mcFMM: Finite mixture age model optimization (using a Markov chain... In numOSL: Numeric Routines for Optically Stimulated Luminescence Dating

Description

Sampling from the joint-likelihood functions of finite mixture age models (include the central age model) using a Markov chain Monte Carlo (MCMC) method.

Usage

 ```1 2``` ```mcFMM(EDdata, ncomp = 1, addsigma = 0, iflog = TRUE, nsim = 50000, inis = list(), control.args = list()) ```

Arguments

 `EDdata` matrix(required): a two-column matrix (i.e., equivalent dose values and associated standard errors) `ncomp` integer(with default): number of components (`1` denotes the central age model) `addsigma` numeric(with default): additional uncertainty `iflog` logical(with default): transform equivalent dose values to log-scale or not `nsim` integer(with default): deseried number of iterations `inis` list(with default): initial state of parameters. Example: `inis=list(p1=1,p2=1,mu1=5,mu2=10)` in FMM2 (the sum of `p1` and `p2` will be normalized to 1 during the simulation) `control.args` list(with default): arguments used in the Slice Sampling algorithm, see details

Details

Function mcFMM is used for sampling from the joint-likelihood functions of finite mixture age models (include the central age model) using a Markov chain Monte Carlo sampling algorithm called Slice Sampling (Neal, 2003). Three arguments (`control.args`) are used for controling the sampling process:
(1) w: size of the steps for creating an interval from which to sample, default `w=1`;
(2) m: limit on steps for expanding an interval, `m<=1` means no limit on the expandation, `m>1` means the interval is expanded with a finite number of iterations, default `m=-100`;
(3) nstart: maximum number of trials for updating a variable in an iteration. It can be used for monitoring the stability of the simulation. For example, a MAM4 is likely to crash down for data sets with small numbers of data points or less dispersed distributions (see section 8.3 of Galbraith and Roberts, 2012 for a discussion), and sometimes more than one trial (i.e., using `nstart>1`) is required to complete the sampling process, default `nstart=1`.

Value

Return an invisible list of S3 class object `"mcAgeModels"` including the following elements:

 `EDdata` equivalent dose values `addsigma` additional uncertainty `model` fitting model `iflog` transform equivalent dose values to log-scale or not `nsim` number of iterations `chains` simulated samples

References

Galbraith RF, Green P, 1990. Estimating the component ages in a finite mixture. International Journal of Radiation Applications and Instrumentation. Part D. Nuclear Tracks and Radiation Measurements, 17: 197-206.

Neal RM, 2003. "Slice sampling" (with discussion). Annals of Statistics, 31(3): 705-767. Software is freely available at http://www.cs.utoronto.ca/~radford/slice.software.html.

 ```1 2 3 4 5``` ``` # Not run. # data(EDdata) # Construct a MCMC chain for FMM3. # obj<-mcFMM(EDdata\$gl11,ncomp=3,nsim=5000) # reportSAM(obj,thin=2,burn=1e3) ```