dlambda: Posterior density function of the lambda parameter.
In MobilePhoneESSnetBigData/pestim: Population Estimations Using Mobile Phone Data

Description Usage Arguments Details Value References See Also Examples

Compute the unnormalized posterior density function of the parameter λ in the hierarchical model to estimate population counts given by

f(λ\big | N^{\textrm{MNO}}; N^{\textrm{Nreg}})\propto f(λ)\cdot \textrm{dpois}(N^{\textrm{MNO}}; λ)\cdot S(λ; N^{\textrm{MNO}}, N^{\textrm{Nreg}}),

where dpois is the probability density function of a Poisson distribution and S is defined in the bibliographic reference.

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dlambda(lambda, nMNO, nReg, fu, fv, flambda, relTol = 1e-06, nSim = 1000,
  nStrata = c(1, 100), verbose = FALSE,
  nThreads = RcppParallel::defaultNumThreads())

`lambda`	numeric vector
`nMNO,`	nReg non-negative integer vectors with the number of individuals detected in each cell according to the network operator and the register
`fu,`	fv named lists with the prior marginal distributions of the two-dimensional points for the Monte Carlo integration
`flambda`	named list with the prior distribution of the lambda parameter
`relTol`	relative tolerance in the computation of the `kummer` function. Default value is `1e-6`
`nSim`	number of two-dimensional points to generate to compute the integral. Default value is `1e3`
`nStrata`	integer vector of length 2 with the number of strata in each dimension. Default value is `c(1, 1e2)`
`verbose`	logical (default `FALSE`) to report progress of the computation
`nThreads`	number (default the number of all cores, including logical cores) to use for computation

The lengths of the input vectors nMNO and nReg must be both equal to 1 and independent of the length of the input vector lambda. The integral is computed using with Monte Carlo techniques using nSim points for each of the values lambda specified so that the final data.table has length(lambda) rows.

The prior distributions are specified as named lists where the first component of each list must be the name of distribution ('unif', 'triang', 'degen', 'gamma') and the rest components must be named according to the name of the parameters of the random generator of the corresponding distribution according to:

unif: xMin, xMax for the minimum, maximum of the sampled interval.
degen: x0 for the degenerate value of the random variable.
triang: xMin, xMax, xMode for minimum, maximum and mode (see qtriang).
gamma: scale and shape with the same meaning as in rgamma.

It is important to know that currently this function accepts only parameters for a single cell at a time. In case of interest for the density function values for a set of cells, the user should program his/her own routine to apply this function to every cell.

dlambda returns a data.table with the values of the density function (column probLambda) for each value of lambda together with additional variables:

The common length of nMNO and nReg identifies the number of territorial cells in which the number of individuals detected by the telecommunication network and official data. The column cellID identifies these territorial cells.
The length of lambda identifies the number of parameters upon which the integral will be computed in each cell. The column parID identifies each of these input parameters.
The inputs nMNO and nReg are also included in the output data.table in columns under the same name.
The value on the integral times the Poisson density function ifalso included under the column integral

https://github.com/MobilePhoneESSnetBigData

genUV, Phi for related functions.

# This data.table must have 5x3= 15 rows
dlambda(seq(0, 1, length.out = 5),
        nMNO = c(20, 17, 25), nReg = c(115, 123, 119),
        fu = list('unif', xMin = 0.3, xMax = 0.5), fv = list('gamma', shape = 11, scale = 12),
        flambda = list('gamma', shape = 11, scale = 12))

# Easily, a function to draw conditioned on the parameters:
f <- function(x){
  dlambda(x, nMNO = 20, nReg = 115,
          fu = list('unif', xMin = 0.3, xMax = 0.5), fv = list('unif', xMin = 100, xMax = 120),
          flambda = list('gamma', shape = 11, scale = 12))$probLambda
}
curve(f, xlim = c(0, 150))