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ParaMonte Fortran 2.0.0
Parallel Monte Carlo and Machine Learning Library
See the latest version documentation. |
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ParaMonte Fortran 2.0.0
Parallel Monte Carlo and Machine Learning Library
See the latest version documentation. |
This module contains the types, classes, and procedures relevant to weights of random samples. More...
Data Types | |
| type | aweight_type |
| This is a concrete derived type whose instances are exclusively used to signify the aweight type of sample weights. More... | |
| type | fweight_type |
| This is a concrete derived type whose instances are exclusively used to signify the fweight type of sample weights. More... | |
| interface | getReweight |
Generate and return a reweighting of the input weight vector, such that the sequence represented by output reweight is the refined (skipped by the amount skip) version of the sequence represented by the input weight.More... | |
| type | rweight_type |
| This is a concrete derived type whose instances are exclusively used to signify the rweight type of sample weights. More... | |
| interface | setReweight |
Generate and return a reweighting of the input weight vector, such that the sequence represented by output reweight is the refined (skipped by the amount skip) version of the sequence represented by the input weight.More... | |
| type | weight_type |
This is an abstract derived type for constructing concrete derived types to distinguish various procedure signatures that require different sample weights (e.g., fweight, aweight, rweight, ...).More... | |
Variables | |
| character(*, SK), parameter | MODULE_NAME = "@pm_sampleWeight" |
| type(aweight_type), parameter | aweight = aweight_type() |
This is a scalar parameter object of type aweight_type that is exclusively used to signify the Symmetric class of a given matrix within an interface of a procedure of the ParaMonte library.More... | |
| type(fweight_type), parameter | fweight = fweight_type() |
This is a scalar parameter object of type fweight_type that is exclusively used to signify the Symmetric class of a given matrix within an interface of a procedure of the ParaMonte library.More... | |
| type(rweight_type), parameter | rweight = rweight_type() |
This is a scalar parameter object of type rweight_type that is exclusively used to signify the Symmetric class of a given matrix within an interface of a procedure of the ParaMonte library.More... | |
This module contains the types, classes, and procedures relevant to weights of random samples.
Within the world of statistics, particularly, traditional frequentist statistics, there is absolute confusion on what types of weights exist and what their implications are.
The most relevant definitions, which are also currently used in the ParaMonte library, are the following,
There are also other definitions of weight which special use cases, for example:
\begin{equation} \mathrm{ESS} = \frac{ \big( \sum_{i = 1}^{N} w_i \big)^2 }{ \sum_{i = 1}^{N} w_i^2 } ~, \end{equation}
If the weights \(w_i\) are normalized such that \(\sum_{i = 1}^{N} w_i = N\), then,\begin{equation} \mathrm{ESS} = \frac{ N }{ 1 + \mathrm{VAR}(w) } ~, \end{equation}
where \(\mathrm{VAR}(w)\) represents the variance of the weights.
Final Remarks ⛓
If you believe this algorithm or its documentation can be improved, we appreciate your contribution and help to edit this page's documentation and source file on GitHub.
For details on the naming abbreviations, see this page.
For details on the naming conventions, see this page.
This software is distributed under the MIT license with additional terms outlined below.
This software is available to the public under a highly permissive license.
Help us justify its continued development and maintenance by acknowledging its benefit to society, distributing it, and contributing to it.
| type(aweight_type), parameter pm_sampleWeight::aweight = aweight_type() |
This is a scalar parameter object of type aweight_type that is exclusively used to signify the Symmetric class of a given matrix within an interface of a procedure of the ParaMonte library.
Precision (or Analytic) weights are weights that are inversely proportional to the variance of an observation.
The variance of the \(i\)th observation is assumed to be \(\sigma^2/w_i\).
Typically, the observations represent averages and the weights are the number of elements that gave rise to the average.
For example usage, see the documentation of the target procedure requiring this object.
Final Remarks ⛓
If you believe this algorithm or its documentation can be improved, we appreciate your contribution and help to edit this page's documentation and source file on GitHub.
For details on the naming abbreviations, see this page.
For details on the naming conventions, see this page.
This software is distributed under the MIT license with additional terms outlined below.
This software is available to the public under a highly permissive license.
Help us justify its continued development and maintenance by acknowledging its benefit to society, distributing it, and contributing to it.
Definition at line 175 of file pm_sampleWeight.F90.
| type(fweight_type), parameter pm_sampleWeight::fweight = fweight_type() |
This is a scalar parameter object of type fweight_type that is exclusively used to signify the Symmetric class of a given matrix within an interface of a procedure of the ParaMonte library.
Frequency weights, represent the number of duplications of each observation in the sample.
For example usage, see the documentation of the target procedure requiring this object.
Final Remarks ⛓
If you believe this algorithm or its documentation can be improved, we appreciate your contribution and help to edit this page's documentation and source file on GitHub.
For details on the naming abbreviations, see this page.
For details on the naming conventions, see this page.
This software is distributed under the MIT license with additional terms outlined below.
This software is available to the public under a highly permissive license.
Help us justify its continued development and maintenance by acknowledging its benefit to society, distributing it, and contributing to it.
Definition at line 233 of file pm_sampleWeight.F90.
| character(*, SK), parameter pm_sampleWeight::MODULE_NAME = "@pm_sampleWeight" |
Definition at line 90 of file pm_sampleWeight.F90.
| type(rweight_type), parameter pm_sampleWeight::rweight = rweight_type() |
This is a scalar parameter object of type rweight_type that is exclusively used to signify the Symmetric class of a given matrix within an interface of a procedure of the ParaMonte library.
For example usage, see the documentation of the target procedure requiring this object.
Final Remarks ⛓
If you believe this algorithm or its documentation can be improved, we appreciate your contribution and help to edit this page's documentation and source file on GitHub.
For details on the naming abbreviations, see this page.
For details on the naming conventions, see this page.
This software is distributed under the MIT license with additional terms outlined below.
This software is available to the public under a highly permissive license.
Help us justify its continued development and maintenance by acknowledging its benefit to society, distributing it, and contributing to it.
Definition at line 290 of file pm_sampleWeight.F90.
1.9.3