Sample from the stacked posterior distribution

A helper function to sample from the stacked posterior distribution to obtain final posterior samples that can be used for subsequent analysis. This function applies on outputs of functions spLMstack() and spGLMstack().

Usage

stackedSampler(mod_out, n.samples)

Arguments

mod_out: an object of class spLMstack or spGLMstack.
n.samples: (optional) If missing, inherits the number of posterior samples from the original output. Otherwise, it specifies number of posterior samples to draw from the stacked posterior. If it exceeds the number of posterior draws used in the original function, then a warning is thrown and the samples are obtained by resampling. It is recommended, to run the original function with enough samples.

Value

An object of class stacked_posterior, which is a list that includes the following tags -

beta: samples of the fixed effect from the stacked joint posterior.
z: samples of the spatial random effects from the stacked joint posterior.

In case of model output of class spLMstack, the list additionally contains sigmaSq which are the samples of the variance parameter from the stacked joint posterior of the spatial linear model. For model output of class spGLMstack, the list also contains xi which are the samples of the fine-scale variation term from the stacked joint posterior of the spatial generalized linear model.

Details

After obtaining the optimal stacking weights $\hat{w}_1, \ldots, \hat{w}_G$, posterior inference of quantities of interest subsequently proceed from the stacked posterior, $$ \tilde{p}(\cdot \mid y) = \sum_{g = 1}^G \hat{w}_g p(\cdot \mid y, M_g), $$ where $\mathcal{M} = \{M_1, \ldots, M_g\}$ is the collection of candidate models.

Author

Soumyakanti Pan span18@ucla.edu,
Sudipto Banerjee sudipto@ucla.edu

Examples

data(simGaussian)
dat <- simGaussian[1:100, ]

mod1 <- spLMstack(y ~ x1, data = dat,
                  coords = as.matrix(dat[, c("s1", "s2")]),
                  cor.fn = "matern",
                  params.list = list(phi = c(1.5, 3),
                                     nu = c(0.5, 1),
                                     noise_sp_ratio = c(1)),
                  n.samples = 1000, loopd.method = "exact",
                  parallel = FALSE, solver = "ECOS", verbose = TRUE)
#> 
#> STACKING WEIGHTS:
#> 
#>           | phi | nu  | noise_sp_ratio | weight |
#> +---------+-----+-----+----------------+--------+
#> | Model 1 |  1.5|  0.5|               1| 0.000  |
#> | Model 2 |  3.0|  0.5|               1| 0.213  |
#> | Model 3 |  1.5|  1.0|               1| 0.000  |
#> | Model 4 |  3.0|  1.0|               1| 0.787  |
#> +---------+-----+-----+----------------+--------+
#> 
print(mod1$solver.status)
#> [1] "optimal"
print(mod1$run.time)
#>    user  system elapsed 
#>   0.384   0.553   0.286 

post_samps <- stackedSampler(mod1)
post_beta <- post_samps$beta
print(t(apply(post_beta, 1, function(x) quantile(x, c(0.025, 0.5, 0.975)))))
#>                 2.5%      50%    97.5%
#> (Intercept) 1.665128 2.364626 3.039489
#> x1          4.850326 4.976093 5.103667