Sequential Gibbs sampling / Conditional Re-sampling

All the available types of prior models allow perturbing one realization of a prior into a new realization of the prior, where the degree of perturbation can be controlled (from a new independent realization to a very small change).

This means that a random walk, with an arbitrary 'step-length' can be performed for any of the a priori types available in SIPPI.

For the a priori types 'FFTMA', 'VISIM', 'CHOLESKY', 'SISIM', 'SNESIM', sequential Gibbs sampling HCM12 is applied. Sequential Gibbs is in essence a type of conditional re-simulation. From a current realization of a prior model, a number of model parameters are discarded and treated as unknown. The unknown model parameters are then re-simulated conditional to the known model parameters.

In order to generate a new realization 'm2' in the vicinity of the realization 'm1' use

[m1,prior]=sippi_prior(prior);
[m2,prior]=sippi_prior(prior,m1);

If this process is iterated, then a random walk in the space of a priori acceptable models will be perform. Moreover, the collection of realization obtained in this way will represent a sample from prior distribution.

Note that in order to use sequential Gibbs sampling prior must be given both as an input variable, and as an (possibly update) output variable.

Controlling sequential Gibbs sampling / Conditional Re-sampling

All properties related to sequential Gibbs sampling can be set in the 'seq_gibbs' structure (which will be avaiable the first time sippi_prior is called, or if sippi_prior_init is called), for the individual prior models.

The step-length (i.e. the degree of perturbation) is determined by the prior{m}.seq_gibbs.step` parameter.

For the 'uniform' and 'gaussian' type a priori models a step-length closer to 0 zeros imples a 'shorter' step, while a step-length close to 1, implies a 'longer' step-length. A step length of 1, will generate a new independent realization of the prior, while a step length of 0, will return the same realization of the prior

prior{m}.seq_gibbs.step=.1;
[m2,prior]=sippi_prior(prior,m1);

For the 'FFTMA', 'VISIM', 'CHOLESKY', 'SISIM', and 'SNESIM' type a priori models two types (defined in the prior{m}.seq_gibbs.type variable).

The default 'type' is 2, defined as

prior{m}.seq_gibbs.step=1;
prior{m}.seq_gibbs.type=2;

where the step length defines the percentage of the of model parameters (selected at random) defined in prior{im} is conditionally re-sampled. Thus, a step-length closer to 0 zeros imples a 'shorter' step, while a step-length close to 1, implies a 'longer' step-length.

If prior{m}.seq_gibbs.step=1, then prior{m}.seq_gibbs.step defines the size of a square rectangle/cube which is to be conditionally re-simulated using sequential Gibbs sampling.