Posterior Sampling Differential Evolution Proposal Size¶
Class providing proposal sizes for differential evolution posterior samplers. Specifically, this class provides the proposal size parameter, \(\gamma\) (the fraction of the vector connecting to chain state to be used as the proposal for another chain), for use in differential evolution simulations.
Methods¶
gamma→double precisionReturn the proposal size parameter \(\gamma\) given the current simulation state and convergence status, scaling the vector difference between two randomly selected chain states to form the differential evolution proposal.
class(posteriorSampleStateClass ), intent(inout) :: simulationStateclass(posteriorSampleConvergenceClass), intent(inout) :: simulationConvergence
posteriorSampleDffrntlEvltnProposalSizeAdaptive¶
This class adaptively changes \(\gamma\) in an attempt to maintain the acceptance rate at an acceptable level. The algorithm is controlled by the following sub-parameters:
[gammaInitial]The initial value for \(\gamma\).
[gammaFactor]The multiplicative factor by which \(\gamma\) should be increased or decreased if the acceptance rate is out of range.
[gammaMinimum]The smallest value allowed for \(\gamma\).
[gammaMaximum]The largest value allowed for \(\gamma\).
[acceptanceRateMinimum]The minimum acceptance rate to accept before reducing \(\gamma\).
[acceptanceRateMaximum]The maximum acceptance rate to accept before reducing \(\gamma\).
[updateCount]The number of steps between successive checks of the acceptance rate.
Parameters
[timeStepMinimum](default0.01d0) — The minimum time step to use in tabulations of star formation histories [Gyr].[countTimeStepsMaximum](default10_c_size_t) — The maximum number of timesteps to track in any star formation history.[massScaleAbsolute](default1.0d0) — The absolute tolerance scale (for the mass in each bin of star formation history) to use during ODE solution.[metallicityBoundaries]— The metallicities corresponding to boundaries between metallicity bins to use when tabulating star formation histories.[countMetallicities](default10_c_size_t) — The number of bins in metallicity to use when tabulating star formation histories.[metallicityMinimum](default1.0d-4) — The upper limit to the metallicity in the lowest metallicity bin when tabulating star formation histories [Solar units].[metallicityMaximum](default1.0d+1) — The upper limit to the metallicity in the highest metallicity bin when tabulating star formation histories [Solar units].[logFileName]— The name of a file to which to log reports of adjustments to \(\gamma\). If empty, no reports are logged.[gammaInitial]— The initial value of the proposal scaling parameter \(\gamma\) used before the acceptance rate has been assessed and any adaptive adjustment has been made.[gammaMinimum]— The minimum value to which the proposal scaling parameter \(\gamma\) is permitted to be reduced during adaptive adjustment, preventing the step size from becoming vanishingly small.[gammaMaximum]— The maximum value to which the proposal scaling parameter \(\gamma\) is permitted to be increased during adaptive adjustment, preventing excessively large steps that would degrade acceptance rates.[gammaAdjustFactor]— The multiplicative factor by which \(\gamma\) is increased or decreased at each adaptation step when the current acceptance rate falls outside the target range.[acceptanceRateMinimum]— The minimum acceptable chain acceptance rate; if the measured acceptance rate falls below this threshold \(\gamma\) is reduced to produce smaller, more easily accepted proposals.[acceptanceRateMaximum]— The maximum acceptable chain acceptance rate; if the measured acceptance rate exceeds this threshold \(\gamma\) is increased to produce larger proposals that explore the posterior more efficiently.[updateCount]— The number of steps between potential updates of the proposal size.[outliersInAcceptanceRate](default.true.) — The number of steps between potential updates of the proposal size.[appendLog](default.false.) — If true, append to the existing log file, otherwise overwrite.[restoreFromLog](default.false.) — If true, restore the value of \(\gamma\) from the log file.[flushLog](default.false.) — If true, logs are flushed to file after every update.[exponentInitial]— The initial value of the temperature-scaling exponent \(\alpha\) used before any adaptive adjustment based on the acceptance-rate gradient has been applied.[exponentMinimum]— The minimum value to which the temperature-scaling exponent \(\alpha\) may be reduced during adaptive adjustment, preventing the temperature dependence from becoming negligibly weak.[exponentMaximum]— The maximum value to which the temperature-scaling exponent \(\alpha\) may be increased during adaptive adjustment, preventing the proposal size from growing too steeply with temperature.[exponentAdjustFactor]— The additive increment by which the temperature-scaling exponent \(\alpha\) is increased or decreased at each adaptation step when the acceptance-rate gradient falls outside the target range.[gradientMinimum]— The minimum acceptable gradient of acceptance rate with log-temperature.[gradientMaximum]— The maximum acceptable gradient of acceptance rate with log-temperature.[updateCount]— The number of steps between potential updates of the temperature exponent.
posteriorSampleDffrntlEvltnProposalSizeFixed¶
A posterior sampling differential evolution proposal size class in which the proposal size is a fixed value \(\gamma=\)[gamma].
