Add discrete noise distributions

Adds Poisson, binomial, and negative binomial distributions to the list of noise distributions.

Author: dweindl

doc/v2/documentation_data_format.rst

@@ -748,9 +748,11 @@ Noise distributions
 
 Denote by :math:`m` the measured value,
 :math:`y:=\text{observableFormula}` the simulated value
-(the location parameter of the noise distribution),
-and :math:`\sigma` the scale parameter of the noise distribution
-as given via the ``noiseFormula`` field (the standard deviation of a normal,
+(for continuous noise distributions,
+the location parameter of the noise distribution),
+and :math:`\sigma` the distribution parameter as given via the ``noiseFormula``
+field (the scale parameter of the continuous noise distributions,
+i.e. the standard deviation of a normal,
 or the scale parameter of a Laplace model).
 Then we have the following effective noise distributions:
 
@@ -779,6 +781,25 @@ Then we have the following effective noise distributions:
     - ``log-laplace``
     - .. math::
          \pi(m|y,\sigma) = \frac{1}{2\sigma m}\exp\left(-\frac{|\log m - \log y|}{\sigma}\right)
+  * - Poisson distribution
+    - ``poisson``
+    - .. math::
+         \pi(m|\lambda) = \frac{\lambda^m\exp(-\lambda)}{m!}
+        where the rate :math:`\lambda` is given via ``observableFormula``.
+        ``noiseFormula`` must be empty in this case.
+  * - Binomial distribution
+    - ``binomial``
+    - .. math::
+         \pi(m|n,p) = \binom{n}{m}p^m(1-p)^{n-m}
+      where :math:`n` is the number of trials given via ``observableFormula``
+      and :math:`p` the probability of success given via ``noiseFormula``.
+  * - Negative binomial distribution
+    - ``negative-binomial``
+    - .. math::
+         \pi(m|r,p) = \binom{m+r-1}{m}p^r(1-p)^m
+      where :math:`r` is the number of successes given via ``observableFormula``
+      and :math:`p` the probability of success given via ``noiseFormula``.
+
 
 The distributions above are for a single data point.
 For a collection :math:`D=\{m_i\}_i` of data points and corresponding