Posterior Sampling State Initialization¶
Class providing state initialization for Bayesian posterior sampling simulations—the strategy for choosing the starting point of each Markov chain before the main sampling loop begins. Implementations draw initial parameter vectors from the prior (random prior sampling), from a multivariate Gaussian centered on a maximum-likelihood estimate, or from a user-supplied restart file. Proper initialization helps the chains reach the high-probability region quickly and avoids premature convergence or long burn-in periods.
Default implementation: posteriorSampleStateInitializePriorRandom
Methods¶
initialize→voidSet the initial parameter vector of the simulation state before the main sampling loop begins, also returning the initial log-likelihood, log-posterior, and elapsed evaluation time for the starting point.
class (posteriorSampleStateClass ), intent(inout) :: simulationStatetype (modelParameterList ), intent(inout), dimension(:) :: modelParameters_class (posteriorSampleLikelihoodClass), intent(inout) :: modelLikelihooddouble precision , intent( out) :: timeEvaluatePrevious, logLikelihood, logPosterior
posteriorSampleStateInitializeGaussianSphere¶
A posterior sampling state initialization class which initializes states using random draws from a Gaussian sphere centered on the mode of the prior distribution.
Parameters
[radiusSphere]— The radius of the Gaussian sphere from which each chain’s initial parameter vector is drawn; ifradiusIsRelativeis true this is expressed as a fraction of the prior extent, otherwise it is an absolute radius in parameter space.[radiusIsRelative]— If true, the radius of the sphere is assumed to be relative to the extent of the prior, otherwise it is assumed to be an absolute radius.[position](defaultvar_str('priorMedian')) — The initial position for the sphere. If this is set topriorMedian, then the sphere is placed at the median of the prior in each dimension. Otherwise, this must be a list of starting parameter values.
posteriorSampleStateInitializeLatinHypercube¶
This class uses a Latin hypercube design (in the cumulative prior probability distribution of each parameter) to assign initial state vectors. In particular, a maximin design is used in which a number of trial Latin hypercube are constructed and the hypercube with the greatest minimum distance between any pair of state vectors is selected. The [maximinTrialCount] parameter is used to specify the number of trial hypercubes to construct.
Parameters
[maximinTrialCount](default1000) — The number of trial Latin Hypercubes to construct when seeking the maximum minimum separation sample.
posteriorSampleStateInitializeMaximumLikelihood¶
This class initializes state to the maximum likelihood state from a previous simulation—the state will be the same for all chains. The [logFileRoot] parameter is used to specify the log-file root name used in the previous simulation.
Parameters
[logFileRoot]— The root file name of the state files from which to maximum likelihood state.
posteriorSampleStateInitializeParameterFile¶
This class initializes all chains to values read from a parameter file.
Parameters
[fileName]— The name of the parameter file from which to read initial state.
posteriorSampleStateInitializePosteriorMaximumGaussianSphere¶
Initializes chains to the the maximum posterior point from a set of chain files, with a Gaussian sphere scatter around that point.
Parameters
[logFileRoot]— The root file name of the state files from which to resume.[radiusSphere]— The radius of the Gaussian sphere.[radiusIsRelative]— If true, the radius of the sphere is assumed to be relative to the extent of the prior, otherwise it is assumed to be an absolute radius.
posteriorSampleStateInitializePriorRandom¶
A posterior sampling state initialization class which samples the initial state at random from the prior distribution(s).
(Default implementation)
posteriorSampleStateInitializeResume¶
This class resumes from a previous simulation by setting the chain states to the states at the end of that simulation. The [logFileRoot] parameter is used to specify the log-file root name used in the previous simulation.
Parameters
[logFileRoot]— The root file name (without chain-index suffix) of the binary state files written by a previous run, from which chain positions and optionally full simulation state are restored to resume sampling.[restoreState]— If true, restore the full internal simulation state (step counter, acceptance counts, covariance estimates) from the state files in addition to restoring the chain parameter vectors.
posteriorSampleStateInitializeSwitched¶
A posterior sampling state initialization class which sets initial state by switching between two other options.
Methods
fractionADAF— Return the fraction of the accretion flow to be represented as an ADAF.efficiencyRadiativeScalingADAF— Return the scaling of radiative efficiency of the ADAF component in a switched accretion disk.
Parameters
[modelParameterName1]— Names of parameters to be initialized by initializer number 1.[modelParameterName2]— Names of parameters to be initialized by initializer number 2.[accretionRateThinDiskMinimum](default'0.01d0') — The accretion rate (in Eddington units) below which a switched accretion disk becomes an ADAF.[accretionRateThinDiskMaximum](default'0.3d0') — The accretion rate (in Eddington units) above which a switched accretion disk becomes an ADAF.[accretionRateTransitionWidth](default0.1d0) — The width (in \(\ln[\dot{M}/\dot{M}_\mathrm{Eddington}]\)) over which transitions between accretion disk states occur.[scaleADAFRadiativeEfficiency](default.true.) — Specifies whether the radiative efficiency of the ADAF component in a switched accretion disk scales with accretion rate.