Parameters
[mass](default100.0d0) — The fixed mass (in \(\mathrm{M}_\odot\)) assigned to all newly-formed seed black holes in this implementation, representing the initial black hole mass when a halo first forms a central black hole.[spin](default0.0d0) — The dimensionless spin parameter (between \(-1\) and \(+1\)) assigned to all newly-formed seed black holes, where \(0\) corresponds to a non-rotating Schwarzschild black hole and \(\pm 1\) to a maximally rotating Kerr black hole.[fraction](default0.01d0) — The fixed fraction \(f_\mathrm{outflow}\) of the stellar energy input rate (normalized to a canonical \(1\,\mathrm{M}_\odot\) population) that drives gas outflows, setting the mass loading factor for stellar feedback in the galaxy.[escapeFraction](default0.006d0) — Escape fraction of ionizing photons from young HII regions.[ageLimit](default0.03d0) — The age beyond which all ionizing photons are assumed to escape from HII regions.[timescale](default1.0d0) — The timescale for star formation in the fixed timescale model.[rateStarFormation](default1.0d9) — The rate of star formation in units of \(\mathrm{M}_\odot \hbox{Gyr}^{-1}\).[proposalSize]— The fixed value of the proposal scaling parameter \(\gamma\) used to scale the vector difference between two randomly selected chain states when forming differential evolution proposals.[exponentValue]— The fixed value of the temperature-scaling exponent \(\alpha\) by which the proposal size \(\gamma\) is scaled as \(\gamma \propto T^{\alpha}\) in tempered differential evolution runs.[massResolution](default5.0d9) — The mass resolution to use when building merger trees.[rootVariance]— The root variance of the random error distribution.[velocityRadial](default-0.90d0) — The radial velocity (in units of the host virial velocity) to used for the fixed virial orbits distribution. Default value matches approximate peak in the distribution of Benson (2005).[velocityTangential](default0.75d0) — The tangential velocity (in units of the host virial velocity) to used for the fixed virial orbits distribution. Default value matches approximate peak in the distribution of Benson (2005).[rateCoefficient]— The rate coefficient (in units of cm\(^3\) s\(^{-1}\)) for radiative recombination.[gamma](default0.67d0) — The multiplicative factor, \(\gamma\), used to compute the cooling coefficient.[fractionLossAngularMomentum](default0.3d0) — Specifies the fraction of angular momentum that is lost from cooling/infalling gas.[concentration]— The fixed NFW concentration parameter \(c = r_\mathrm{virial}/r_\mathrm{scale}\) assigned to all halos regardless of mass or redshift, representing the ratio of the virial radius to the scale radius of the dark matter density profile.[metallicity]— The metallicity (relative to Solar) of the IGM.[factor](defaultsqrt(0.5d0)) — The ratio of galaxy radius to \(\lambda r_\mathrm{vir}\) in the “fixed” galactic structure radius solver algorithm. This will be applied to any component for which no component-specific value is provided.[factorDisk](defaultsqrt(0.5d0)) — The ratio of galaxy radius to \(\lambda r_\mathrm{vir}\) in the “fixed” galactic structure radius solver algorithm for disks. This will override the generic value supplied by[factor]for disks.[factorSpheroid](defaultsqrt(0.5d0)) — The ratio of galaxy radius to \(\lambda r_\mathrm{vir}\) in the “fixed” galactic structure radius solver algorithm for spheroids. This will override the generic value supplied by[factor]for spheroids.[radiusFixed](defaultvar_str('virial')) — The radius to use in the “fixed” galactic structure radius solver algorithm. Allowed options are “virial” and “turnaround”.[overdensity]— The fixed linear overdensity \(\delta\) of the large-scale environment assigned uniformly to all halos; a positive value places halos in an overdense region, while negative values simulate voids.[radiusEnvironment](default0.0d0) — The radius of the sphere used to determine the variance in the environmental density.[massEnvironment](default1.0d15) — The mass within the sphere sphere used to determine the variance in the environmental density.[densityContrastValue](default200.0d0) — The virial density contrast to use in the fixed value model.[densityType](defaultvar_str('critical')) — The reference density to use in the fixed value virial density contrast model. Either ofcriticalandmeanare allowed.[turnAroundOverVirialRadius](default2.0d0) — The ratio of the turnaround to virial radii in the fixed value model.[criticalOverdensity](default(3.0d0/20.0d0)*(12.0d0*Pi)**(2.0d0/3.0d0)) — The value to use for the critical overdensity for collapse of dark matter halos when using a fixed value.