract contains a duplicated 'to' in 'up to to 99.5%', and Section 4.3/Figure 14 say the inference used '0.4% (2) of the data' while Table 3 reports 150 data; these statements should be reconciled under the same counting convention.
  6. [§3.3, Eq. (6)] The 'occupation rate' in Eq. (6) is not formally defined; please specify how it is computed from the particle cloud and use consistent subscript notation for the measurement time t_k.

Circularity Check

0 steps flagged · score 0.0 of 10

No circular derivation: the paper's central claims are empirical comparisons, with the main validity caveat being device drift rather than circularity.

full rationale

The paper's derivation chain is not circular. The headline hardware claims (Tables 2 and 3) are empirical comparisons between SMC/MCMC posteriors computed from stated likelihoods (Eqs. 7 and 10) and Qiskit/SciPy curve fits on IBMQ data; no parameter is fitted to the target uncertainty reductions and then renamed as a prediction. The adaptive heuristic in Eq. 6 is a variance proxy offered as a design heuristic and is benchmarked on a toy multimodal problem, not tuned to force Table 1's median sigma. Self-citations ([24], [26], [25]) are used for background, the particle-guess heuristic, and Gaussian rejection filtering; none carries the central 'Bayesian samplers beat Qiskit' conclusion. The paper itself flags the main non-circular validity threat: Appendix F states 'variations as high as 50% were observed between consecutive calibrations,' and Section 4.3 warns that 'T*_2 is susceptible to large variations, so comparisons are susceptible to time fluctuations,' so the Table 2/3 gap may be partly drift; this is a correctness risk, not a circular reduction. Nor is the abstract's 10x/3x factor swap a circularity. No equation is equal to another by construction, and no fitted quantity is relabeled as a prediction.

Assumptions & free parameters 8 free parameters · 4 assumptions · 0 invented entities

This is an empirical and numerical paper rather than a derivation, so the ledger consists mainly of hand-chosen hyperparameters and modeling assumptions. The free parameters (particle counts, resampling thresholds, HMC step sizes, tempering schedules) are tuned per experiment but are not fitted to the target calibration values. The principal axioms are the correctness of the physical likelihood models and the asymptotic convergence of the samplers. No new physical entities are introduced.

free parameters (8)
  • Liu-West parameter a = 0.98
    Used in SMC simulations per Granade et al. [7]; controls kernel shrinkage and is chosen by hand.
  • SMC particle counts = 50, 100, 225, 200 per experiment
    Chosen per hardware experiment; affects accuracy and computational cost.
  • Resampling threshold dESS = 0.8 or 0.5
    Set per experiment; triggers resampling when effective sample size is low.
  • RWM proposal variance scaling = proportional to current variance, tuned for ~65% acceptance
    Tuned manually in Section 4 to stabilize acceptance; not fitted to target parameters.
  • HMC hyperparameters (L, epsilon, mass) = L=20, epsilon=0.001, mass=sigma_curr^2
    Set in Section 4.4 to reach 68% acceptance.
  • Number of tempering coefficients = 10
    Used in TLE; spacing and count chosen by hand.
  • Baseline constants C1, C2 = optimized in a parameter sweep
    Used only for the 'increasing random' baseline in Table 1, not for the proposed adaptive method.
  • Prior bounds = e.g., T2 in ]0,250] us, T1 in ]0,100] us, frequency in ]0,10] MHz
    Flat priors chosen by hand; influence low-data results.
assumptions (4)
  • domain assumption The likelihood models in Section 4 (single exponential decay, damped cosine with Lorentzian noise) describe the IBMQ devices
    Used to write Eqs. 7, 8, 10; misspecification would bias both Bayesian and curve-fit estimates.
  • domain assumption SMC with MCMC moves converges to the target posterior
    Relies on standard MCMC and SMC asymptotic theory (Appendix D) without finite-sample guarantees.
  • standard math Bernstein-von Mises theorem applies so prior dependence vanishes with data
    Invoked in Section 2 to justify Bayesian asymptotics.
  • ad hoc to paper The classical and quantum limits plotted in Figure 13 correspond to 1/sqrt(T) and 1/T scaling of standard deviation with cumulative evolution time
    The paper does not define the limits; the surpassing standard quantum limit claim depends on this unspecified scaling.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Calibration of Quantum Devices via Robust Statistical Methods." pith.science (2026). https://pith.science/paper/AK7LYLZK

@misc{pith2026250706941,
  author       = {Pith},
  title        = {Pith review of: Calibration of Quantum Devices via Robust Statistical Methods},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/AK7LYLZK}},
  note         = {Machine review of arXiv:2507.06941}
}
read the original abstract

Bayesian inference is a widely used technique for real-time characterization of quantum systems. It excels in experimental characterization in the low data regime, and when the measurements have degrees of freedom. A decisive factor for its performance is the numerical representation of the Bayesian probability distributions. In this work, we explore advanced statistical methods for this purpose, and numerically analyze their performance against the state-of-the-art in quantum parameter learning. In particular, we consider sequential importance resampling, tempered likelihood estimation, Markov Chain Monte Carlo, random walk Metropolis (RWM), Hamiltonian Monte Carlo (HMC) and variants (stochastic gradients with and without friction, energy conserving subsampling), block pseudo-marginal Metropolis-Hastings with subsampling, hybrid HMC-RWM approaches, and Gaussian rejection filtering. We demonstrate advantages of these approaches over existing ones, namely robustness under multi-modality and high dimensionality. We apply these algorithms to the calibration of superconducting qubits from IBMQ, surpassing the standard quantum limit and achieving better results than Qiskit's default tools. In Hahn echo and Ramsey experiments, we reduce the uncertainty by factors of 10 and 3 respectively, without increasing the number of measurements; conversely, we match the performance of Qiskit's methods while using up to to 99.5% less experimental data. We additionally investigate the roles of adaptivity, dataset ordering and heuristics in quantum characterization. Our findings have applications in challenging quantum characterization tasks, namely learning the dynamics of open quantum systems.

