Update the parameters of the Voigt peaks using marginal Metropolis-Hastings.

Updates all of the parameters (location, amplitude, std. dev., and scale) using a single Metropolis- Hastings step, such that the baseline cancels out in the MH ratio, using the marginalisation identity of Chib (1995). Note: if npart > 1, then multiple MCMC chains will be executed independently in parallel using OpenMP. This means that all functions used for the proposal distributions and to evaluate the MH ratio need to be thread-safe. Specifically, no calls to R::rnorm, R::dnorm, nor their Rcpp equivalents, can be made from within the parallel portion of the code.

Usage

mhUpdateVoigt(
  spectra,
  n,
  kappa,
  conc,
  wavenum,
  thetaMx,
  logThetaMx,
  mhChol,
  priors
)

Arguments

spectra

n_y * nwl Matrix of observed Raman spectra.

n

number of observations to use in calculating the likelihood.

kappa

likelihood tempering parameter.

conc

Vector of n_y nanomolar (nM) dye concentrations

wavenum

Vector of nwl wavenumbers at which the spetra are observed.

thetaMx

(4+npeaks*4) x npart Matrix of parameter values for each peak.

logThetaMx

(4+npeaks*4) x npart Matrix of logarithms of the parameters.

mhChol

lower-triangular Cholesky factorisation of the covariance matrix for the random walk proposals.

priors

List of hyperparameters for the prior distributions.

Value

The number of RWMH proposals that were accepted.

References

Chib (1995) "Marginal Likelihood from the Gibbs Output," JASA 90(432): 1313–1321, doi:10.1080/01621459.1995.10476635

Rosenthal (2000) "Parallel computing and Monte Carlo algorithms" Far East J. Theor. Stat. 4(2): 207–236, URL: https://www.pphmj.com/abstract/1961.htm