mcmc.optmisation

Wrapper function for mcmc.metropolis_hastings and mcmc.goodman_weare.

Usage

obj = mcmc;
out = obj.optimisation( data, mask, weights, parameters, fitting, FWDfunc, varargin);

I/O overview

Input	Description
data	(Unmasked) N-D (imaging) data , first 3 diemnsions reserved for spatial info (x,y,z)
mask	[1 or 3]D signal mask
weights	N-D wieghts, same dimension as ‘data’ (optional)
parameters	structure variable containing starting points of all model parameters to be estimated
fitting	structure contains fitting algorithm parameters
fitting.model_params	1xM cell variable, name of the model parameters, e.g. {‘S0’,’R2star’,’noise’};
fitting.lb	1xM numeric variable, fitting lower bound, same order as field ‘model_params’, e.g. [0.5, 0, 0.001];
fitting.ub	1xM numeric variable, fitting upper bound, same order as field ‘model_params’, e.g. [2, 1, 0.1];
fitting.algorithm	MCMC algorithm, ‘MH’ (Metropolis-Hastings)\|’GW’ (Affline-invariant ensemble)
fitting.iteration	# MCMC iterations
fitting.repetition	# repetition of MCMC proposal
fitting.thinning	sampling interval between iterations
fitting.burnin	iterations to be discarded at the beginning, if >1, the exact number will be used; else iteration*burnin
fitting.xStepSize	step size of model parameter in MCMC proposal, same size and order as ‘model_params’ (‘MH’ only)
fitting.StepSize	step size for ‘GW’ in MCMC proposal (‘GW’ only)
fitting.Nwalker	# random walkers (‘GW’ only)
fitting.metric	cell variable, metric(s) derived from posterior distribution, ‘mean’\|’std’\|’median’\|’iqr’ (can be multiple)
FWDfunc	function handle for forward signal generation; size of the output must match size of ‘data’
varargin	additional input for FWDfunc other than ‘parameter’ and ‘mask’ (same order as FWDfunc)

Output	Description
out	structure contains optimisation result
out.posterior	structure contains MCMC posterior samples
out.posterior.(model_params{k})	Model parameter MCMC posterior samples, masked and unshaped for memory preservation
out.{metric}.(model_params{k})	Posterior statistics chosen in fitting.metric

Note

‘noise’ is always required in fitting.model_params.