estimateL.EoA: estimateL.EoA - Estimate rate parameter Lambda for a...
In tmcd82070/EoAR: Evidence of Absence Regression (EoAR)

Description Usage Arguments Value Examples

This routine computes lambda, the mean number of search targets out there per season, using information from the number of found targets and the g-value (=probatility of discovery). This differs from the eoar() function in that this routine does not allow covariates (mean model only). The method is Bayesian and allows either an uniform prior for lambda or an informed prior. Estimation is direct in the sense that this routine uses numerical integration to compute the posterior of lambda.

estimateL.EoA(
  X,
  beta.params,
  Lprior = "jeffreys",
  Lprior.mean = NULL,
  Lprior.sd = NULL,
  conf.level = 0.9
)

`X`	Total number of search targets found at all searched sites during the entire search season.
`beta.params`	A list containing, at a minimum, components named $alpha and $beta. These are the all-site alpha and beta parameters for g. In many cases, these parameters are computed using function `getFleetG`.
`Lprior`	A string naming the prior distribution to use for lambda. The following priors are implimented: "normal" : uses a normal(`Lprior.mean`,`Lprior.sd`) prior for lambda. "gamma" : uses a gamma(alpha,beta) prior for lambda, where alpha = `Lprior.mean^2`/`Lprior.sd^2` and beta = `Lprior.mean`/ `Lprior.sd^2`. That is, alpha and beta are the method of moment estimates for the shape and rate parameter of a gamma distribution. "jefferys" : uses a beta(L + 0.5, 0.5) function as the prior for lambda. This prior is improper and really close to the actual Jeffery's prior for a poisson random variable. This is the Jeffery's prior implemented by Dalthorp's eoa package.
`Lprior.mean`	Mean of lambda prior when Lprior == "normal" or "gamma".
`Lprior.sd`	Standard deviation of normal when Lprior == "normal" or "gamma".
`conf.level`	Confidence level for the confidence intervals on lambda.

List containing two components:

$L.ests is a data frame containing the lambda estiamtes (point estimate and confidence interval).
$L.posterior is a data frame containing the posterior, posterior cdf, prior, and likelihood. This is returned in case you want to plot them.

syr <- data.frame(species=c("LBBA","LBBA","LBBA"),
   facility=c("f1","f2","f2"),
   gFac.a = c( 69.9299, 63.5035,  84.6997),
   gFac.b = c(  736.4795,  318.3179, 759.9333 ),
   year = c(2015,2015,2016))
g <- getFleetG(syr, "LBBA"))

eoa <- estimateL.EoA( 1, g )  # Un-informed EoA

ieoa <- estimateL.EoA( 1, g, Lprior="normal", Lprior.mean=20, Lprior.sd=4) # Informed EoA

# interesting plot showing movement of posterior
plot(ieoa$L.posterior$L, ieoa$L.posterior$pdf, type="l")
lines(ieoa$L.posterior$L, ieoa$L.posterior$like.pdf, col="red")
lines(ieoa$L.posterior$L, ieoa$L.posterior$prior.pdf, col="blue")
legend("topright", legend=c("prior","likelihood","posterior"), col=c("blue","red","black"), lty=1)

# to check that integral is correct.
flike <- function(x, est){
  approx(est$L.posterior$L, est$L.posterior$like.pdf,xout=x, rule=2)$y
  }
integrate( flike, min(ieoa$L.posterior$L), max(ieoa$L.posterior$L), est=ieoa)