LocalLogistic: LocalLogistic

In alastair-JL/StochasticCIB: Stochastic CIB tools

LocalLogistic

Description

A Local stochastic succession rule. For all adjacent states (states where only one descriptor has changed), calculate the relative change in score (compared to staying in the current location). Take the logistic function (1/(exp^-x+1) ) of this value to get the relative probability. Stated mathematically, if P_{A\rightarrow B} is the transition rate from A to B, and S_A(B) is the score of the state B, from the point of view of A, then

P_{A\rightarrow B= \frac{1/(1+exp[-\beta (S_A(B)-S_A(A))])}}{\sum 1/(1+exp[-\beta (S_A(C)-S_A(A))])}

Where here we sum over all states that involve changing at most one descriptor.

Usage

LocalLogistic(TheList, TransRelAdj = NA, beta = 1, shift = 0)

Arguments

TheList	a list containing the CIB matrix, and a "shape" vector. The output of InputCibBanner is an appropriate input here.
TransRelAdj	a list containing a blank transition matrix, a relative score matrix, and an adjacency matrix. The output of MakeScoreMatrix is appropriate here.
beta	Optional parameter used to scale score values. Large beta leads to a sharp ‘switch’ from low to high probabilitiy
shift	Optional parameter used to determine location of switch point between low and high probability. By default, this value is 0, indicating that the switch point occurs as a worldstates relative score passes the score of the current worldstate.

Details

The net result of this behavior is to make "Negative" transitions exceedingly unlikely, while all “positive” transitions recieve roughly equal weight, regardless of score.

Value

A matrix describing the transition probability from each world state (rows) to each other world state (columns).

Note

Behaves very similat to LocalArctan

Author(s)

Alastair Jamieson Lane. <[e-mail]>

Examples

data(ExampleCIBdata)
LocalLogistic(ExampleCIBdata)

alastair-JL/StochasticCIB documentation built on July 27, 2023, 1:12 a.m.