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IKL <- function( params, # parameters over which to calculate
theta, # a single estimate of theta
delta = .1, # the indifference region specification
quad = 33 ) # the number of quadrature points
{
# This function finds Integrated KL-Information:
#~~~~~~~~~~~~~~~~~~~~~~~#
# Bounds of Integration #
#~~~~~~~~~~~~~~~~~~~~~~~#
# Indicate the lower/upper bounds of integration and density:
range <- theta + c(-1, 1)*delta
l <- range[1]; u <- range[2]
# Set up the bounds of integration:
X <- seq(l, u, length = quad) # region of integration
X.theta <- (X + theta)/2 # shifting center of indifference region
X.delta <- X - X.theta # half-width of indifference region
# The integral is int_{theta' - delta}^{theta' + delta}KL(theta | theta')
# --> So we have several KL information thingies
# --> The center of each KL information: theta'' = (theta + theta')/2
# --> The half-width of the corresponding indifference region: abs(theta'' - theta)
# Note: 1) Shifted KL information as we go from theta' - delta to theta' + delta
# 2) X.theta - X.delta will always/must always equal theta for all points.
#~~~~~~~~~~~~~~~~#
# KL-Information #
#~~~~~~~~~~~~~~~~#
# The KL-Information for all of the items thus far across range:
Y <- KL(params = params, theta = X.theta, delta = X.delta)$item
#~~~~~~~~~~~~~~~#
# And Integrate #
#~~~~~~~~~~~~~~~#
info <- apply(Y, MARGIN = 2, FUN = integrate.q, x = X)
return( list(item = info) )
} # END IKL FUNCTION
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