#' Convert from physical to intrinsic RSM parameters
#'
#' Convert \strong{physical} RSM parameters \eqn{\lambda_i}' and \eqn{\nu_i}' to the
#' \strong{intrinsic} RSM parameters \eqn{\lambda_i} and \eqn{\nu_i}. The physical
#' parameters are more meaningful but they depend on \eqn{\mu}. The intrinsic
#' parameters are independent of \eqn{\mu}. See book for details.
#'
#' @param mu The mean of the Gaussian distribution for the ratings of latent LLs,
#' i.e. continuous ratings of lesions that were found by the search mechanism
#' ~ N(\eqn{\mu},1). The corresponding distribution for the ratings of
#' latent NLs is N(0,1)
#'
#' @param lambda The Poisson \eqn{\lambda_i} parameter, which describes the
#' distribution of random numbers of latent NLs (suspicious regions that do
#' not correspond to actual lesions) per case; the mean of these random
#' numbers asymptotically approaches lambda
#'
#' @param nu The \eqn{\nu_i} parameter; it is the success probability
#' of the binomial distribution describing the random number of latent LLs
#' (suspicious regions that correspond to actual lesions) per diseased case
#'
#' @return A list containing \eqn{\lambda_i} and \eqn{\nu_i}, the RSM search parameters
#'
#' @details RSM is the Radiological Search Model described in the book. A latent mark
#' becomes an actual mark if the corresponding rating exceeds the lowest reporting
#' threshold zeta1. See also \code{\link{Util2Physical}}.
#'
#' @references
#' Chakraborty DP (2006) A search model and figure of merit for observer data acquired according to the free-response
#' paradigm, Phys Med Biol 51, 3449-3462.
#'
#' Chakraborty DP (2006) ROC Curves predicted by a model of visual search, Phys Med Biol 51, 3463--3482.
#'
#' Chakraborty DP (2017) \emph{Observer Performance Methods for Diagnostic Imaging - Foundations,
#' Modeling, and Applications with R-Based Examples}, CRC Press, Boca Raton, FL.
#' \url{https://www.routledge.com/Observer-Performance-Methods-for-Diagnostic-Imaging-Foundations-Modeling/Chakraborty/p/book/9781482214840}
#'
#' @examples
#' mu <- 2;lambda <- 10;nu <- 0.9
#' lambda_i <- Util2Intrinsic(mu, lambda, nu)$lambda_i
#' nu_i <- Util2Intrinsic(mu, lambda, nu)$nu_i
#' ## note that the physical values are only constrained to be positive, e.g., nu_i is not constrained
#' ## to be between 0 and one.
#'
#' @export
Util2Intrinsic<- function(mu, lambda, nu) {
lambda_i <- lambda * mu
nu_i <- -log(1-nu)/mu
return (list(
lambda_i = lambda_i,
nu_i = nu_i))
}
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