Figures

Figures reproduced from arXiv: 2507.06941 by the authors.

Figure 1
Figure 1. Iterative phase estimation circuit dia￾gram. Several routes are possible within IPE. A com￾mon approach is to deterministically obtain bits of the phase from last to first, using successive calls to the circuit in [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Evolution of the sampling process through the iterations/steps for Bayesian phase estimation, [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Evolution of the sampling process through the iterations/steps for precession frequency es [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figures from the paper (17 more)
Figure 4
Figure 4. Figure 4: Results of multi-parameter (2-dimensional) inference for a multimodal sum-of-sinusoids like [PITH_FULL_IMAGE:figures/full_fig_p009_4.png]
Figure 5
Figure 5. Figure 5: Results of multi-parameter (4- dimensional) inference for a multimodal sum￾of-sinusoids likelihood (Equation 5) for two variations of sequential Monte Carlo: with the prior as importance function (5a and 5b), and tempered likelihood estimation (5c and 5d). The modes ar…
Figure 6
Figure 6. Figure 6: Pulse schedule for measuring T2. done. The sharp drop in the uncertainty, followed by a plateau, and the larger inter-run variability in the first case are signs of a sharp drop in effec￾tive sample size and undue particle concentration (owing to particle collapse). Co…
Figure 7
Figure 7. Figure 7: Evolution of the standard deviation of the dephasing time [PITH_FULL_IMAGE:figures/full_fig_p011_7.png]
Figure 9
Figure 9. Figure 9: Pulse schedule for measuring T1 [PITH_FULL_IMAGE:figures/full_fig_p011_9.png]
Figure 10
Figure 10. Figure 10: Evolution of the standard deviation during the estimation of the energy relaxation time constant T1 of IBMQ device ibmq guadalupe. The dataset contemplated 1500 observations. The shaded region represents the interquartile range. As expected, the behavior is quite simi…
Figure 11
Figure 11. Figure 11: Pulse schedule for estimating the detun [PITH_FULL_IMAGE:figures/full_fig_p012_11.png]
Figure 14
Figure 14. Figure 14: Results for detuning frequency [PITH_FULL_IMAGE:figures/full_fig_p013_14.png]
Figure 13
Figure 13. Figure 13: Evolution of the standard deviation dur [PITH_FULL_IMAGE:figures/full_fig_p013_13.png]
Figure 15
Figure 15. Figure 15: Evolution of the standard deviation dur [PITH_FULL_IMAGE:figures/full_fig_p014_15.png]
Figure 16
Figure 16. Figure 16: Evolution of the standard deviation during the estimation of a detuning frequency on the IBMQ device ibmq armonk, using Bayesian in￾ference with tempered likelihood estimation with Hamiltonian Monte Carlo. The dataset contem￾plated 75 observations, and ten tempering c…
Figure 17
Figure 17. Figure 17: Results of using tempered likelihood estimation with random walk Metropolis resampling [PITH_FULL_IMAGE:figures/full_fig_p015_17.png]
Figure 18
Figure 18. Figure 18: Binary tree illustrating the computation of the expected utility for a set of experiments [PITH_FULL_IMAGE:figures/full_fig_p018_18.png]
Figure 19
Figure 19. Figure 19: Results of multi-parameter inference for a multimodal sum-of-sinusoids likelihood (equation [PITH_FULL_IMAGE:figures/full_fig_p021_19.png]
Figure 20
Figure 20. Figure 20: Estimated time fluctuations of the reso [PITH_FULL_IMAGE:figures/full_fig_p032_20.png]
Figure 22
Figure 22. Figure 22: Pulse schedule for measuring Ω0 = Ωe0+δmeas in an echoed Ramsey experiment (Hahn￾Ramsey sequence) [61]. Within the scope of this work, the purpose of such an arrangement is to make the coherence time large relative to the duration of at least a few oscil￾lation cycles…
Figure 23
Figure 23. Figure 23: Effect of inserting a refocusing pulse in [PITH_FULL_IMAGE:figures/full_fig_p033_23.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

102 extracted references · 54 canonical work pages

  1. [1]

    Entanglement-free Heisenberg-limited phase estimation

    B. L. Higgins et al. “Entanglement-free Heisenberg-limited phase estimation”. In: Nature450.7168 (Nov. 2007), pp. 393–396. doi:10 . 1038 / nature06257.url:https : //doi.org/10.1038%2Fnature06257

    2007

  2. [2]

    Adaptive Hamiltonian Estimation Using Bayesian Experimental Design

    Chris Ferrie, Cassandra Granade, and D. Cory. “Adaptive Hamiltonian Estimation Using Bayesian Experimental Design”. In: AIP Conference Proceedings1443 (Nov. 2011).doi:10.1063/1.3703632

    work page doi:10.1063/1.3703632 2011

  3. [4]

    Computationally efficient Bayesian quantum state tomogra- phy

    Joseph M. Lukens et al. “Computationally efficient Bayesian quantum state tomogra- phy”. In:2020 IEEE Photonics Conference (IPC). IEEE, Sept. 2020.doi:10 . 1109 / ipc47351 . 2020 . 9252416.url:https : / / doi . org / 10 . 1109 % 2Fipc47351 . 2020 . 9252416

    2020

  4. [5]

    Practical Bayesian tomogra- phy

    Cassandra Granade, Joshua Combes, and D G Cory. “Practical Bayesian tomogra- phy”. In:New Journal of Physics18.3 (Mar. 2016), p. 033024.doi:10.1088/1367-2630/ 18/3/033024.url:https://doi.org/10. 1088/1367-2630/18/3/033024

    doi:10.1088/1367-2630/ 2016

  5. [6]

