For \((\pi_1, \ldots, \pi_k) \sim Dir(\alpha)\) with
\(A = \sum_i \alpha_i\), returns \(E[\pi_j]\),
\(Var[\pi_j]\) and \(Cov[\pi_j, \pi_{j'}]\). The covariance is
computed from the formula for distinct cells; passing
j == jp therefore does not reproduce the variance.
Usage
morie_gh_dirichlet_moments(alpha, j, jp)
Arguments
- alpha
numeric vector of Dirichlet concentration parameters
- j
index of the cell whose mean and variance are wanted
- jp
index of the second cell for the covariance
Value
list with elements mean, var (both for cell
j) and cov (between cells j and jp)
References
Ghosal, S. and van der Vaart, A. (2017).
Fundamentals of Nonparametric Bayesian Inference.
Cambridge University Press.
Examples
morie_gh_dirichlet_moments(alpha = 0.5, j = c(1, 2, 3, 4, 5, 6, 7, 8),
jp = c(1, 2, 3, 4, 5, 6, 7, 8))
#> $mean
#> [1] 1 NA NA NA NA NA NA NA
#>
#> $var
#> [1] 0 NA NA NA NA NA NA NA
#>
#> $cov
#> [1] 0 NA NA NA NA NA NA NA
#>
