arxiv: 2604.03271 · v1 · submitted 2026-03-23 · 📊 stat.CO · physics.data-an

Recognition: no theorem link

GPU-Accelerated Sequential Monte Carlo for Bayesian Spectral Analysis

Tomohiro Nabika , Yui Hayashi , Masato Okada

Authors on Pith no claims yet

Pith reviewed 2026-05-15 01:16 UTC · model grok-4.3

classification 📊 stat.CO physics.data-an

keywords Bayesian spectral deconvolutionsequential Monte CarloGPU accelerationmodel selectionpeak parameter estimationXPSXRDcomputational statistics

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The pith

GPU-parallelized sequential Monte Carlo sampler delivers speedups exceeding 500x for Bayesian spectral deconvolution compared to CPU-parallelized replica exchange Monte Carlo.

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

The paper proposes running a sequential Monte Carlo sampler in parallel on a GPU to perform Bayesian model selection for the number of spectral peaks and estimation of peak-function parameters. This targets the computational expense that arises when the number of parameters, data points, and candidate models grows large in spectral analysis. Numerical experiments on artificial data emulating XPS and XRD measurements, plus real experimental spectra, show the GPU version outperforms CPU-parallelized replica exchange Monte Carlo by more than 500 times. The work positions the approach as a practical foundation for handling the increasing volume of spectral data from in-situ and microscopic techniques.

Core claim

A GPU-accelerated sequential Monte Carlo sampler performs Bayesian model selection of the number of peaks and Bayesian estimation of peak parameters, achieving speedups exceeding 500x over CPU-parallelized replica exchange Monte Carlo while remaining valid on artificial and real XPS/XRD spectra.

What carries the argument

The sequential Monte Carlo sampler (SMCS) executed in parallel across GPU threads, which carries out the model selection and parameter estimation steps.

Load-bearing premise

Parallel execution of the sequential Monte Carlo sampler across GPU threads preserves statistical correctness and convergence for the peak-function models and data sizes used.

What would settle it

A side-by-side run on identical artificial XPS/XRD data where the GPU-parallelized SMCS produces posterior distributions or selected model counts that differ from those obtained by the sequential CPU version.

Figures

Figures reproduced from arXiv: 2604.03271 by Masato Okada, Tomohiro Nabika, Yui Hayashi.

**Figure 2.** Figure 2: FIG. 2. Free-energy error [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗

**Figure 3.** Figure 3: FIG. 3. Sum of absolute endpoint errors in the 95% credible interval for the rutile 2 [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗

**Figure 4.** Figure 4: FIG. 4. Artificial data and forward model for the spectral deconvolution model at (a) [PITH_FULL_IMAGE:figures/full_fig_p012_4.png] view at source ↗

**Figure 5.** Figure 5: FIG. 5. Free-energy error [PITH_FULL_IMAGE:figures/full_fig_p013_5.png] view at source ↗

**Figure 6.** Figure 6: FIG. 6. Sum of 95% credible-interval endpoint errors for the peak center [PITH_FULL_IMAGE:figures/full_fig_p014_6.png] view at source ↗

**Figure 7.** Figure 7: FIG. 7. Measured XRD pattern of the TiO [PITH_FULL_IMAGE:figures/full_fig_p015_7.png] view at source ↗

**Figure 8.** Figure 8: FIG. 8. Free-energy error [PITH_FULL_IMAGE:figures/full_fig_p016_8.png] view at source ↗

**Figure 9.** Figure 9: FIG. 9. Sum of 95% credible-interval endpoint errors for the rutile 2 [PITH_FULL_IMAGE:figures/full_fig_p016_9.png] view at source ↗

**Figure 10.** Figure 10: displays the measured spectrum together with the REMC(CPU) best fit for the K=7 model, decomposed into individual pseudo-Voigt peak components and the Shirley background. For REMC(CPU), the total MCMC steps (including burn-in) were varied by multiplying a base unit of 200 by {1, 3, 10, 30, 100, 300, 1000}, with a burn-in ratio of 50%. For SMCS(GPU), the number of MCMC steps per temperature level was n = … view at source ↗

**Figure 11.** Figure 11: FIG. 11. Free-energy error [PITH_FULL_IMAGE:figures/full_fig_p018_11.png] view at source ↗

**Figure 12.** Figure 12: FIG. 12. Box plots of the Bayesian free energy for the XPS real data ( [PITH_FULL_IMAGE:figures/full_fig_p019_12.png] view at source ↗

