Action: TD_PRODUCT_COMBINATION

Module	ves
Description	Usage
Target distribution given by product combination of distributions (static or dynamic).

Details and examples

Target distribution given by product combination of distributions (static or dynamic).

Employ a target distribution that is a product combination of the other distributions, defined as

$$p(\mathbf{s}) = \frac{\prod_{i} p_{i}(\mathbf{s})} {\int d \mathbf{s} \prod_{i} p_{i}(\mathbf{s})}$$

where the distributions $p_{i}(\mathbf{s})$ are in full dimensional space of the arguments used.

Note the difference between this target distribution and the one defined in TD_PRODUCT_DISTRIBUTION. Here we have a non-separable distribution given as a product of distribution $p_{i}(\mathbf{s})$ which are in full dimensional space of the arguments used.

The labels of the distributions $p_{i}(\mathbf{s})$ to be used in the product combination are given in the DISTRIBUTIONS keyword.

The target distribution resulting from the product combination will be automatically normalized. Therefore, the product combination needs to be a proper distribution that is non-negative and that can be normalized. The code will perform checks to make sure that this is indeed the case.

The product combination 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 the overall interval on which the target distribution is defined is from 0.23 to 0.8. We employ a product combination of a well-tempered distribution and a uniform distribution that decays to zero at 0.6. This results in a target distribution that is well-tempered from 0.23 to 0.6 and then decays to zero. In other words, we cut off the tail of the well-tempered distribution at 0.6

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

td_welltemp: TD_WELLTEMPEREDWell-tempered target distribution (dynamic). More details BIASFACTORThe bias factor used for the well-tempered distribution=5
The TD_WELLTEMPERED action with label td_welltemp calculates somethingtd_uniform: TD_UNIFORMUniform target distribution (static). More details MINIMAThe minimum of the intervals where the target distribution is taken as uniform=0.23 MAXIMAThe maximum of the intervals where the target distribution is taken as uniform=0.6 SIGMA_MAXIMAThe standard deviation parameters of the Gaussian switching functions for the maximum of the intervals=0.05
The TD_UNIFORM action with label td_uniform calculates somethingtd_combination: TD_PRODUCT_COMBINATIONTarget distribution given by product combination of distributions (static or dynamic). More details DISTRIBUTIONSThe labels of the target distribution actions to be used in the product combination=td_uniform,td_welltemp
The TD_PRODUCT_COMBINATION action with label td_combination calculates something

In the following example the overall interval on which the target distribution is defined is from -4 to 4. We employ a product of a Gaussian distribution with two centers and distribution that is uniform on the interval -3 to 3 and then smoothly decays to zero outside that interval. The overall effect will then be to cut off the tails of the Gaussian distribution

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

TD_GAUSSIANTarget distribution given by a sum of Gaussian kernels (static). More details ...
 CENTER1The centers of the Gaussian distributions=-2.9 SIGMA1The standard deviations of the Gaussian distributions=1.0
 CENTER2The centers of the Gaussian distributions=+2.9 SIGMA2The standard deviations of the Gaussian distributions=0.4
 LABELa label for the action so that its output can be referenced in the input to other actions=td_gauss
... TD_GAUSSIAN

The TD_GAUSSIAN action with label td_gauss calculates somethingTD_UNIFORMUniform target distribution (static). More details ...
 MINIMAThe minimum of the intervals where the target distribution is taken as uniform=-3.0 SIGMA_MINIMAThe standard deviation parameters of the Gaussian switching functions for the minima of the intervals=0.20
 MAXIMAThe maximum of the intervals where the target distribution is taken as uniform=+3.0 SIGMA_MAXIMAThe standard deviation parameters of the Gaussian switching functions for the maximum of the intervals=0.15
 LABELa label for the action so that its output can be referenced in the input to other actions=td_uni
... TD_UNIFORM

The TD_UNIFORM action with label td_uni calculates somethingtd_pc: TD_PRODUCT_COMBINATIONTarget distribution given by product combination of distributions (static or dynamic). More details DISTRIBUTIONSThe labels of the target distribution actions to be used in the product combination=td_gauss,td_uni
The TD_PRODUCT_COMBINATION action with label td_pc 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
DISTRIBUTIONS	compulsory	none	The labels of the target distribution actions to be used in the product combination
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