This vignette introduces a new feature of *revdbayes*:
reducing posterior simulation time by performing the most time-consuming
tasks using C++ functions. This achieved using a new facility in the
*rust* package (Northrop 2017),
which in turn uses the **Rcpp** package (Eddelbuettel and Francois 2011). The result is
a new function `rpost_rcpp`

, which has the same structure as
the existing function `rpost`

. From a user’s perspective the
only difference between these two functions occurs if they wish to
supply their own prior distribution: `rpost_rcpp`

requires an
external pointer to a C++ function (see Providing a
user-defined prior), whereas `rpost`

requires an input R
function (see the vignette Introducing revdbayes.

Before we deal with user-supplied priors we compare posterior
simulation times using `rpost`

and `rpost_rcpp`

for examples based on in-built prior distributions. We use the default
settings of `rpost`

and `rpost_rcpp`

throughout.
We also compare the speed of these functions with the function
`posterior`

in the **evdbayes** package (Stephenson and Ribatet 2014), using the
**microbenchmark** package (Mersmann
2015).

```
library(revdbayes)
# Is the microbenchmark package available?
got_microbenchmark <- requireNamespace("microbenchmark", quietly = TRUE)
if (got_microbenchmark) {
library(microbenchmark)
}
# Set the number of posterior samples required.
n <- 1000
set.seed(46)
```

We repeat the analysis of the Gulf of Mexico Wave Height Data from the Introducing revdbayes vignette to check that using Rcpp does indeed reduce computation time.

```
u <- quantile(gom, probs = 0.65)
fp <- set_prior(prior = "flat", model = "gp", min_xi = -1)
if (got_microbenchmark) {
res <- microbenchmark(
rpost = rpost(n = n, model = "gp", prior = fp, thresh = u, data = gom),
rpost_rcpp = rpost_rcpp(n = n, model = "gp", prior = fp, thresh = u,
data = gom)
)
print(res, signif = 3)
options(microbenchmark.unit = "relative")
print(res, signif = 2)
}
#> Unit: milliseconds
#> expr min lq mean median uq max neval
#> rpost 81.1 85.6 96.3 88.5 94.7 285.0 100
#> rpost_rcpp 16.2 17.4 20.3 18.8 20.4 57.3 100
#> Unit: relative
#> expr min lq mean median uq max neval
#> rpost 5 4.9 4.7 4.7 4.7 5 100
#> rpost_rcpp 1 1.0 1.0 1.0 1.0 1 100
```

In this example `rpost_rcpp`

is indeed much faster than
`rpost`

.

We repeat the analysis of the Port Pirie annual maximum sea level data from the Introducing revdbayes.

```
mat <- diag(c(10000, 10000, 100))
pn <- set_prior(prior = "norm", model = "gev", mean = c(0,0,0), cov = mat)
if (got_microbenchmark) {
res <- microbenchmark(
rpost = rpost(n = n, model = "gev", prior = pn, data = portpirie),
rpost_rcpp = rpost_rcpp(n = n, model = "gev", prior = pn,
data = portpirie)
)
}
options(microbenchmark.unit = NULL)
print(res, signif = 3)
#> Unit: milliseconds
#> expr min lq mean median uq max neval
#> rpost 216.0 226.0 240.0 232.0 243.0 391 100
#> rpost_rcpp 59.1 63.9 69.6 66.7 69.7 197 100
options(microbenchmark.unit = "relative")
print(res, signif = 2)
#> Unit: relative
#> expr min lq mean median uq max neval
#> rpost 3.6 3.5 3.5 3.5 3.5 2 100
#> rpost_rcpp 1.0 1.0 1.0 1.0 1.0 1 100
```

Comparison to the example calculations that feature in the
**evdbayes** user guide, based on the
`posterior`

function, are not shown because
**evdbayes** is archived on CRAN. This comparison shows
that `rpost_rcpp`

is approximately a factor 3 faster than
`posterior`

. This comparison is generous to
`posterior`

because the burn-in was set to zero and
`posterior`

produces a dependent sample rather than a random
sample. The *effective sample size* of an MCMC sample from
`posterior`

varies between simulations and across parameters.
The `effectiveSize`

function in the **coda**
package (Plummer et al. 2006) suggests
that the effective sample size in this example is of the order of 100 to
200, whereas the **revdbayes** functions `rpost`

and `rpost_rcpp`

produce random samples of size 1000.
`rpost`

is a little slower than `posterior`

.

We compare the computational efficiencies of `rpost`

and
`rpost_rcpp`

when performing the analysis of daily rainfall
totals from the Introducing
revdbayes.

```
# Informative prior set using revdbayes
pr2 <- set_prior(prob = 10^-(1:3), shape = c(38.9, 7.1, 47),
scale = c(1.5, 6.3, 2.6), model = "gev", prior = "quant")
if (got_microbenchmark) {
res <- microbenchmark(
rpost = rpost(n = n, model = "pp", prior = pr2, data = rainfall,
thresh = 40, noy = 54),
rpost_rcpp = rpost_rcpp(n = n, model = "pp", prior = pr2,
data = rainfall, thresh = 40, noy = 54)
)
}
options(microbenchmark.unit = NULL)
print(res, signif = 3)
#> Unit: milliseconds
#> expr min lq mean median uq max neval
#> rpost 365.0 389.0 409.0 399.0 423.0 594 100
#> rpost_rcpp 36.2 39.9 43.2 41.9 44.8 86 100
options(microbenchmark.unit = "relative")
print(res, signif = 2)
#> Unit: relative
#> expr min lq mean median uq max neval
#> rpost 10 9.8 9.5 9.5 9.4 6.9 100
#> rpost_rcpp 1 1.0 1.0 1.0 1.0 1.0 100
```

Again, a comparison with the function `posterior`

in
**evdbayes** is not shown, but `rpost`

is slower
and `rpost_rcpp`

substantially faster than
`posterior`

.