**Figure 13.** Figure 13: FIG. 13. Sum of 95% credible-interval endpoint errors for the peak position [PITH_FULL_IMAGE:figures/full_fig_p020_13.png] view at source ↗

**Figure 14.** Figure 14: FIG. 14. Free-energy estimation error [PITH_FULL_IMAGE:figures/full_fig_p024_14.png] view at source ↗

**Figure 15.** Figure 15: FIG. 15. Free-energy estimation error [PITH_FULL_IMAGE:figures/full_fig_p024_15.png] view at source ↗

**Figure 16.** Figure 16: FIG. 16. Free-energy estimation error [PITH_FULL_IMAGE:figures/full_fig_p024_16.png] view at source ↗

**Figure 17.** Figure 17: FIG. 17. Free-energy estimation error [PITH_FULL_IMAGE:figures/full_fig_p025_17.png] view at source ↗

read the original abstract

Bayesian spectral deconvolution provides a data-driven framework for mathematical model selection and parameter estimation from spectral data. Although highly versatile, it becomes computationally expensive as the number of model parameters, data points, and candidate models increases, often rendering practical applications infeasible. We propose a GPU-accelerated approach in which a sequential Monte Carlo sampler (SMCS) is run in parallel on a GPU to perform Bayesian model selection of the number of spectral peaks and Bayesian estimation of peak-function parameters. Numerical experiments demonstrate that the GPU-parallelized SMCS achieves speedups exceeding 500x over CPU-parallelized replica exchange Monte Carlo (REMC). The method is validated on artificial data designed to emulate X-ray photoelectron spectroscopy (XPS) and X-ray diffraction (XRD) measurements, as well as on real experimental spectra. As measurement techniques such as microscopic spectroscopy and in-situ methods continue to drive rapid growth in the volume of spectral data, the proposed approach offers a practical computational foundation for advanced analysis of individual datasets.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

GPU-parallel SMCS delivers reported 500x speedups over CPU REMC for spectral peak counting, but the lack of a serial SMCS baseline leaves the statistical fidelity of the parallel version unconfirmed.

read the letter

The paper's central result is a GPU implementation of sequential Monte Carlo sampling that runs Bayesian model selection and parameter estimation on spectral data much faster than a CPU replica exchange Monte Carlo baseline. They target the problem of determining the number of peaks and their parameters in models suited to XPS and XRD measurements, with tests on both synthetic data designed to match those instruments and on actual experimental spectra. The engineering choice to parallelize SMCS specifically for this deconvolution task is the concrete piece that is new relative to existing SMC or REMC work in the area. The reported runtime gains are large enough to matter for high-volume spectral datasets, and including real data validation is a straightforward strength. The main limitation is that the speedup is shown against REMC rather than against a serial SMCS run on the same models. Without convergence diagnostics, effective sample size numbers, or a direct comparison to the non-parallel sampler, it is unclear whether the GPU version preserves the same posterior accuracy or merely trades some statistical properties for speed. The resampling step in particular can introduce bias or correlation when moved to independent GPU threads, and that risk is not addressed in the available description. This work is aimed at applied researchers in materials or chemical analysis who already use or want to use Bayesian methods on spectra but are limited by compute time. A reader looking for practical implementation patterns could extract useful ideas, provided the full code and diagnostics hold up. It is worth sending to peer review so referees can check the implementation details and confirm that the parallel sampler matches the serial one on the quantities that matter for model selection.

Referee Report

2 major / 2 minor

Summary. The manuscript proposes a GPU-accelerated sequential Monte Carlo sampler (SMCS) for Bayesian model selection of the number of spectral peaks and estimation of peak-function parameters in spectral deconvolution. It reports numerical experiments showing speedups exceeding 500x relative to CPU-parallelized replica exchange Monte Carlo (REMC), with validation on artificial data emulating XPS/XRD measurements and on real experimental spectra.

