Action: TD_PRODUCT_DISTRIBUTION

Module	ves
Description	Usage
Target distribution given by a separable product of one-dimensional distributions (static or dynamic).

Details and examples

Target distribution given by a separable product of one-dimensional distributions (static or dynamic).

Employ a target distribution that is a separable product of one-dimensional distributions, defined as

$$p(\mathbf{s}) = \prod_{k}^{d} p_{k}(s_{k})$$

where $d$ is the number of arguments used and $p_{k}(s_{k})$ is the one-dimensional distribution corresponding to the $k$-th argument.

Note the difference between this target distribution and the one defined in TD_PRODUCT_COMBINATION. Here we have a separable distribution given as a product of one-dimensional distribution $p_{k}(s_{k})$.

The labels of the one-dimensional distributions $p_{k}(s_{k})$ to be used in the product distribution are given in the DISTRIBUTIONS keyword. Note that the order of the labels is very important.

It is assumed that all the distributions to be used in the product distribution are normalized. If that is not the case you need to normalize the distributions by using the NORMALIZE keyword. Here it does not matter if you normalize each distribution separately or the overall product, it will give the same results.

The product distribution will be a dynamic target distribution if one or more of the distributions used is a dynamic distribution. Otherwise it will be a static distribution.

Examples

In the following example we employ a uniform distribution for argument 1 and a Gaussian distribution for argument 2.

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

target_uniform: TD_UNIFORMUniform target distribution (static). More details

The TD_UNIFORM action with label target_uniform calculates somethingtarget_Gaussian: TD_GAUSSIANTarget distribution given by a sum of Gaussian kernels (static). More details CENTER1The centers of the Gaussian distributions=-2.0 SIGMA1The standard deviations of the Gaussian distributions=0.5

The TD_GAUSSIAN action with label target_Gaussian calculates somethingtd_pd: TD_PRODUCT_DISTRIBUTIONTarget distribution given by a separable product of one-dimensional distributions (static or dynamic). More details DISTRIBUTIONSLabels of the one-dimensional target distribution actions for each argument to be used in the product distribution=target_uniform,target_Gaussian
The TD_PRODUCT_DISTRIBUTION action with label td_pd calculates something

Note that order of the labels is important, using DISTRIBUTIONS=target_Gaussian,target_uniform would mean that we would employ a Gaussian distribution for argument 1 and a uniform distribution for argument 2, which would lead to completely different results.

Full list of keywords

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

Keyword	Type	Default	Description
DISTRIBUTIONS	compulsory	none	Labels of the one-dimensional target distribution actions for each argument to be used in the product distribution
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
NORMALIZEThis keyword do not have examples	optional	false	Renormalized the target distribution over the intervals on which it is defined to make sure that it is properly normalized to 1