    Ian Hincks et al.Hamiltonian Learning with Online Bayesian Experiment Design in Practice. 2018. arXiv:1806 . 02427 [quant-ph]

    2018

  6. [7]

    Robust online Hamiltonian learning

    Cassandra E Granade et al. “Robust online Hamiltonian learning”. In:New Journal of Physics14.10 (Oct. 2012), p. 103013.doi: 10.1088/1367- 2630/14/10/103013.url: 33 https://doi.org/10.1088%2F1367-2630% 2F14%2F10%2F103013

    doi:10.1088/1367- 2012

  7. [8]

    Learning models of quantum systems from experiments

    Antonio A. Gentile et al. “Learning models of quantum systems from experiments”. In: Nature Physics17.7 (Apr. 2021), pp. 837– 843.doi:10 . 1038 / s41567 - 021 - 01201 - 7.url:https : / / doi . org / 10 . 1038 % 2Fs41567-021-01201-7

    2021

  8. [9]

    Learning quantum systems

    Valentin Gebhart et al. “Learning quantum systems”. In:Nature Reviews Physics5.3 (2023), pp. 141–156.doi:10.1038/s42254- 022-00552-1.url:https://doi.org/10. 1038/s42254-022-00552-1

    doi:10.1038/s42254- 2023

Show all 102 references
  1. [10]

    Quantum Computation of Molecular Structure Us- ing Data from Challenging-To-Classically- Simulate Nuclear Magnetic Resonance Ex- periments

    Thomas E. O’Brien et al. “Quantum Computation of Molecular Structure Us- ing Data from Challenging-To-Classically- Simulate Nuclear Magnetic Resonance Ex- periments”. In:PRX Quantum3 (3 2022), p. 030345.doi:10 . 1103 / PRXQuantum . 3 . 030345.url:https://link.aps.org/doi/ 10.1...

    2022 doi

  2. [11]

    How to best sample a peri- odic probability distribution, or on the accu- racy of Hamiltonian finding strategies

    Christopher Ferrie, Cassandra E. Granade, and D. G. Cory. “How to best sample a peri- odic probability distribution, or on the accu- racy of Hamiltonian finding strategies”. In: Quantum Information Processing12.1 (Apr. 2012), pp. 611–623.doi:10.1007/s11128- 012- 0407- 6.url:ht...

    2012 doi

  3. [12]

    Modern Bayesian Ex- perimental Design

    Tom Rainforth et al. “Modern Bayesian Ex- perimental Design”. In:Statistical Science 39.1 (Feb. 2024).issn: 0883-4237.doi:10. 1214/23-sts915

    2024

  4. [13]

    Michael Betancourt.A Conceptual Intro- duction to Hamiltonian Monte Carlo. 2018. arXiv:1701.02434 [stat.ME]

    2018 arXiv

  5. [14]

    Inference with Hamiltonian Sequential Monte Carlo Simulators

    Remi Daviet. “Inference with Hamiltonian Sequential Monte Carlo Simulators”. In: SSRN Electronic Journal(2016).doi:10. 2139/ssrn.2888242.url:https://doi. org/10.2139%2Fssrn.2888242

    2016

  6. [15]

    An Introduction to Sequential Monte Carlo Methods

    Arnaud Doucet, Nando Freitas, and Neil Gordon. “An Introduction to Sequential Monte Carlo Methods”. In:Sequential Monte Carlo Methods in Practice. Springer New York, 2001, pp. 3–14.doi:10.1007/ 978 - 1 - 4757 - 3437 - 9 _ 1.url:https : / / doi.org/10.1007%2F978- 1- 4757- 3437- 9_1

    2001

  7. [16]

    Structured filtering

    Cassandra Granade and Nathan Wiebe. “Structured filtering”. In:New Journal of Physics19.8 (Aug. 2017), p. 083014.doi: 10.1088/1367-2630/aa77cf.url:https: / / doi . org / 10 . 1088 % 2F1367 - 2630 % 2Faa77cf

    2017 doi

  8. [17]

    2021.url:http : / / community

    Stan Development Team.Stan Modeling Language Users Guide and Reference Man- ual 2.27. 2021.url:http : / / community . qiskit.org/textbook

    2021

  9. [18]

    Probabilistic pro- gramming in Python using PyMC3

    John Salvatier, Thomas V. Wiecki, and Christopher Fonnesbeck. “Probabilistic pro- gramming in Python using PyMC3”. In: PeerJ Computer Science2 (Apr. 2016), e55. issn: 2376-5992.doi:10.7717/peerj- cs. 55.url:http : / / dx . doi . org / 10 . 7717 / peerj-cs.55

    2016 doi

  10. [19]

    Sequential Monte Carlo samplers

    Pierre Del Moral, Arnaud Doucet, and Ajay Jasra. “Sequential Monte Carlo samplers”. In:Journal of the Royal Statistical Soci- ety: Series B (Statistical Methodology)68.3 (June 2006), pp. 411–436.doi:10.1111/j. 1467 - 9868 . 2006 . 00553 . x.url:https : / / doi . org / 10 . 111...