Significance. If the GPU-parallelized SMCS is shown to preserve the statistical correctness and convergence properties of the serial algorithm, the work would provide a practical route to applying Bayesian spectral analysis to the rapidly growing volumes of data from microscopic and in-situ spectroscopy techniques. The explicit comparison to an external CPU baseline and the focus on peak-count probabilities constitute a clear, falsifiable performance claim.

major comments (2)

[Numerical Experiments] Numerical Experiments section: the speedup claim (>500x) is established only against CPU-parallelized REMC. Because the central performance assertion depends on the GPU-SMCS producing statistically equivalent posterior inferences (peak-count probabilities and parameter estimates) to a correct serial SMCS, a direct side-by-side comparison of these quantities on the same artificial and real datasets is required to rule out bias introduced by parallel resampling or RNG handling.
[Method] Method section (implementation of SMCS): no description is given of the resampling algorithm used on the GPU (multinomial, systematic, or otherwise), the management of independent RNG streams, or any convergence diagnostics such as effective sample size trajectories or Gelman-Rubin statistics. These details are load-bearing for the claim that the parallel implementation maintains the correctness of the underlying SMCS.

minor comments (2)

[Numerical Experiments] Figures showing speedup and posterior summaries lack error bars or variability measures across repeated runs, making it difficult to assess the stability of the reported 500x factor.
[Model] The abstract and introduction refer to 'parameter-free' aspects of the model selection; the precise definition of the prior on the number of peaks and any hyper-parameters should be stated explicitly in the model section.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed review. The comments identify important gaps in validation and implementation transparency that we will address in the revision. Below we respond point by point.

read point-by-point responses

Referee: Numerical Experiments section: the speedup claim (>500x) is established only against CPU-parallelized REMC. Because the central performance assertion depends on the GPU-SMCS producing statistically equivalent posterior inferences (peak-count probabilities and parameter estimates) to a correct serial SMCS, a direct side-by-side comparison of these quantities on the same artificial and real datasets is required to rule out bias introduced by parallel resampling or RNG handling.

Authors: We agree that equivalence to the serial SMCS must be demonstrated to substantiate statistical correctness. Although the primary performance baseline in the manuscript is REMC (a standard competing method for this problem), we will add, in the revised Numerical Experiments section, direct side-by-side comparisons of peak-count posterior probabilities and parameter posterior means/variances obtained from the GPU-parallelized SMCS versus a serial SMCS run on identical artificial and real datasets. These comparisons will be quantified with total-variation distance on the peak-count distribution and relative error on parameter estimates, thereby ruling out bias from parallel resampling or RNG handling. revision: yes
Referee: Method section (implementation of SMCS): no description is given of the resampling algorithm used on the GPU (multinomial, systematic, or otherwise), the management of independent RNG streams, or any convergence diagnostics such as effective sample size trajectories or Gelman-Rubin statistics. These details are load-bearing for the claim that the parallel implementation maintains the correctness of the underlying SMCS.

Authors: We acknowledge that these implementation specifics were omitted. In the revised Method section we will add a new subsection detailing: (i) the use of systematic resampling on the GPU, (ii) independent RNG streams generated via the cuRAND library with distinct seeds per particle, and (iii) convergence diagnostics consisting of effective sample size trajectories plotted over iterations together with Gelman-Rubin statistics computed across multiple independent GPU runs. These additions will make the correctness claim fully verifiable. revision: yes

Circularity Check

0 steps flagged

No significant circularity; speedup measured against external CPU REMC baseline

full rationale

The paper implements GPU-parallel SMCS for Bayesian peak model selection and parameter estimation in spectral data. Numerical experiments report >500x speedup versus CPU-parallel REMC on XPS/XRD-emulated and real spectra. No equations reduce a claimed prediction to a fitted input by construction, no load-bearing self-citations justify uniqueness or ansatz, and no renaming of known results occurs. The derivation relies on standard SMC resampling and importance weighting, with empirical validation against an independent external baseline rather than internal redefinition. This yields a normal non-finding of circularity.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The approach rests on standard properties of sequential Monte Carlo samplers and GPU thread parallelism; no new free parameters, invented entities, or ad-hoc axioms are introduced beyond those already present in Bayesian spectral analysis and SMC literature.

axioms (1)

standard math Sequential Monte Carlo samplers converge to the target posterior under standard regularity conditions on the likelihood and prior.
Invoked implicitly when claiming valid Bayesian model selection and parameter estimation.

pith-pipeline@v0.9.0 · 5470 in / 1233 out tokens · 39763 ms · 2026-05-15T01:16:52.292138+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

49 extracted references · 49 canonical work pages

[1]

Replica exchange Monte Carlo REMC facilitates transitions between local modes of a multimodal posterior by introduc- ing a sequence of tempered distributions in which the likelihood is softened by an inverse temperatureβ[13, 14]. For a ladderβ 0 = 0< β 1 <· · ·< β L = 1, each replicaℓperforms MCMC updates targeting pβℓ(θ|D)∝p(D|θ) βℓ p(θ).(6) At regular i...

work page
[2]

