.. _physics-posteriorSampleDffrntlEvltnPrpslSzTmpExp:

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, :math:`\alpha`, for the temperature scaling of the proposal size parameter, :math:`\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 :math:`\alpha` for the current simulation state, which controls how the proposal size :math:`\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``

.. _physics-posteriorSampleDffrntlEvltnPrpslSzTmpExpAdaptive:

``posteriorSampleDffrntlEvltnPrpslSzTmpExpAdaptive``
----------------------------------------------------

This class adaptively changes :math:`\alpha` in an attempt to maintain the gradient of the acceptance rate with the logarithm of temperature, :math:`\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 :math:`\alpha`;

``[exponentFactor]``
   The additive factor by which :math:`\alpha` should be increased or decreased if the acceptance rate gradient is out of range;

``[exponentMinimum]``
   The smallest value allowed for :math:`\alpha`;

``[exponentMaximum]``
   The largest value allowed for :math:`\alpha`;

``[acceptanceRateMinimum]``
   The minimum acceptance rate gradient to accept before reducing :math:`\alpha`;

``[acceptanceRateMaximum]``
   The maximum acceptance rate gradient to accept before reducing :math:`\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 :math:`\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 :math:`\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 :math:`\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 :math:`\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.

.. _physics-posteriorSampleDffrntlEvltnPrpslSzTmpExpFixed:

``posteriorSampleDffrntlEvltnPrpslSzTmpExpFixed``
-------------------------------------------------

This class uses a fixed :math:`\alpha=`\ ``[alpha]``.

**Parameters**

* ``[exponentValue]`` (real) — The fixed value of the temperature-scaling exponent :math:`\alpha` by which the proposal size :math:`\gamma` is scaled as :math:`\gamma \propto T^{\alpha}` in tempered differential evolution runs.