    2006 arXiv

  11. [20]

    Quantum model learning agent: characterisation of quantum systems through machine learning

    Brian Flynn et al. “Quantum model learning agent: characterisation of quantum systems through machine learning”. In:New Journal of Physics24.5 (2022), p. 053034.doi:10. 1088/1367- 2630/ac68ff.url:https:// dx.doi.org/10.1088/1367-2630/ac68ff

    2022 doi

  12. [21]

    2021.doi:10.5281/zenodo.2573505

    MD SAJID ANIS et al.Qiskit: An Open- source Framework for Quantum Computing. 2021.doi:10.5281/zenodo.2573505

    2021 doi

  13. [22]

    com / alexandra - frca / bayesianlearning

    Alexandra Ramˆ oa.Quantum parameter es- timation via Bayesian learning.https : / / github . com / alexandra - frca / bayesianlearning. 2021

    2021

  14. [23]

    Cassandra Granade et al.QInfer: Library for Statistical Inference in Quantum Infor- mation. Sept. 2016.doi:10.5281/zenodo. 157007.url:http : / / dx . doi . org / 10 . 5281/zenodo.157007

    2016 doi

  15. [24]

    2024.doi:10

    Alexandra Ramˆ oa.Learning the physics of open quantum systems from experiments. 2024.doi:10 . 48550 / arXiv . 2412 . 00078. arXiv:2412 . 00078 [quant-ph]. url:https : / / arxiv . org / abs / 2412 . 00078

    2024

  16. [25]

    Effi- cient Bayesian Phase Estimation

    Nathan Wiebe and Chris Granade. “Effi- cient Bayesian Phase Estimation”. In:Phys- ical Review Letters117.1 (June 2016).doi: 10 . 1103 / physrevlett . 117 . 010503. url:https : / / doi . org / 10 . 1103 % 2Fphysrevlett.117.010503

    2016

  17. [26]

    Hamiltonian Learn- ing and Certification Using Quantum Re- sources

    Nathan Wiebe et al. “Hamiltonian Learn- ing and Certification Using Quantum Re- sources”. In:Physical Review Letters112.19 (May 2014).doi:10 . 1103 / physrevlett . 112.190501.url:https://doi.org/10. 1103%2Fphysrevlett.112.190501. 34

    2014

  18. [27]

    A. W. van der Vaart.Asymptotic Statis- tics. Cambridge University Press, Oct. 1998. Chap. 10.2 Bernstein–von Mises Theo- rem.doi:10 . 1017 / cbo9780511802256. url:https : / / doi . org / 10 . 1017 % 2Fcbo9780511802256

    1998

  19. [28]

    Combined Pa- rameter and State Estimation in Simulation- Based Filtering

    Jane Liu and Mike West. “Combined Pa- rameter and State Estimation in Simulation- Based Filtering”. In:Sequential Monte Carlo Methods in Practice. Springer New York, 2001, pp. 197–223.doi:10 . 1007 / 978- 1- 4757- 3437- 9_10.url:https:// doi.org/10.1007%2F978- 1- 4757- 3437- 9_10

    2001

  20. [29]

    Single-shot parameter estimation via con- tinuous quantum measurement

    Bradley A. Chase and J. M. Geremia. “Single-shot parameter estimation via con- tinuous quantum measurement”. In:Phys. Rev. A79 (2 Feb. 2009), p. 022314.doi:10. 1103 / PhysRevA . 79 . 022314.url:https : //link.aps.org/doi/10.1103/PhysRevA. 79.022314

    2009 doi

  21. [30]

    Quantum Hamilto- nian learning using imperfect quantum re- sources

    Nathan Wiebe et al. “Quantum Hamilto- nian learning using imperfect quantum re- sources”. In:Physical Review A89.4 (Apr. 2014).doi:10.1103/physreva.89.042314. url:https : / / doi . org / 10 . 1103 % 2Fphysreva.89.042314

    2014 doi

  22. [31]

    Experimental quantum Hamiltonian learning

    Jianwei Wang et al. “Experimental quantum Hamiltonian learning”. In:Nature Physics 13.6 (Mar. 2017), pp. 551–555.issn: 1745- 2481.doi:10.1038/nphys4074.url:http: //dx.doi.org/10.1038/nphys4074

    2017 doi

  23. [32]

    Evans, Robin Harper, and Steven T

    Tim J. Evans, Robin Harper, and Steven T. Flammia.Scalable Bayesian Hamilto- nian learning. 2019. arXiv:1912 . 07636 [quant-ph]

    2019

  24. [33]

    Sequential Monte Carlo Sam- plers with Independent Markov Chain Monte Carlo Proposals

    L. F. South, A. N. Pettitt, and C. C. Drovandi. “Sequential Monte Carlo Sam- plers with Independent Markov Chain Monte Carlo Proposals”. In:Bayesian Anal- ysis14.3 (Sept. 2019).doi:10 . 1214 / 18 - ba1129.url:https://doi.org/10.1214% 2F18-ba1129

    2019

  25. [34]

    Equation of State Calculations by Fast Computing Machines

    Nicholas Metropolis et al. “Equation of State Calculations by Fast Computing Machines”. In:The Journal of Chemical Physics21.6 (June 1953), pp. 1087–1092. doi:10.1063/1.1699114

    1953 doi

  26. [35]

    Pseudo- Bayesian quantum tomography with rank- adaptation

    The Tien Mai and Pierre Alquier. “Pseudo- Bayesian quantum tomography with rank- adaptation”. In:Journal of Statistical Plan- ning and Inference184 (May 2017), pp. 62– 76.doi:10 . 1016 / j . jspi . 2016 . 11 . 003. url:https : / / doi . org / 10 . 1016 % 2Fj . jspi.2016.11.003

    2017

  27. [36]

    A controlled-NOT gate for frequency-bin qubits

    Hsuan-Hao Lu et al. “A controlled-NOT gate for frequency-bin qubits”. In:npj Quantum Information5.1 (Mar. 2019).doi: 10 . 1038 / s41534 - 019 - 0137 - z.url: https : / / doi . org / 10 . 1038 % 2Fs41534 - 019-0137-z

    2019

  28. [37]

    Quantum state estimation when qubits are lost: a no-data-left-behind approach

    Brian P Williams and Pavel Lougovski. “Quantum state estimation when qubits are lost: a no-data-left-behind approach”. In: New Journal of Physics19.4 (Apr. 2017), p. 043003.doi:10 . 1088 / 1367 - 2630 / aa65de.url:https://doi.org/10.1088% 2F1367-2630%2Faa65de

