alphaPrior: Generate prior distributions for parameters of the Dirichlet...
In MobilePhoneESSnetBigData/pestim: Population Estimations Using Mobile Phone Data

Description Usage Arguments Details Value Examples

Generate a list of prior distributions for the parameters of the Dirichlet distribution in the hierarchical model. Each component of the list corresponds to the prior distribution of the parameter α_{ij}(t_{0}, t_{n}) for each cell j. This function initial works over a fixed initial cell i. Each returned distribution is specified as a list with an identification name as first component and named components with the distribution parameters for the rest of components.

1	alphaPrior(nMNOfrom, names, variation)

`nMNOfrom`	numeric vector with the number of individuals moving from the initial cell to the rest of cells (including those remaining)
`names`	character vector with the names of the prior distributions for each cell
`variation`	list of lists whose components are parameters providing a measure of variation of each prior distribution

The function takes the number of cells from the input parameter nMNOfrom which specifies the number of individuals detected by the network moving from the initial cell to each of the cells (including those remaining in the same). The function executes the same construction for each final cell. It takes the name of prior distribution from the input parameter names and construct the corresponding prior distribution for each cell j with mode at u_{j}^{*}=N_{j}, where N_{j} is taken from nMNOfrom. Next the rest of parameters of the distribution are computed according to the dispersion parameters specified in variation.

As accepted distribution names, currently the user can specify unif, degen, triang, and gamma.

The dispersion parameters recognised so far are the coefficients of variation only (standard deviation divided by the mean of the distribution). These dispersion parameters must be specified by a named component cv with a numeric value in [0, 1].

For each distribution the parameters are computed as follows:

unif: This is the uniform distribution with parameters xMax and xMin. Both parameters are computed by u_{j}^{*}\cdot(1\pm√{3}\textrm{cv}), respectively, in each cell j.
degen: This is the degenerate distribution with parameter X0 taken as u_{j}^{*} in each cell j.
triang: This is the triangular distribution dtriang with parameters xMax, xMin, and xMode. The latter is taken directly from nMNOfrom. The distribution is assumed to be symmetrical so that the two former parameters are computed by u_{j}^{*}\cdot(1\pm√{3}\textrm{cv}), respectively, in each cell j.
gamma: This is the gamma distribution with parameters shape and scale. The former is computed as \frac{1}{\textrm{cv}^2} and the latter as frac{u_{j}^{*}}{\textrm{scale} - 1}.

Return a list with a list in each component specifying the prior for each cell

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# Three cells. Cell 1 under study. 10 individuals remain.
alphaPrior(c(10, 3, 4), c('unif', 'triang', 'gamma'),
           list(list(cv = 0.1), list(cv = 0.05), list(cv = 0.15)))