Action: TD_VONMISES

Module	ves
Description	Usage
Target distribution given by a sum of Von Mises distributions (static).

Details and examples

Target distribution given by a sum of Von Mises distributions (static).

Employ a target distribution that is given by a sum where each term is a product of one-dimensional Von Mises distributions,

$$p(\mathbf{s}) = \sum_{i} \, w_{i} \prod_{k}^{d} \frac{\exp\left(\kappa_{k,i} \, \cos (s_{k}-\mu_{k,i}) \right)} {2\pi I_{0}(\kappa_{k,i})}$$

where $(\mu_{1,i},\mu_{2,i},\ldots,\mu_{d,i})$ are the centers of the distributions, $(\kappa_{1,i},\kappa_{2,i},\ldots,\kappa_{d,i})$ are parameters that determine the extend of each distribution, and $I_{0}(x)$ is the modified Bessel function of order 0. The weights $w_{i}$ are normalized to 1, $\sum_{i}w_{i}=1$.

The Von Mises distribution is defined for periodic variables with a periodicity of $2\pi$ and is analogous to the Gaussian distribution. The parameter $\sqrt{1/\kappa}$ is comparable to the standard deviation $\sigma$ for the Gaussian distribution.

To use this target distribution you need to give the centers $(\mu_{1,i},\mu_{2,i},\ldots,\mu_{d,i})$ by using the numbered CENTER keywords and the "standard deviations" $(\sqrt{1/\kappa_{1,i}},\sqrt{1/\kappa_{2,i}},\ldots,\sqrt{1/\kappa_{d,i}})$ using the numbered SIGMA keywords.

Examples

Sum of two Von Mises distribution in one dimension that have equal weights as no weights are given.

Click on the labels of the actions for more information on what each action computes

TD_VONMISESTarget distribution given by a sum of Von Mises distributions (static). More details ...
 CENTER1The centers of the Von Mises distributions=+2.0 SIGMA1The standard deviations of the Von Mises distributions=0.6
 CENTER2The centers of the Von Mises distributions=-2.0 SIGMA2The standard deviations of the Von Mises distributions=0.7
 LABELa label for the action so that its output can be referenced in the input to other actions=td
... TD_VONMISES
The TD_VONMISES action with label td calculates something

Sum of two Von Mises distribution in two dimensions that have different weights. Note that the weights are automatically normalized to 1 such that specifying WEIGHTS=1.0,2.0 is equal to specifying WEIGHTS=0.33333,0.66667.

Click on the labels of the actions for more information on what each action computes

TD_VONMISESTarget distribution given by a sum of Von Mises distributions (static). More details ...
 CENTER1The centers of the Von Mises distributions=+2.0,+2.0 SIGMA1The standard deviations of the Von Mises distributions=0.6,0.7
 CENTER2The centers of the Von Mises distributions=-2.0,+2.0 SIGMA2The standard deviations of the Von Mises distributions=0.7,0.6
 WEIGHTSThe weights of the Von Mises distributions=1.0,2.0
 LABELa label for the action so that its output can be referenced in the input to other actions=td
... TD_VONMISES
The TD_VONMISES action with label td calculates something

Full list of keywords

The following table describes the keywords and options that can be used with this action

Keyword	Type	Default	Description
CENTER	optional	not used	The centers of the Von Mises distributions
SIGMA	optional	not used	The standard deviations of the Von Mises distributions
WEIGHTS	optional	not used	The weights of the Von Mises distributions
WELLTEMPERED_FACTORThis keyword do not have examples	optional	not used	Broaden the target distribution such that it is taken as [p(s)]^(1/gamma) where gamma is the well tempered factor given here
SHIFT_TO_ZEROThis keyword do not have examples	optional	false	Shift the minimum value of the target distribution to zero