    2017

  29. [38]

    A practical and ef- ficient approach for Bayesian quantum state estimation

    Joseph M Lukens et al. “A practical and ef- ficient approach for Bayesian quantum state estimation”. In:New Journal of Physics 22.6 (July 2020), p. 063038.doi:10.1088/ 1367 - 2630 / ab8efa.url:https : / / doi . org/10.1088%2F1367-2630%2Fab8efa

    2020

  30. [39]

    The Tien Mai.Efficient adaptive MCMC implementation for Pseudo-Bayesian quan- tum tomography. 2021. arXiv:2106.00577 [stat.AP]

    2021 arXiv

  31. [40]

    MCMC Methods for Functions: Modifying Old Algorithms to Make Them Faster

    S. L. Cotter et al. “MCMC Methods for Functions: Modifying Old Algorithms to Make Them Faster”. In:Statistical Science 28.3 (Aug. 2013).doi:10.1214/13-sts421. url:https : / / doi . org / 10 . 1214 % 2F13 - sts421

    2013 doi

  32. [41]

    Geometric MCMC for infinite-dimensional inverse problems

    Alexandros Beskos et al. “Geometric MCMC for infinite-dimensional inverse problems”. In:Journal of Computational Physics335 (Apr. 2017), pp. 327–351. doi:10.1016/j.jcp.2016.12.041.url: https : / / doi . org / 10 . 1016 % 2Fj . jcp . 2016.12.041

    2017 doi

  33. [42]

    Pseudo-Marginal Hamiltonian Monte Carlo

    Johan Alenl¨ ov, Arnoud Doucet, and Fredrik Lindsten. “Pseudo-Marginal Hamiltonian Monte Carlo”. In:Journal of Machine Learning Research22.141 (2021), pp. 1–45. url:http://jmlr.org/papers/v22/19- 486.html

    2021

  34. [43]

    Hybrid Monte Carlo

    Simon Duane et al. “Hybrid Monte Carlo”. In:Physics Letters B195.2 (1987), pp. 216– 222.issn: 0370-2693.doi:https : / / doi . org / 10 . 1016 / 0370 - 2693(87 ) 91197 - X.url:https : / / www . sciencedirect . com / science / article / pii/037026938791197X

    1987

  35. [44]

    MCMC Using Hamilto- nian Dynamics

    Radford Neal. “MCMC Using Hamilto- nian Dynamics”. In:Chapman & Hall/CRC Handbooks of Modern Statistical Methods. Chapman and Hall/CRC, May 2011.doi: 10 . 1201 / b10905 - 6.url:https : / / doi . org/10.1201%2Fb10905-6. 35

    2011

  36. [45]

    Annealed importance sampling

    Radford M. Neal. “Annealed importance sampling”. In:Statistics and Computing 11.2 (Apr. 2001), pp. 125–139.issn: 1573- 1375.doi:10 . 1023 / A : 1008923215028. url:https : / / doi . org / 10 . 1023 / A : 1008923215028

    2001

  37. [46]

    Characteriza- tion of a qubit Hamiltonian using adaptive measurements in a fixed basis

    Alexandr Sergeevich et al. “Characteriza- tion of a qubit Hamiltonian using adaptive measurements in a fixed basis”. In:Physical Review A84.5 (Nov. 2011).doi:10.1103/ physreva.84.052315.url:https://doi. org/10.1103%2Fphysreva.84.052315

    2011

  38. [47]

    Resource-efficient adap- tive Bayesian tracking of magnetic fields with a quantum sensor

    K Craigie et al. “Resource-efficient adap- tive Bayesian tracking of magnetic fields with a quantum sensor”. In:Journal of Physics: Condensed Matter33.19 (Apr. 2021), p. 195801.doi:10.1088/1361-648x/ abe34f.url:https://doi.org/10.1088% 2F1361-648x%2Fabe34f

    2021 doi

  39. [48]

    Neural-Network Heuristics for Adaptive Bayesian Quantum Estimation

    Lukas J. Fiderer, Jonas Schuff, and Daniel Braun. “Neural-Network Heuristics for Adaptive Bayesian Quantum Estimation”. In:PRX Quantum2.2 (Apr. 2021).doi:10. 1103/prxquantum.2.020303.url:https: / / doi . org / 10 . 1103 % 2Fprxquantum . 2 . 020303

    2021

  40. [49]

    Likelihood-Free Methods for Quantum Parameter Estimation

    Christopher Ferrie and Cassandra E. Granade. “Likelihood-Free Methods for Quantum Parameter Estimation”. In: Physical Review Letters112.13 (Apr. 2014). doi:10 . 1103 / physrevlett . 112 . 130402. url:https : / / doi . org / 10 . 1103 % 2Fphysrevlett.112.130402

    2014

  41. [50]

    Quantum model aver- aging

    Christopher Ferrie. “Quantum model aver- aging”. In:New Journal of Physics16.9 (Sept. 2014), p. 093035.doi:10 . 1088 / 1367 - 2630 / 16 / 9 / 093035.url:https : //doi.org/10.1088%2F1367-2630%2F16% 2F9%2F093035

    2014

  42. [51]

    Andrew Gelman, Daniel Lee, and Jiqiang Guo. “Stan”. In:Journal of Educational and Behavioral Statistics40.5 (Oct. 2015), pp. 530–543.doi:10 . 3102 / 1076998615606113.url:https : / / doi . org/10.3102%2F1076998615606113

    2015

  43. [52]

    Quantum measurements and the abelian stabilizer problem

    A. Yu. Kitaev. “Quantum measurements and the abelian stabilizer problem”. In: Electronic Colloquium on Computational Complexity3 (1996)

    1996

  44. [53]

