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 that is an output of a model fit or a prediction task, i.e., the class should be either spLMstack, 'pp.spLMstack', spGLMstack, pp.spGLMstack, stvcGLMexact, or pp.stvcGLMexact.
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 message is thrown and the samples are obtained by resampling. We recommended running the original model fit/prediction 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.

The list may also include other scale parameters corresponding to the 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| 0.285  |
#> | Model 3 |  1.5|  1.0|               1| 0.000  |
#> | Model 4 |  3.0|  1.0|               1| 0.715  |
#> +---------+-----+-----+----------------+--------+
#> 
print(mod1$solver.status)
#> [1] "optimal"
print(mod1$run.time)
#>    user  system elapsed 
#>   0.324   0.412   0.239 

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) 1.635782 2.385281 3.015839
#> x1          4.849262 4.978038 5.107169