Posterior Sampling Differential Evolution Proposal Size Temperature Exponent

Class providing temperature-dependence exponents for proposal sizes for differential evolution posterior samplers. Specifically, this class provides the exponent, \(\alpha\), for the temperature scaling of 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 tempered differential evolution simulations

Methods

exponent → double precision

Return the temperature-scaling exponent \(\alpha\) for the current simulation state, which controls how the proposal size \(\gamma\) scales with the chain temperature in tempered differential evolution runs.

• class (posteriorSampleStateClass ), intent(inout), dimension(:) :: temperedStates

• double precision , intent(in ), dimension(:) :: temperatures

• class (posteriorSampleStateClass ), intent(inout) :: simulationState

• class (posteriorSampleConvergenceClass), intent(inout) :: simulationConvergence

posteriorSampleDffrntlEvltnPrpslSzTmpExpAdaptive

This class adaptively changes \(\alpha\) in an attempt to maintain the gradient of the acceptance rate with the logarithm of temperature, \(\mathrm{d} R/\mathrm{d}\ln T\), at an acceptable level. The algorithm is controlled by the following sub-parameters:

[exponentInitial]

The initial value for \(\alpha\);

[exponentFactor]

The additive factor by which \(\alpha\) should be increased or decreased if the acceptance rate gradient is out of range;

[exponentMinimum]

The smallest value allowed for \(\alpha\);

[exponentMaximum]

The largest value allowed for \(\alpha\);

[acceptanceRateMinimum]

The minimum acceptance rate gradient to accept before reducing \(\alpha\);

[acceptanceRateMaximum]

The maximum acceptance rate gradient to accept before reducing \(\alpha\);

[updateCount]

The number of steps between successive checks of the acceptance rate gradient.

Parameters

• [exponentInitial] (real) — The initial value of the temperature-scaling exponent \(\alpha\) used before any adaptive adjustment based on the acceptance-rate gradient has been applied.

• [exponentMinimum] (real) — 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] (real) — 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] (real) — 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] (real) — The minimum acceptable gradient of acceptance rate with log-temperature.

• [gradientMaximum] (real) — The maximum acceptable gradient of acceptance rate with log-temperature.

• [updateCount] (integer) — The number of steps between potential updates of the temperature exponent.

posteriorSampleDffrntlEvltnPrpslSzTmpExpFixed

This class uses a fixed \(\alpha=\)[alpha].

Parameters

• [exponentValue] (real) — 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.