Update all of the parameters using a single Metropolis-Hastings step.

Updates all of the parameters using a single Metropolis-Hastings step, such that the baseline cancels out in the MH ratio, using the marginalisation identity of Chib (1995). 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

marginalMetropolisUpdate(
  spectra,
  n,
  conc,
  wavelengths,
  peakWL,
  betaMx,
  scaleMx,
  sigma,
  expMx,
  baselines,
  sd_mh,
  priors
)

Arguments

spectra

n_y * nwl Matrix of observed Raman spectra.

n

number of observations to use in calculating the likelihood

conc

Vector of n nanomolar (nM) dye concentrations

wavelengths

Vector of nwl wavenumbers at which the spetra are observed.

peakWL

Vector of locations for each peak (cm^-1)

betaMx

npeaks * npart Matrix of regression coefficients to update.

scaleMx

npeaks * npart Matrix of scale parameters to update.

sigma

Vector of npart standard deviations to update.

expMx

nwl * npart Matrix of expectations of the Lorentzian or Gaussian function.

baselines

nKnots * n_y * npart Array of smoothing splines.

sd_mh

Vector of 2 * npeaks bandwidths 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