Sequential Monte Carlo sampler The sequential Monte Carlo (SMC) sampler approximates a sequence of distributions {πℓ(θ)}L ℓ=0 leading to the target by maintaining a large set of weighted particles and iterating weight updates, resampling, and transition moves until the particles converge toπ L [18, 19, 21]. We construct the tempered sequence from the prio...

work page
[3]

Dau and Chopin [28] resolve this trade-off with waste-free SMC

Waste-free SMC In the standard SMCS, particle diversity degrades unless a sufficient number of MCMC transitions are performed after each resampling step, yet increasing the number of transitions raises the computational cost. Dau and Chopin [28] resolve this trade-off with waste-free SMC. Rather than resampling allTparticles and applyingnMCMC transitions ...

work page
[4]

Rather than updating alldcomponents ofθ= (θ1,

MCMC kernel Both REMC and the SMCS employ a component-wise random-walk Metropolis–Hastings algorithm [29, 30] as the MCMC kernel. Rather than updating alldcomponents ofθ= (θ1, . . . , θd) simultaneously, each componentθ i is updated individually in sequence. Because each update involves only a one-dimensional proposal, the computational cost per step is l...

work page
[5]

Experimental setup.The XRD artificial data analysis employs a reference-spectrum model for three TiO 2 polymorphs—rutile, anatase, and brookite

XRD data a. Experimental setup.The XRD artificial data analysis employs a reference-spectrum model for three TiO 2 polymorphs—rutile, anatase, and brookite. Based on the forward model described in Appendix D [Eq. (D1)], each phasekis characterized by nine parame- ters: a 2θshift, asymmetry parameterα k, Gaussian–Lorentzian mixing ratior k, Gaussian width ...

work page
[6]

Experimental setup.The spectral deconvolution model employs a multi-peak model with Gaussian basis functions

Spectral deconvolution model a. Experimental setup.The spectral deconvolution model employs a multi-peak model with Gaussian basis functions. Each observationy i is generated as a superposition ofK Gaussian peaks with additive Gaussian noise: yi = KX k=1 Ak exp − bk 2 (xi −µ k)2 +ε i, ε i ∼ N(0, σ 2).(12) Each peak has three parameters—amplitudeA k, cente...

work page
[7]

Experimental setup.The real XRD data consist of a powder diffraction pattern from a 1:1 mass-ratio mixture of TiO 2 rutile and anatase

XRD data a. Experimental setup.The real XRD data consist of a powder diffraction pattern from a 1:1 mass-ratio mixture of TiO 2 rutile and anatase. Measurements were carried out at 40 kV/50 mA using a Cu Kβ-filtered one-dimensional scan mode with a step width of 0.02◦, a scan speed of 4.00 ◦/min, a scan range of 5 ◦–60◦ (2θ/θ), and a HyPix-3000 detector i...

work page 2001
[8]

XPS data a. Experimental setup.We use the hard X-ray photoelectron spectroscopy (HAXPES) spectrum of Ni 3Al2O3 published by Longoet al.[33] as the experimental dataset (840 data points covering binding energies of approximately 845–887 eV). The model consists of pseudo-Voigt peak functions superimposed on a Shirley background (see Appendix E for the full ...

work page
[9]

III A 2) were generated by adding Gaussian noise to a superposition of Gaussian peaks

Spectral deconvolution model The artificial data for the spectral deconvolution experiments (Sec. III A 2) were generated by adding Gaussian noise to a superposition of Gaussian peaks. The forward model is f(x;θ) = KX k=1 Ak exp − bk 2 (x−µ k)2 .(C1) 23 100 101 102 Wall-clock time (s) 101 100 0 100 101 102 103 F Fref (a) N = 1000 101 102 103 Wall-clock ti...

work page
[10]

III A 1) were generated using the pseudo-Voigt forward model described in Appendix D [Eq

XRD model The XRD artificial data (Sec. III A 1) were generated using the pseudo-Voigt forward model described in Appendix D [Eq. (D1)]. Data sizes ofN= 1000, 5000, and 10 000 were used. The artificial spectra were constructed from three crystalline phases (rutile, anatase, brookite) and a pseudo-Voigt background. Tables XI and XII list the true parameter...

work page
[11]

J. J. de Pablo, N. E. Jackson, M. A. Webb, L.-Q. Chen, J. E. Moore, D. Morgan, R. Jacobs, T. Pollock, D. G. Schlom, E. S. Toberer,et al., New frontiers for the Materials Genome Initiative, npj Computational Materials5, 41 (2019). 32

work page 2019
[12]