If the user wishes to supply their own prior to
`rpost_rcpp`

then they must first write a C++ function that
evaluates the log of the prior density. The general way that
**rust** (and hence **revdbayes**) enables
users to provide their own C++ log-prior functions uses external
pointers and is based on the Rcpp
Gallery article Passing
user-supplied C++ functions by Dirk Eddelbuettel.

The implementation in **rust** requires this C++
function to have a particular structure: it must take a constant
reference to an `Rcpp::NumericVector`

, say `x`

, a
constant reference to an `Rcpp::List`

, say
`ppars`

, and return a `double`

precision scalar.
Here `x`

is the argument of the prior density, i.e. the
parameter vector of the extreme value model, and `ppars`

is a
list containing the values of prior parameters whose values are not
specified inside the function. Thus values of any parameters in the
prior can be changed without editing the function. If there are no such
parameters then the argument `ppars`

must still be present in
the C++ function, even though the list provided to the function will be
empty.

A simple way to provide C++ log-prior functions is to put them in a
file, say `user_fns.cpp`

, perhaps taking advantage of the
R-like syntax made available by Rcpp
sugar. Example content is provided below. This file is available on
the revdbayes
Github page.The functions in this file are compiled and made
available to R, either using the `Rcpp::sourceCpp`

function
(e.g. `Rcpp::sourceCpp("user_fns.cpp")`

) or using RStudio’s
Source button on the editor toolbar. The example content below also
includes the function `create_prior_xptr`

, which creates an
external pointer to a C++ function. See . It is this external pointer
that is passed to `set_prior`

to set the prior. If the user
has written a C++ function, say `new_name`

, they need to add
to `create_prior_xptr`

two lines of code:

```
else if (fstr == "new_name")
return(Rcpp::XPtr<funcPtr>(new funcPtr(&new_name))) ;
```

in order that they can create an external pointer for
`new_name`

using `create_xptr`

.

The following excerpt from the example `user_fns.cpp`

file
contains a C++ function `user_gp_flat`

to evaluate (the log
of) a prior density \(\pi(\sigma, \xi) \propto
\sigma^{-1}, \, \sigma > 0\), with an extra parameter
`min_xi`

enabling a prior lower bound to be set for \(\xi\). The same prior can be set, using an
in-built prior function, using
`set_prior(prior = "flat", model = "gp", min_xi = -1)`

, where
we have set `min_xi = -1`

. Note that . Hence in
`user_gp_flat`

\(\sigma\)
and \(\xi\) are `x[0]`

and
`x[1]`

not `x[1]`

and `x[2]`

.

```
// [[Rcpp::depends(Rcpp)]]
#include <Rcpp.h>
using namespace Rcpp;
// [[Rcpp::interfaces(r, cpp)]]
// Generalized Pareto log-priors
// [[Rcpp::export]]
double user_gp_flat(const Rcpp::NumericVector& x, const Rcpp::List& ppars) {
double min_xi = ppars["min_xi"] ;
if (x[0] <= 0 || x[1] < min_xi)
return R_NegInf ;
return -log(x[0]) ;
}
// [[Rcpp::export]]
SEXP create_prior_xptr(std::string fstr) {
typedef double (*priorPtr)(const Rcpp::NumericVector& x,
const Rcpp::List& ppars) ;
if (fstr == "gp_flat")
return(Rcpp::XPtr<priorPtr>(new priorPtr(&user_gp_flat))) ;
else
return(Rcpp::XPtr<priorPtr>(R_NilValue)) ;
}
// We could create an external pointer when this file is sourced using
// this embedded R code below and/or (re)create them using the relevant
// pointer-creation functions in an R session or R package.
/*** R
ptr_gp_flat <- create_prior_xptr("gp_flat")
*/
```

Once the external pointer to the user-supplied prior C++ function has
been created it is passed to `set_prior`

, along with any
required parameter values. The following example repeats the example in
Generalised Pareto (GP) model. The difference
is that now we create the pointer `ptr_gp_flat`

and pass it
to `set_prior`

using `prior = ptr_gp_flat`

rather
than using the arguments `prior = "flat", model = "gp"`

to
specify the equivalent in-built prior.

Eddelbuettel, D., and R. Francois. 2011. “Rcpp: Seamless
R and C++ Integration.” *Journal of
Statistical Software* 40 (8): 1–18. doi:10.18637/jss.v040.i08.

Mersmann, O. 2015. *Microbenchmark: Accurate Timing Functions*.
https://CRAN.R-project.org/package=microbenchmark.

Northrop, P. J. 2017. *rust:
Ratio-of-Uniforms Simulation with Transformation*. https://CRAN.R-project.org/package=rust.

Plummer, M., N. Best, K. Cowles, and K. Vines. 2006. “CODA:
Convergence Diagnosis and Output Analysis for MCMC.”
*R News* 6 (1): 7–11. https://www.r-project.org/doc/Rnews/Rnews_2006-1.pdf.

Stephenson, A., and M. Ribatet. 2014. *evdbayes: Bayesian Analysis in Extreme Value
Theory*. https://CRAN.R-project.org/package=evdbayes.