Bayesian Modelling of Raman Spectroscopy
Compute the log-likelihood.
Initialise the vector of Metropolis-Hastings proposals.
Compute the effective sample size (ESS) of the particles.
Fit the model using Markov chain Monte Carlo.
Fit the model using Sequential Monte Carlo (SMC).
Fit the model with Voigt peaks using iterated batch importance samplin...
Fit the model with Voigt peaks using Sequential Monte Carlo (SMC).
Compute cubic B-spline basis functions for the given wavenumbers.
Compute the pseudo-Voigt mixing ratio for each peak.
Update all of the parameters using a single Metropolis-Hastings step.
Update the parameters of the Voigt peaks using marginal Metropolis-Has...
Compute the spectral signature using Voigt peaks.
Resample in place to avoid expensive copying of data structures, using...
Compute an ancestry vector for residual resampling of the SMC particle...
Update the importance weights of each particle.
Bayesian modelling and quantification of Raman spectroscopy
Sum log-likelihoods of i.i.d. exponential.
Sum log-likelihoods of i.i.d. lognormal.
Sum log-likelihoods of Gaussian.
Compute the spectral signature using Gaussian peaks.
Compute the spectral signature using Lorentzian peaks.
Compute the weighted arithmetic means of the particles.
Compute the weighted variance of the particles.
Sequential Monte Carlo (SMC) algorithms for fitting a generalised additive mixed model (GAMM) to surface-enhanced resonance Raman spectroscopy (SERRS), using the method of Moores et al. (2016) <arXiv:1604.07299>. Multivariate observations of SERRS are highly collinear and lend themselves to a reduced-rank representation. The GAMM separates the SERRS signal into three components: a sequence of Lorentzian, Gaussian, or pseudo-Voigt peaks; a smoothly-varying baseline; and additive white noise. The parameters of each component of the model are estimated iteratively using SMC. The posterior distributions of the parameters given the observed spectra are represented as a population of weighted particles.
Useful links