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.

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: http://www.pphmj.com/abstract/1961.htm