estimateM.EoA: estimateM.EoA
In tmcd82070/evoab: Evidence of Absence (EoA)

Description Usage Arguments Details Value Author(s) See Also Examples

Estimate single-site or multiple-class M (=mortalities) parameter of Evidence of Absence (EoA) using objective or informed priors.

1 2	estimateM.EoA(X, beta.params, Mprior = "objective", Mprior.mean, Mprior.sd, conf.level = 0.9)

`X`	Total number of carcasses found.
`beta.params`	A list or data frame containing at a minimum components named `$alpha` and `$beta`. These are the alpha and beta parameters of a Beta distribution which is used for g=Pr(discovery).
`Mprior`	Character string specifying the prior distribution for M. "objective" uses an objective prior very close to the Jeffery's prior for a Poisson, i.e., sqrt(m+1)-sqrt(m). "normal" uses a truncated and descretized normal(Mprior.mean,Mprior.sd). "gamma" uses a descretized gamma with mean Mprior.mean and standard deviation Mprior.sd. Note, this always assigns zero prior probability to M=0.
`Mprior.mean`	Mean of M prior when Mprior == "normal" or "gamma".
`Mprior.sd`	Standard deviation of M prior when Mprior == "normal" or "gamma".
`conf.level`	Confidence level for the confidence intervals on posterior estimates of M and g.

This routine replicates the M estimates of the 'Single Year' and 'Multiple Classes' modules in package eoa. To repeat either case, input the composite g parameter's "a" and "b" parameters here, along with the number of carcasses "X", and specify the "objective" prior. See Examples.

List containing the following components.

M.est : A data frame containing the following:
- M = usual point estimate of M = median of M posterior distribution.
- M.mu = mean of M posterior distribution
- M.sd = standard deviation of M posterior distribution
- M.lo = lower endpoint of a 100(conf.level) interval for M.
- M.hi = upper endpoint of a 100(conf.level) interval for M.
- g = mean of g posterior distribution
- g.lo = lower endpoint of a 100(conf.level) interval for g. Note, this does not agree with the analogous number from package eoa because this comes from the posterior for g. eoa reports the quantile from the prior for g.
- g.hi = upper endpoint of a 100(conf.level) interval for g. Note, this does not agree with the analogous number from package eoa because this comes from the posterior for g. eoa reports the quantile from the prior for g.
- ci.level = confidence level of the credible intervals (same as input conf.level).
M.margin : the full posterior marginal distribution for M. This is a data frame with the following columns
- M : value of M in its support.
- pdf : posterior probability mass function for M. Pr(M=m)
- cdf : posterior cummulative probability mass function for M. Pr(M<=m).
- prior.pdf : prior probability mass function for M.
- like.pdf : likelihood probability mass function for M.
Note, all three of the pdf columns sum to 1.0, even in the case of an improper prior. These columns can be plotted together using the plot method for Mest objects.
g.margin : the full posterior marginal distribution for g. This is a data frame with columns $g, $pdf.g, and $cdf.g corresponding to g, probability of g, and probability of being less than or equal to g, respectively. Note, sum(result$g.margin$pdf.g) *diff(result$g.margin$g)[1] == 1.0.

Trent McDonald

estimateL.EoA, plot.Mest

g.params <- list(alpha=600, beta=1200)
X <- 5
m.ests <- estimateM.EoA(X,g.params)
print(m.ests$M.est)

m.ests <- estimateM.EoA(X, g.params, Mprior = "normal", Mprior.mean = 50, Mprior.sd = 30)
print(m.ests$M.est)

m.ests <- estimateM.EoA(X, g.params, Mprior = "gamma", Mprior.mean = 50, Mprior.sd = 30)
print(m.ests$M.est)