    Kitaev, A

    A. Kitaev, A. Shen, and M. Vyalyi.Clas- sical and Quantum Computation. American Mathematical Society, May 2002.doi:10. 1090/gsm/047.url:https://doi.org/10. 1090%2Fgsm%2F047

    2002

  45. [54]

    Faster phase estima- tion

    Krysta M. Svore, Matthew B. Hastings, and Michael Freedman. “Faster phase estima- tion”. In:Quantum Information and Com- putation14.3&4 (Mar. 2014), pp. 306–328. doi:10.26421/qic14.3-4-7.url:https: //doi.org/10.26421%2Fqic14.3-4-7

    2014 doi

  46. [55]

    Arbitrary accu- racy iterative quantum phase estimation algorithm using a single ancillary qubit: A two-qubit benchmark

    Miroslav Dobˇ s ´ ıˇ cek et al. “Arbitrary accu- racy iterative quantum phase estimation algorithm using a single ancillary qubit: A two-qubit benchmark”. In:Physical Re- view A76.3 (Sept. 2007).doi:10 . 1103 / physreva.76.030306.url:https://doi. org/10.1103%2Fphysreva.76.030306

    2007

  47. [56]

    Sophia Simon et al.Dividing and Conquer- ing the Van Vleck Catastrophe. 2025. eprint: arXiv:2504.03465

    2025 arXiv

  48. [57]

    IBM, 2020.url: http : / / community

    Abraham Asfaw et al.Learn Quantum Com- putation Using Qiskit. IBM, 2020.url: http : / / community . qiskit . org / textbook

    2020

  49. [58]

    Experimental Bayesian Quantum Phase Estimation on a Silicon Photonic Chip

    S. Paesani et al. “Experimental Bayesian Quantum Phase Estimation on a Silicon Photonic Chip”. In:Physical Review Let- ters118.10 (Mar. 2017).doi:10 . 1103 / physrevlett.118.100503.url:https:// doi . org / 10 . 1103 % 2Fphysrevlett . 118 . 100503

    2017

  50. [59]

    Discontinuous Hamiltonian Monte Carlo for discrete parameters and discontinuous likelihoods

    Akihiko Nishimura, David B Dunson, and Jianfeng Lu. “Discontinuous Hamiltonian Monte Carlo for discrete parameters and discontinuous likelihoods”. In:Biometrika 107.2 (Mar. 2020), pp. 365–380.doi:10 . 1093/biomet/asz083.url:https://doi. org/10.1093%2Fbiomet%2Fasz083

    2020

  51. [60]

    Zwiebach.Two state systems

    B. Zwiebach.Two state systems. 2013.url: https://ocw.mit.edu/courses/physics/ 8- 05- quantum- physics- ii- fall- 2013/ lecture-notes/MIT8_05F13_Chap_07.pdf (visited on 09/20/2021)

    2013

  52. [61]

    Fault-tolerant Hahn-Ramsey interferometry with pulse se- quences of alternating detuning

    Nikolay V. Vitanov et al. “Fault-tolerant Hahn-Ramsey interferometry with pulse se- quences of alternating detuning”. In:Phys- ical Review A91.3 (Mar. 2015).doi:10 . 1103 / physreva . 91 . 033406.url:https : / / doi . org / 10 . 1103 % 2Fphysreva . 91 . 033406

    2015

  53. [62]

    The classical Bloch equations

    Martin Frimmer and Lukas Novotny. “The classical Bloch equations”. In:American Journal of Physics82.10 (Oct. 2014), pp. 947–954.doi:10 . 1119 / 1 . 4878621. url:https : / / doi . org / 10 . 1119 % 2F1 . 4878621. 36

    2014

  54. [63]

    2024.doi:10

    Alexandra Ramˆ oa and Luis Paulo San- tos.Bayesian Quantum Amplitude Estima- tion. 2024.doi:10 . 48550 / arXiv . 2412 . 04394. arXiv:2412 . 04394 [quant-ph]. url:https : / / arxiv . org / abs / 2412 . 04394

    2024

  55. [64]

    Quan- tum Theory of Phase Estimation

    Luca Pezz´ e and Augusto Smerzi. “Quan- tum Theory of Phase Estimation”. In:Atom Interferometry188 (Nov. 2014).doi:10 . 3254/978-1-61499-488-0-691

    2014

  56. [65]

    Magnetic-Field Learn- ing Using a Single Electronic Spin in Dia- mond with One-Photon Readout at Room Temperature

    R. Santagati et al. “Magnetic-Field Learn- ing Using a Single Electronic Spin in Dia- mond with One-Photon Readout at Room Temperature”. In:Phys. Rev. X9 (2 Apr. 2019), p. 021019.doi:10.1103/PhysRevX. 9.021019.url:https://link.aps.org/ doi/10.1103/PhysRevX.9.021019

    2019 doi

  57. [66]

    Online adaptive quan- tum characterization of a nuclear spin

    Timo Joas et al. “Online adaptive quan- tum characterization of a nuclear spin”. In: npj Quantum Information7.1 (2021), p. 56. doi:10.1038/s41534-021-00389-z.url: https://doi.org/10.1038/s41534-021- 00389-z

    2021 doi

  58. [67]

    Bayesian Quantum Multiphase Estimation Algorithm

    Valentin Gebhart, Augusto Smerzi, and Luca Pezz` e. “Bayesian Quantum Multiphase Estimation Algorithm”. In:Physical Re- view Applied16.1 (July 2021).issn: 2331- 7019.doi:10.1103/physrevapplied.16. 014035.url:http : / / dx . doi . org / 10 . 1103/physrevapplied.16.014035

    2021 doi

  59. [68]

    Lorenzo Fioroni, Ivan Rojkov, and Florentin Reiter.A learning agent-based approach to the characterization of open quantum sys- tems. 2025. arXiv:2501.05350 [quant-ph]. url:https : / / arxiv . org / abs / 2501 . 05350

