Add a documentation page for FABADA

Refs #11541

Code/Mantid/docs/source/concepts/FABADA.rst

@@ -0,0 +1,70 @@
+.. _FABADA:
+
+FABADA
+======
+
+FABADA is a fitting algorithm for Bayesian data analysis, the theory of which is
+detailed here: http://dx.doi.org/10.1088/1742-6596/325/1/012006
+
+This documentation covers details of it's implementation in Mantid.
+
+Important Notes
+---------------
+
+Currently in order to use FABADA the cost function must be set to Least Squares.
+
+The values for ChainLength and MaxIterations should be set to relatively high
+values where :math:`MaxIterations > 2 * ChainLength` (e.g. MaxIterations = 20^6
+and ChainLength = 10^6).
+
+Currently the starting values used for each parameter are required to be a
+fairly good estimate of the actual value, in the event that a parameter is not
+estimated to sufficient accuracy convergence of the parameters will not be
+reached and an error message will inform of the unconverged parameters.
+
+FABADA Specific Parameters
+--------------------------
+
+ChainLength
+  Number of steps done by the algorithm once all of the parameters have
+  converged.
+
+StepsBetweenValues
+  Specifies interval at which to record parameter and cost function values in
+  the chain outputs.
+
+ConvergenceCriteria
+  The threshold variation in the cost function due to the change in a parameter
+  under which it is assumed that the parameter has reached convergence.
+
+JumpAcceptanceRate
+  The desired percentage of acceptance for new parameters (typically 0.666)
+
+FABADA Specific Outputs
+-----------------------
+
+PDF
+  Probability Density Function for each fitted parameter and the cost function.
+  This is output as a :ref:`MatrixWorkspace`.
+
+Chains
+  The value of each parameter and the cost function for each step taken.
+  This is output as a :ref:`MatrixWorkspace`.
+
+ConvergedChain
+  A subset of Chains containing only the section after which the parameters have
+  converged.
+  This records the parameters at step intervals given by StepsBetweenValues.
+  This is output as a :ref:`MatrixWorkspace`.
+
+CostFunctionTable
+  Table containing the minimum and most probable values of the cost function as
+  well as their reduced values.
+  This is output as a TableWorkspace.
+
+Parameters
+  Similar to the standard parameter table but also includes left and right
+  errors for each parameter (cost function is not included).
+  This is output as a TableWorkspace.
+
+.. categories:: Concepts