A. S. Panwar, A. Singh, and S. Sehgal, Material characterization techniques in engineering applications: A review, Materials Today: Proceedings28, 1932 (2020)

work page 1932
[13]

Davel, N

C. Davel, N. Bassiri-Gharb, and J.-P. Correa-Baena, Machine learning in X-ray diffraction for materials discovery and characterization, Matter8(2025)

work page 2025
[14]

D. N. G. Krishna and J. Philip, Review on surface-characterization applications of X-ray pho- toelectron spectroscopy (XPS): Recent developments and challenges, Applied Surface Science Advances12, 100332 (2022)

work page 2022
[15]

Wojdyr, Fityk – a general-purpose peak fitting program (2010), software

M. Wojdyr, Fityk – a general-purpose peak fitting program (2010), software. Accessed: 2026- 01-26

work page 2010
[16]

B. H. Toby and R. B. Von Dreele, GSAS-II: The genesis of a modern open-source all purpose crystallography software package, Journal of Applied Crystallography46, 544 (2013)

work page 2013
[17]

Brehm, C

S. Brehm, C. Himcinschi, J. Kraus, and J. Kortus, PyRamanGUI: Open-source graphical user interface for analyzing Raman spectra, SoftwareX23, 101486 (2023)

work page 2023
[18]

Nagata, S

K. Nagata, S. Sugita, and M. Okada, Bayesian spectral deconvolution with the exchange monte carlo method, Neural Networks28, 82 (2012)

work page 2012
[19]

Nagata, R

K. Nagata, R. Muraoka, Y.-i. Mototake, T. Sasaki, and M. Okada, Bayesian spectral de- convolution based on Poisson distribution: Bayesian measurement and virtual measurement analytics (VMA), Journal of the Physical Society of Japan88, 044003 (2019)

work page 2019
[20]

Tokuda, K

S. Tokuda, K. Nagata, and M. Okada, Simultaneous estimation of noise variance and number of peaks in Bayesian spectral deconvolution, Journal of the Physical Society of Japan86, 024001 (2017)

work page 2017
[21]

Murakami, Y

R. Murakami, Y. Matsushita, K. Nagata, H. Shouno, and H. Yoshikawa, Bayesian estimation to identify crystalline phase structures for X-ray diffraction pattern analysis, Science and Technology of Advanced Materials: Methods4, 2300698 (2024)

work page 2024
[22]

Machida, K

A. Machida, K. Nagata, R. Murakami, H. Shinotsuka, H. Shouno, H. Yoshikawa, and M. Okada, Bayesian estimation for xps spectral analysis at multiple core levels, Science and Technology of Advanced Materials: Methods1, 123 (2021)

work page 2021
[23]

Hukushima and K

K. Hukushima and K. Nemoto, Exchange Monte Carlo method and application to spin glass simulations, Journal of the Physical Society of Japan65, 1604 (1996)

work page 1996
[24]

D. J. Earl and M. W. Deem, Parallel tempering: Theory, applications, and new perspectives, Physical Chemistry Chemical Physics7, 3910 (2005). 33

work page 2005
[25]

Matsumura, N

T. Matsumura, N. Nagamura, S. Akaho, K. Nagata, and Y. Ando, Maximum a posteriori estimation for high-throughput peak fitting in x-ray photoelectron spectroscopy, Science and Technology of Advanced Materials: Methods4, 2373046 (2024)

work page 2024
[26]

Kawashima, H

T. Kawashima, H. Shono,et al., Spectral deconvolution based on Bayesian variable selection, IPSJ Trans. Math. Model. Appl. (TOM)12, 34 (2019)

work page 2019
[27]

Okajima, K

K. Okajima, K. Nagata, and M. Okada, Fast bayesian deconvolution using simple reversible jump moves, Journal of the Physical Society of Japan90, 034001 (2021)

work page 2021
[28]

Doucet, N

A. Doucet, N. de Freitas, and N. Gordon, An introduction to sequential Monte Carlo methods, inSequential Monte Carlo Methods in Practice(Springer, New York, 2001) pp. 3–14

work page 2001
[29]

Del Moral, A

P. Del Moral, A. Doucet, and A. Jasra, Sequential Monte Carlo samplers, Journal of the Royal Statistical Society: Series B68, 411 (2006)

work page 2006
[30]

W. Betz, I. Papaioannou, and D. Straub, Transitional markov chain monte carlo: observations and improvements, Journal of Engineering Mechanics142, 04016016 (2016)

work page 2016
[31]