    2025 arXiv

  60. [69]

    Qiskit pulse: pro- gramming quantum computers through the cloud with pulses

    Thomas Alexander et al. “Qiskit pulse: pro- gramming quantum computers through the cloud with pulses”. In:Quantum Science and Technology5.4 (Aug. 2020), p. 044006. issn: 2058-9565.doi:10.1088/2058-9565/ aba404.url:http : / / dx . doi . org / 10 . 1088/2058-9565/aba404

    2020 doi

  61. [70]

    Gross, A

    R. Gross, A. Marx, and F. Deppe.Lecture notes on applied superconductivity, 10.3: control of quantum two-level systems. 2013. url:https : / / www . wmi . badw . de / teaching / Lecturenotes / AS / AS2013 _ Chapter10 _ 2 _ Slides . pdf(visited on 05/08/2021)

    2013

  62. [71]

    2005.url:http : / / info.phys.unm.edu/ ~ideutsch/Classes/ Sandia%20F05/QI_Lecture8.pdf(visited on 09/26/2021)

    Ivan Deutsch.Short Course in Quantum In- formation: Lecture 8. 2005.url:http : / / info.phys.unm.edu/ ~ideutsch/Classes/ Sandia%20F05/QI_Lecture8.pdf(visited on 09/26/2021)

    2005

  63. [72]

    Experimen- tal Phase Estimation Enhanced by Ma- chine Learning

    Alessandro Lumino et al. “Experimen- tal Phase Estimation Enhanced by Ma- chine Learning”. In:Physical Review Ap- plied10.4 (Oct. 2018).doi:10 . 1103 / physrevapplied.10.044033.url:https: //doi.org/10.1103%2Fphysrevapplied. 10.044033

    2018

  64. [73]

    A Tu- torial on Particle Filtering and Smoothing: Fifteen Years Later

    Arnaud Doucet and Adam Johansen. “A Tu- torial on Particle Filtering and Smoothing: Fifteen Years Later”. In:Handbook of Non- linear Filtering12 (Jan. 2009)

    2009

  65. [74]

    Subsampling se- quential Monte Carlo for static Bayesian models

    David Gunawan et al. “Subsampling se- quential Monte Carlo for static Bayesian models”. In:Statistics and Computing30.6 (Sept. 2020), pp. 1741–1758.doi:10.1007/ s11222-020-09969-z.url:https://doi. org/10.1007%2Fs11222-020-09969-z

    2020

  66. [75]

    An Introduc- tion to MCMC for Machine Learning

    Christophe Andrieu et al. “An Introduc- tion to MCMC for Machine Learning”. In: Machine Learning50.1 (Jan. 2003), pp. 5– 43.issn: 1573-0565.doi:10 . 1023 / A : 1020281327116.url:https : / / doi . org / 10.1023/A:1020281327116

    2003 doi

  67. [76]

    Speagle.A Conceptual Introduc- tion to Markov Chain Monte Carlo Methods

    Joshua S. Speagle.A Conceptual Introduc- tion to Markov Chain Monte Carlo Methods

  68. [77]

    Monte Carlo sampling methods using Markov chains and their ap- plications

    W. K. Hastings. “Monte Carlo sampling methods using Markov chains and their ap- plications”. In:Biometrika57.1 (Apr. 1970), pp. 97–109.doi:10.1093/biomet/57.1. 97.url:https : / / doi . org / 10 . 1093 % 2Fbiomet%2F57.1.97

    1970 doi

  69. [78]

    On thin- ning of chains in MCMC

    William Link and Mitchell Eaton. “On thin- ning of chains in MCMC”. In:Methods in Ecology and Evolution3 (June 2011), pp. 112–115.doi:10.1111/j.2041- 210X. 2011.00131.x

    2011 arXiv

  70. [79]

    Adaptively Scaling the Metropolis Algo- rithm Using Expected Squared Jumped Dis- tance

    Andrew Gelman and Cristian Pasarica. “Adaptively Scaling the Metropolis Algo- rithm Using Expected Squared Jumped Dis- tance”. In:SSRN Electronic Journal(2007). doi:10.2139/ssrn.1010403.url:https: //doi.org/10.2139%2Fssrn.1010403

    2007 doi

  71. [80]

    Hamiltonian and Langevin Monte Carlo

    Adrian Barbu and Song Zhu. “Hamiltonian and Langevin Monte Carlo”. In: Springer Singapore, Feb. 2020, pp. 281–325.isbn: 978-981-13-2970-8.doi:10.1007/978-981- 13-2971-5_9

    2020 doi

  72. [81]

    The No-U-Turn Sampler: Adaptively Set- ting Path Lengths in Hamiltonian Monte Carlo

    Matthew Hoffman and Andrew Gelman. “The No-U-Turn Sampler: Adaptively Set- ting Path Lengths in Hamiltonian Monte Carlo”. In:Journal of Machine Learning Re- search15 (Nov. 2011). 37

    2011

  73. [82]

    Rie- mann manifold Langevin and Hamiltonian Monte Carlo methods

    Mark Girolami and Ben Calderhead. “Rie- mann manifold Langevin and Hamiltonian Monte Carlo methods”. In:Journal of the Royal Statistical Society: Series B (Statisti- cal Methodology)73.2 (Mar. 2011), pp. 123– 214.doi:10 . 1111 / j . 1467 - 9868 . 2010 . 00765.x.url:https://doi...

