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We propose an approach utilizing gamma-distributed random variables, coupledwith log-Gaussian modeling, to generate synthetic datasets suitable fortraining neural networks. This addresses the challenge of limited realobservations in various applications. We apply this methodology to both Ramanand coherent anti-Stokes Raman scattering (CARS) spectra, using experimentalspectra to estimate gamma process parameters. Parameter estimation is performedusing Markov chain Monte Carlo methods, yielding a full Bayesian posteriordistribution for the model which can be sampled for synthetic data generation.Additionally, we model the additive and multiplicative background functions forRaman and CARS with Gaussian processes. We train two Bayesian neural networksto estimate parameters of the gamma process which can then be used to estimatethe underlying Raman spectrum and simultaneously provide uncertainty throughthe estimation of parameters of a probability distribution. We apply thetrained Bayesian neural networks to experimental Raman spectra ofphthalocyanine blue, aniline black, naphthol red, and red 264 pigments and alsoto experimental CARS spectra of adenosine phosphate, fructose, glucose, andsucrose. The results agree with deterministic point estimates for theunderlying Raman and CARS spectral signatures.

Log-Gaussian Gamma Processes for Training Bayesian Neural Networks in Raman and CARS Spectroscopies