  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$_2$.
