  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.