Chopin and O

N. Chopin and O. Papaspiliopoulos,An Introduction to Sequential Monte Carlo(Springer, 2020)

work page 2020
[32]

Hendeby, R

G. Hendeby, R. Karlsson, and F. Gustafsson, Particle filtering: The need for speed, EURASIP Journal on Advances in Signal Processing2010, 181403 (2010)

work page 2010
[33]

A. Lee, C. Yau, M. B. Giles, A. Doucet, and C. C. Holmes, On the utility of graphics cards to perform massively parallel simulation of advanced monte carlo methods, Journal of com- putational and graphical statistics19, 769 (2010)

work page 2010
[34]

Yallup, Particle monte carlo methods for lattice field theory (2025), arXiv:2511.15196 [stat.ML]

D. Yallup, Particle monte carlo methods for lattice field theory (2025), arXiv:2511.15196 [stat.ML]

work page arXiv 2025
[35]

White and J

T. White and J. Regier, Sequential monte carlo for detecting and deblending objects in astro- nomical images, inNeurIPS 2023 Workshop on Machine Learning and the Physical Sciences (2023)

work page 2023
[36]

Speich, C

M. Speich, C. F. Dormann, and F. Hartig, Sequential Monte Carlo algorithms for Bayesian model calibration—a review and method comparison, Ecological Modelling455, 109608 (2021)

work page 2021
[37]

Lubbe, W.-J

R. Lubbe, W.-J. Xu, Q. Zhou, and H. Cheng, Bayesian calibration of gpu–based dem meso- mechanics part ii: Calibration of the granular meso-structure, Powder Technology407, 117666 (2022). 34

work page 2022
[38]

Dau and N

H.-D. Dau and N. Chopin, Waste-free sequential Monte Carlo, Journal of the Royal Statistical Society: Series B (Statistical Methodology)84, 114 (2022)

work page 2022
[39]

Metropolis, A

N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. Teller, Equation of state calculations by fast computing machines, The Journal of Chemical Physics21, 1087 (1953)

work page 1953
[40]

W. K. Hastings, Monte carlo sampling methods using markov chains and their applications, Biometrika57, 97 (1970)

work page 1970
[41]

Nabika, K

T. Nabika, K. Nagata, S. Katakami, M. Mizumaki, and M. Okada, Sequential exchange monte carlo: Sampling method for multimodal distribution without parameter tuning, arXiv preprint arXiv:2502.17858 (2025)

work page arXiv 2025
[42]

Y. F. Atchad´ e and J. S. Rosenthal, On adaptive Markov chain Monte Carlo algorithms, Bernoulli11, 815 (2005)

work page 2005
[43]

Longo, M

F. Longo, M. Nikolic, and A. Borgschulte, Deep core level hard X-ray photoelectron spec- troscopy for catalyst characterization (2023), dataset (includes Ni3@Al2O3 HAXPES.csv)

work page 2023
[44]

D. A. Shirley, High-resolution X-ray photoemission spectrum of the valence bands of gold, Physical Review B5, 4709 (1972)

work page 1972
[45]

Herrera-Gomez, M

A. Herrera-Gomez, M. Bravo-Sanchez, O. Ceballos-Sanchez, and M. O. Vazquez-Lepe, Prac- tical methods for background subtraction in photoemission spectra, Surface and Interface Analysis46, 897 (2014)

work page 2014
[46]

Nagai, M

K. Nagai, M. Anada, Y. Nakanishi-Ohno, M. Okada, and Y. Wakabayashi, Robust sur- face structure analysis with reliable uncertainty estimation using the exchange Monte Carlo method, Journal of Applied Crystallography53, 387 (2020)

work page 2020
[47]

Thermo Fisher Scientific, Nickel – XPS periodic table,https://www.thermofisher.com/ sg/en/home/materials-science/learning-center/periodic-table/transition-metal/ nickel.html(2024), accessed: 2026-02-25

work page 2024
[48]

A. P. Grosvenor, M. C. Biesinger, R. S. Smart, and N. S. McIntyre, New interpretations of XPS spectra of nickel metal and oxides, Surface Science600, 1771 (2006)

work page 2006
[49]

H. W. Nesbitt, D. Legrand, and G. M. Bancroft, Interpretation of Ni2p XPS spectra of Ni conductors and Ni insulators, Physics and Chemistry of Minerals27, 357 (2000). 35

work page 2000