dCJS | R Documentation |
nimble
modelsdCJS_**
and rCJS_**
provide Cormack-Jolly-Seber capture-recapture
distributions that can be used directly from R or in nimble
models.
dCJS_ss(x, probSurvive, probCapture, len = 0, log = 0)
dCJS_sv(x, probSurvive, probCapture, len = 0, log = 0)
dCJS_vs(x, probSurvive, probCapture, len = 0, log = 0)
dCJS_vv(x, probSurvive, probCapture, len = 0, log = 0)
rCJS_ss(n, probSurvive, probCapture, len = 0)
rCJS_sv(n, probSurvive, probCapture, len = 0)
rCJS_vs(n, probSurvive, probCapture, len = 0)
rCJS_vv(n, probSurvive, probCapture, len = 0)
x |
capture history vector of 0s (not captured) and 1s (captured).
Include the initial capture, so |
probSurvive |
survival probability, either a time-independent scalar
(for dCJS_s*) or a time-dependent vector (for dCJS_v*) with length
|
probCapture |
capture probability, either a time-independent scalar
(for dCJS_*s) or a time-dependent vector (for dCJS_*v) with length |
len |
length of capture history. Should equal |
log |
TRUE or 1 to return log probability. FALSE or 0 to return probability. |
n |
number of random draws, each returning a vector of length
|
These nimbleFunctions provide distributions that can be used directly in R or
in nimble
hierarchical models (via nimbleCode
and nimbleModel
).
The letters following the 'dCJS_' indicate whether survival and/or capture
probabilities, in that order, are scalar (s, meaning the probability applies
to every x[t]
) or vector (v, meaning the probability is a vector
aligned with x
). When probCapture
and/or probSurvive
is
a vector, they must be the same length as x
.
It is important to use the time indexing correctly for survival.
probSurvive[t]
is the survival probabilty from time t
to time
t + 1
. When a vector, probSurvive
may have length greater than
length(x) - 1
, but all values beyond that index are ignored.
Time indexing for detection is more obvious: probDetect[t]
is the
detection probability at time t
.
When called from R, the len
argument to dCJS_**
is not
necessary. It will default to the length of x
. When used in
nimble
model code (via nimbleCode
), len
must be provided
(even though it may seem redundant).
For more explanation, see package vignette
(vignette("Introduction_to_nimbleEcology")
).
Compared to writing nimble
models with a discrete latent state for
true alive/dead status at each time and a separate scalar datum for each
observation, use of these distributions allows one to directly sum
(marginalize) over the discrete latent states and calculate the probability
of the detection history for one individual jointly.
These are nimbleFunction
s written in the format of user-defined
distributions for NIMBLE's extension of the BUGS model language. More
information can be found in the NIMBLE User Manual at
https://r-nimble.org.
When using these distributions in a nimble
model, the left-hand side
will be used as x
, and the user should not provide the log
argument.
For example, in nimble
model code,
captures[i, 1:T] ~ dCSJ_ss(survive, capture, T)
declares a vector node, captures[i, 1:T]
, (detection history for individual
i
, for example) that follows a CJS distribution
with scalar survival probability survive
and scalar capture probability capture
(assuming survive
and capture
are defined elsewhere in the model).
This will invoke (something like) the following call to dCJS_ss
when nimble
uses the
model such as for MCMC:
dCJS_ss(captures[i, 1:T], survive, capture, len = T, log = TRUE)
If an algorithm using a nimble
model with this declaration
needs to generate a random draw for captures[i, 1:T]
, it
will make a similar invocation of rCJS_ss
, with n = 1
.
If both survival and capture probabilities are time-dependent, use
captures[i,1:T] ~ dCSJ_vv(survive[1:(T-1)], capture[1:T], T)
and so on for each combination of time-dependent and time-independent parameters.
For dCJS_**
: the probability (or likelihood) or log probability of observation vector x
.
For rCJS_**
: a simulated capture history, x
.
The dCJS_**
distributions should all work for models and algorithms
that use nimble's automatic differentiation (AD) system. In that system,
some kinds of values are "baked in" (cannot be changed) to the AD calculations
from the first call, unless and until the AD calculations are reset. For
the dCJS_**
distributions, the lengths of vector inputs and the data
(x
) values themselves are baked in. These can be different for different
iterations through a for loop (or nimble model declarations with different indices,
for example), but the lengths and data values for each specific iteration
will be "baked in" after the first call. In other words, it is assumed that
x
are data and are not going to change.
Ben Goldstein, Perry de Valpine, and Daniel Turek
D. Turek, P. de Valpine and C. J. Paciorek. 2016. Efficient Markov chain Monte Carlo sampling for hierarchical hidden Markov models. Environmental and Ecological Statistics 23:549–564. DOI 10.1007/s10651-016-0353-z
For multi-state or multi-event capture-recapture models, see dHMM
or dDHMM
.
# Set up constants and initial values for defining the model
dat <- c(1,1,0,0,0) # A vector of observations
probSurvive <- c(0.6, 0.3, 0.3, 0.1)
probCapture <- 0.4
# Define code for a nimbleModel
nc <- nimbleCode({
x[1:4] ~ dCJS_vs(probSurvive[1:4], probCapture, len = 4)
probCapture ~ dunif(0,1)
for (i in 1:4) probSurvive[i] ~ dunif(0, 1)
})
# Build the model, providing data and initial values
CJS_model <- nimbleModel(nc, data = list(x = dat),
inits = list(probSurvive = probSurvive,
probCapture = probCapture))
# Calculate log probability of data from the model
CJS_model$calculate()
# Use the model for a variety of other purposes...
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.