# Using the Theory of Belief Functions

Using the Theory of Belief Functions for evidence calculus. Basic probability assignments, or mass functions, can be defined on the subsets of a set of possible values and combined. A mass function can be extended to a larger frame. Marginalization, i.e. reduction to a smaller frame can also be done. These features can be combined to analyze small belief networks and take into account situations where information cannot be satisfactorily described by probability distributions.

Using Dempster-Shafer Theory of Evidence, also called "Theory of Belief Functions". Basic probability assignments, or mass functions, can be defined on the subsets of a set of possible values. Two mass functions can be combined using Dempster's rule of combination. A mass function can be extended to a larger frame. Marginalization, i.e. reduction to a smaller frame can also be done. These features can be combined to analyze small belief networks and take into account situations where information cannot be satisfactorily described by probability distributions.

# Installation

Install from CRAN: install.package("dst")

# Examples

See the vignette: Monty-hall-Example.

# News

dst v 1.3.0

• added utility functions 'matrixToMarray' and 'marrayToMatrix' to execute the product space conversion of multidimensional data represented by a matrix, and vice-versa.

• debugging of function 'extmin' (extension of data to a larger product space).

• debugging of function 'elim' (reduction of a product space by elimination of one variable).

================ dst v1.2.0.9001 2018-07-07.

• Correction to fn dsrwon: added the parameter relnb in the call of the function, to allow for specification the result with a new relation number.

================ dst v1.2.0.9000 2018-05-01.

• Correction to fn tabresul: added a check for the case of the empty set present with m_empty = 0

================ dst v1.1.0.9000 2018-05-01.

• Correction to fn belplau: added a check for the case of the empty set present with m_empty = 0
• Re-writed the referencing of source code taken on Rpubs

================ dst v1.0.0 (Release date on CRAN: 2018-04-25)

Changes from version 0.3:

• Added a vignette: The Monty hall Game, an introduction to belief functions.

• functions (new and updated):

-- addTobca: New function. Adds some elements of 0 mass to an existing mass function.

-- bca: New version. Sets a class named "bcaspec". Parameters added to work with definitions on product spaces (relations).

-- bcaRel: New function to define a belief function on a product space.

-- belplau: Calculation of measures of belief, plausibility and ratio of plausibility.

-- decode: utility function -- dotprod: utility function -- double: utility function -- shape: utility function -- encode: New utility function. Convert a value to its representation in another chosen base. -- reduction: utility function to obtain the summary of a vector for any operator

-- dsrwon: Combination of two mass functions

-- elim: This is a new function. This function works on a relation defined on a product of two variables or more. Having fixed a variable to eliminate from the relation, the reduced product space is determined and the corresponding reduced bca is computed.This operation is also called "marginalization".

-- extmin: Extension of a relation to a greater product space

-- inters: Intersection of two tables of propositions

-- nameRows: New function: Using the column names of a matrix to construct names for the rows

-- nzdsr: Normalization of results from Dempster's rule of combination.

-- productSpace: New function. Product space representation of a relation

-- plautrans:Plausibility transformation of the singletons of a frame

-- tabresul: Prepare a table of results.

• Removal of obsolete functions: butLast, combmasses, dempster, initsing, rplau, transfo

# Reference manual

install.packages("dst")

1.4.1 by Claude Boivin, a year ago

Report a bug at https://github.com/RAPLER/dst-1/issues

Browse source code at https://github.com/cran/dst

Authors: Claude Boivin , Stat.ASSQ <[email protected]>

Documentation:   PDF Manual