Gaussian prior, Gaussian posterior in Poisson mean problem.
Usage
pois_mean_GP(
x,
s = NULL,
prior_mean = NULL,
prior_var = NULL,
optim_method = "L-BFGS-B",
maxiter = 1000,
tol = 1e-05
)
Arguments
- x
data vector
- s
scaling vector
- prior_mean
prior mean
- prior_var
prior variance
- optim_method
optimization method in `optim` function
- maxiter
max number of iterations
- tol
tolerance for stopping the updates
- w
prior weights
Value
a list of
- posteriorMean:
posterior mean
- posteriorVar:
posterior variance
- obj_value:
objective function values
- prior_mean:
prior mean
- prior_var:
prior variance
@example
n = 10000
mu = rnorm(n)
x = rpois(n,exp(mu))
pois_mean_GG(x)
Details
The problem is
$$x_i\sim Poisson(\exp(\mu_i)),$$
$$\mu_i\sim N(\beta,\sigma^2).$$