The limit of detection (LoD) is the lowest value of a variable x at which an event can
be detected with a given sensitivity. For example, a smoke detector that triggers at a
concentration of 15,000 particles per cm^3 with 95% probability has a 95%-LoD of 15,000.
This package uses a probit or logit model from the GLM package to estimate the LoD, taking as input a vector
containing the values of the variable considered (e.g. smoke concentration) and the corresponding boolean detection status (true = detected).
In addition it performs sampling using AdaptiveMCMC to provide error estimates on the LoD, and
a plot recipee is provided to visualize the results.
using LimitOfDetection
# generate artificial data
x = LinRange(0,1,100)
link = ProbitLink()
f = x -> LimitOfDetection.GLM.linkinv(link, 10*x - 5)
Pcall = f.(x)
detected = [rand() < P for P in Pcall]
# fit model
model = fit(LoDModel, x, detected; Nsamples = 50_000, sensitivity = 0.95, link = ProbitLink())
julia> model
Limit of Detection:
────────────────────────────────────────────────────────────
MLE Mean Std Lower 90% Upper 90%
────────────────────────────────────────────────────────────
95%-LoD 0.670671 0.670189 0.0134975 0.648664 0.693332
────────────────────────────────────────────────────────────
julia> using Plots; plot(model; CI_level = 0.9, label = "x")MLE(model) # returns the maxmimum-likelihood estimator of the LoD
mean(model) # returns the mean aposteriori of the LoD
quantile(model, q) # returns the quantile q of the posterior distribution