*Meixi Chen, Martin Lysy, Reza Ramezan*

A fast Bayesian inference method for spatial random effects modelling
of weather extremes. The latent spatial variables are efficiently
marginalized by a Laplace approximation using the ** TMB**
library, which leverages efficient automatic differentiation in C++. The
models are compiled in C++, whereas the optimization step is carried out
in R. With this package, users can fit spatial GEV models with different
complexities to their dataset without having to formulate the model
using C++. This package also offers a method to sample from the
approximate posterior distributions of both fixed and random effects,
which will be useful for downstream analysis.

Before installing ** SpatialGEV**, make sure you
have

** SpatialGEV** uses several functions from the

`kernel="spde"`

in `spatialGEV_fit()`

), please first install package
To download the stable version of this package, run

`install.packages("SpatialGEV")`

To download the development version of this package, run

`::install_github("meixichen/SpatialGEV") devtools`

Using the simulated data set `simulatedData2`

provided in
the package, we demonstrate how to use this package. Spatial variation
of the GEV parameters are plotted below.

```
library(SpatialGEV)
# GEV parameters simulated from Gaussian random fields
<- simulatedData2$a # location
a <- simulatedData2$logb # log scale
logb <- simulatedData2$logs # log shape
logs <- simulatedData2$locs # coordinate matrix
locs <- nrow(locs) # number of locations
n_loc <- Map(evd::rgev, n=sample(50:70, n_loc, replace=TRUE),
y loc=a, scale=exp(logb), shape=exp(logs)) # observations
filled.contour(unique(locs$x), unique(locs$y), matrix(a, ncol=sqrt(n_loc)),
color.palette = terrain.colors, xlab="Longitude", ylab="Latitude",
main="Spatial variation of a",
cex.lab=1,cex.axis=1)
```

```
filled.contour(unique(locs$x), unique(locs$y), matrix(exp(logb), ncol=sqrt(n_loc)),
color.palette = terrain.colors, xlab="Longitude", ylab="Latitude",
main="Spatial variation of b",
cex.lab=1,cex.axis=1)
```

```
filled.contour(unique(locs$x), unique(locs$y), matrix(exp(logs), ncol=sqrt(n_loc)),
color.palette = terrain.colors, xlab="Longitude", ylab="Latitude",
main="Spatial variation of s",
cex.lab=1,cex.axis=1)
```

To fit a GEV-GP model to the simulated data, use the
`spatialGEV_fit()`

function. We use `random="abs"`

to indicate that all three GEV parameters are treated as random effects.
The shape parameter `s`

is constrained to be positive (log
transformed) by specifying `reparam_s="positive"`

. The
covariance kernel function used here is the SPDE-approximated Matérn
kernel `kernel="spde"`

. Initial parameter values are passed
to `init_param`

using a list.

```
<- spatialGEV_fit(data = y, locs = locs, random = "abs",
fit init_param = list(a = rep(60, n_loc),
log_b = rep(2,n_loc),
s = rep(-3,n_loc),
beta_a = 60, beta_b = 2, beta_s = -2,
log_sigma_a = 1.5, log_kappa_a = -2,
log_sigma_b = 1.5, log_kappa_b = -2,
log_sigma_s = -1, log_kappa_s = -2),
reparam_s = "positive", kernel="spde", silent = TRUE)
class(fit)
#> [1] "spatialGEVfit"
print(fit)
#> Model fitting took 27.9517922401428 seconds
#> The model has reached relative convergence
#> The model uses a spde kernel
#> Number of fixed effects in the model is 9
#> Number of random effects in the model is 1308
#> Hessian matrix is positive definite. Use spatialGEV_sample to obtain posterior samples
```

Posterior samples of the random and fixed effects are drawn using
`spatialGEV_sample()`

. Specify `observation=TRUE`

if we would also like to draw from the posterior predictive
distribution.

```
<- spatialGEV_sample(model = fit, n_draw = 1000, observation = T)
sam print(sam)
#> The samples contains 1000 draws of 1209 parameters
#> The samples contains 1000 draws of response at 400 locations
#> Use summary() to obtain summary statistics of the samples
```

To get summary statistics of the posterior samples, use
`summary()`

on the sample object.

```
<- summary(sam)
pos_summary $param_summary[1:5,]
pos_summary#> 2.5% 25% 50% 75% 97.5% mean
#> a1 59.98220 61.58412 62.39717 63.23451 64.98185 62.40852
#> a2 60.39339 61.75672 62.55552 63.30514 64.95137 62.55192
#> a3 60.01955 61.28410 61.98922 62.71080 64.13772 61.98618
#> a4 59.57800 60.92354 61.66539 62.39592 63.81774 61.66007
#> a5 59.55668 60.86209 61.54278 62.21564 63.68217 61.55340
$y_summary[1:5,]
pos_summary#> 2.5% 25% 50% 75% 97.5% mean
#> y1 39.43693 56.12927 70.41943 87.22232 140.3342 74.81315
#> y2 37.09989 55.68274 67.98861 87.42057 148.5369 74.42377
#> y3 38.46096 55.07948 69.19833 87.29214 152.6150 74.99553
#> y4 38.34585 56.38710 68.56856 86.17946 143.4025 73.64138
#> y5 37.81648 55.14434 69.23200 85.81161 143.7851 74.12148
```

Consider a shorter name, e.g.,

`sgev_*`

, than`spatialGEV_*`

.Argument

`init_params`

adds a lot of complexity to`spatialGEV_fit()`

. Perhaps this function can be broken down into two parts:`spatialGEV_adfun()`

which returns the`adfun`

object, and then`spatialGEV_fit()`

which does the fitting. The advantage is that the`adfun$env$parameters`

object tells you the dimension of the parameter values, which can be useful for initialization. Also, note that`adfun$env$data`

object contains the entire data list for browsing.Write some tests for the

`spde`

kernel. Construct the sparse precision matrix using`get_spde_prec()`

, invert it using`Matrix::solve()`

, apply the scale factor, and pass as variance to`dmvnorm()`

.