    2011

  74. [83]

    M. J. Betancourt.Adiabatic Monte Carlo

  75. [84]

    Shiwei Lan, Jeffrey Streets, and Babak Shahbaba.Wormhole Hamiltonian Monte Carlo. 2014. arXiv:1306.0063 [stat.CO]

    2014 arXiv

  76. [85]

    Minghao Gu and Shiliang Sun.Variational Langevin Hamiltonian Monte Carlo for Dis- tant Multi-modal Sampling. 2019. arXiv: 1906.00229 [cs.LG]

    2019 arXiv

  77. [86]

    M. J. Betancourt.Scalable Bayesian Infer- ence with Hamiltonian Monte Carlo.https: / / www . youtube . com / watch ? v = jUSZboSq1zg & t = 1395s. London Machine Learning Meetup, 2018

    2018

  78. [87]

    The Extended Liu and West Fil- ter: Parameter Learning in Markov Switch- ing Stochastic Volatility Models

    Maria Paula Rios and Hedibert Freitas Lopes. “The Extended Liu and West Fil- ter: Parameter Learning in Markov Switch- ing Stochastic Volatility Models”. In:State- Space Models. Springer New York, 2013, pp. 23–61.doi:10 . 1007 / 978 - 1 - 4614 - 7789 - 1 _ 2.url:https : / / do...

    2013

  79. [88]

    Adaptive Tuning of Hamiltonian Monte Carlo Within Sequential Monte Carlo

    Alexander Buchholz, Nicolas Chopin, and Pierre E. Jacob. “Adaptive Tuning of Hamiltonian Monte Carlo Within Sequential Monte Carlo”. In:Bayesian Analysis16.3 (Sept. 2021).doi:10 . 1214 / 20 - ba1222. url:https : / / doi . org / 10 . 1214 % 2F20 - ba1222

    2021

  80. [89]

    Springer New York, 2004.doi:10.1007/978- 1- 4684- 9393- 1

    Pierre Del Moral.Feynman-Kac Formulae - Genealogical and Interacting Particle Sys- tems with Applications. Springer New York, 2004.doi:10.1007/978- 1- 4684- 9393- 1. url:https://doi.org/10.1007%2F978- 1-4684-9393-1

    2004 doi

  81. [90]

    Pierre del Moral.An introduction to Feynman-Kac particle methods in statistical learning and rare event simulation. 2014

    2014

  82. [91]

    M. J. Betancourt.The Fundamental Incom- patibility of Hamiltonian Monte Carlo and Data Subsampling. 2015. arXiv:1502.01510 [stat.ME]

    2015 arXiv

  83. [92]

    Fox, and Carlos Guestrin.Stochastic Gradient Hamiltonian Monte Carlo

    Tianqi Chen, Emily B. Fox, and Carlos Guestrin.Stochastic Gradient Hamiltonian Monte Carlo. 2014. arXiv:1402 . 4102 [stat.ME]

    2014

  84. [93]

    Speeding up MCMC by Efficient Data Subsampling

    Matias Quiroz et al. “Speeding up MCMC by Efficient Data Subsampling”. In:Jour- nal of the American Statistical Association 114 (Mar. 2018), pp. 1–35.doi:10.1080/ 01621459.2018.1448827

    2018

  85. [94]

    Hamiltonian Monte Carlo with Energy Conserving Subsam- pling

    Khue-Dung Dang et al. “Hamiltonian Monte Carlo with Energy Conserving Subsam- pling”. In:Journal of Machine Learning Re- search20.100 (2019), pp. 1–31.url:http: //jmlr.org/papers/v20/17-452.html

    2019

  86. [95]

    Stochastic gradient Hamil- tonian Monte Carlo with variance reduction for Bayesian inference

    Zhize Li et al. “Stochastic gradient Hamil- tonian Monte Carlo with variance reduction for Bayesian inference”. In:Machine Learn- ing108.8-9 (July 2019), pp. 1701–1727.doi: 10 . 1007 / s10994 - 019 - 05825 - y.url: https : / / doi . org / 10 . 1007 % 2Fs10994 - 019-05825-y

    2019

  87. [96]

    University of Cambridge, 2012.url:https: / / www

    David Tong.Lectures on Kinetic Theory. University of Cambridge, 2012.url:https: / / www . damtp . cam . ac . uk / user / tong / kintheory / three . pdf(visited on 08/15/2021)

    2012

  88. [97]

    A practical guide to pseudo-marginal methods for computa- tional inference in systems biology

    David J. Warne, Ruth E. Baker, and Matthew J. Simpson. “A practical guide to pseudo-marginal methods for computa- tional inference in systems biology”. In: Journal of Theoretical Biology496 (July 2020), p. 110255.doi:10 . 1016 / j . jtbi . 2020.110255.url:https://doi.org/10. 1...

    2020

  89. [98]

    The pseudo-marginal approach for efficient Monte Carlo computations

    Christophe Andrieu and Gareth O. Roberts. “The pseudo-marginal approach for efficient Monte Carlo computations”. In:The Annals of Statistics37.2 (Apr. 2009).doi:10.1214/ 07 - aos574.url:https : / / doi . org / 10 . 1214%2F07-aos574

    2009

  90. [99]

    M. -N. Tran et al.The Block Pseudo- Marginal Sampler. 2017. arXiv:1603.02485 [stat.ME]

    2017 arXiv

  91. [100]

    SciPy 1.0: Funda- mental Algorithms for Scientific Computing in Python

    Pauli Virtanen et al. “SciPy 1.0: Funda- mental Algorithms for Scientific Computing in Python”. In:Nature Methods17 (2020), pp. 261–272.doi:10 . 1038 / s41592 - 019 - 0686-2

    2020

  92. [101]

    Spin Echoes

    Erwin Hahn. “Spin Echoes”. In:Phys. Rev. 80 (Nov. 1950), pp. 580–594.doi:10.1063/ 1.3066708. 38

    1950

  93. [2015]

    arXiv:1405.3489 [stat.ME]

    arXiv

  94. [2020]

    arXiv:1909.12313 [stat.OT]

    1909 arXiv

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.