Kenji Nagata

Kensuke Muto, Hirotaka Sakamoto, Kenji Nagata et al.

Currently, an excessive amount of event data is being obtained in four-dimensional inelastic neutron-scattering experiments. A method for automatic bin-width optimization of multidimensional histograms has been developed and recently validated on real inelastic neutron-scattering data. However, measuring beyond the equipment resolution leads to inefficient use of valuable beam time. To improve experimental efficiency, an automatic termination strategy is essential. We propose a Bayesian-optimization-based method to compute stopping criteria and determine whether to continue or terminate the experiment in real time. In the proposed method, the bin-width optimization is performed using Bayesian optimization to efficiently compute the optimal bin widths. The experiment is terminated when the optimal bin widths become smaller than the target resolutions. In numerical experiments using real inelastic neutron-scattering data, the optimal bin widths decrease as the number of events increases. Even the optimal bin widths for data downsampled to 1/5 are comparable with the resolutions limited by the sample size, choppers, and so on. This implies excessive measurement of the inelastic neutron experiments for the moment. Moreover, we found that Bayesian optimization can reduce the search cost to approximately 10% of an exhaustive search in our numerical experiments.

Tomohiro Nabika, Kenji Nagata, Shun Katakami et al.

In this study, we demonstrate a sequential experimental design for spectral measurements by active learning using parametric models as predictors. In spectral measurements, it is necessary to reduce the measurement time because of sample fragility and high energy costs. To improve the efficiency of experiments, sequential experimental designs are proposed, in which the subsequent measurement is designed by active learning using the data obtained before the measurement. Conventionally, parametric models are employed in data analysis; when employed for active learning, they are expected to afford a sequential experimental design that improves the accuracy of data analysis. However, due to the complexity of the formulas, a sequential experimental design using general parametric models has not been realized. Therefore, we applied Bayesian inference-based data analysis using the exchange Monte Carlo method to realize a sequential experimental design with general parametric models. In this study, we evaluated the effectiveness of the proposed method by applying it to Bayesian spectral deconvolution and Bayesian Hamiltonian selection in X-ray photoelectron spectroscopy. Using numerical experiments with artificial data, we demonstrated that the proposed method improves the accuracy of model selection and parameter estimation while reducing the measurement time compared with the results achieved without active learning or with active learning using the Gaussian process regression.

Kenji Nagata, Yoh-ichi Mototake, Rei Muraoka et al.

In this paper, we propose a new method of Bayesian measurement for spectral deconvolution, which regresses spectral data into the sum of unimodal basis function such as Gaussian or Lorentzian functions. Bayesian measurement is a framework for considering not only the target physical model but also the measurement model as a probabilistic model, and enables us to estimate the parameter of a physical model with its confidence interval through a Bayesian posterior distribution given a measurement data set. The measurement with Poisson noise is one of the most effective system to apply our proposed method. Since the measurement time is strongly related to the signal-to-noise ratio for the Poisson noise model, Bayesian measurement with Poisson noise model enables us to clarify the relationship between the measurement time and the limit of estimation. In this study, we establish the probabilistic model with Poisson noise for spectral deconvolution. Bayesian measurement enables us to perform virtual and computer simulation for a certain measurement through the established probabilistic model. This property is called "Virtual Measurement Analytics(VMA)" in this paper. We also show that the relationship between the measurement time and the limit of estimation can be extracted by using the proposed method in a simulation of synthetic data and real data for XPS measurement of MoS$_2$.

Satoru Tokuda, Kenji Nagata, Masato Okada

The heuristic identification of peaks from noisy complex spectra often leads to misunderstanding of the physical and chemical properties of matter. In this paper, we propose a framework based on Bayesian inference, which enables us to separate multipeak spectra into single peaks statistically and consists of two steps. The first step is estimating both the noise variance and the number of peaks as hyperparameters based on Bayes free energy, which generally is not analytically tractable. The second step is fitting the parameters of each peak function to the given spectrum by calculating the posterior density, which has a problem of local minima and saddles since multipeak models are nonlinear and hierarchical. Our framework enables the escape from local minima or saddles by using the exchange Monte Carlo method and calculates Bayes free energy via the multiple histogram method. We discuss a simulation demonstrating how efficient our framework is and show that estimating both the noise variance and the number of peaks prevents overfitting, overpenalizing, and misunderstanding the precision of parameter estimation.