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, Eddelbuettel (2013)). 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)
# Are microbenchmark and evdbayes available?
got_microbenchmark <- requireNamespace("microbenchmark", quietly = TRUE)
got_evdbayes <- requireNamespace("evdbayes", quietly = TRUE)
if (got_microbenchmark) {
library(microbenchmark)
}
if (got_evdbayes) {
library(evdbayes)
}
# 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 111.0 119.0 125.77119 123 129.0 213 100
#> rpost_rcpp 19.6 20.2 26.98988 21 23.7 293 100
#> Unit: relative
#> expr min lq mean median uq max neval
#> rpost 5.7 5.9 4.659939 5.9 5.4 0.73 100
#> rpost_rcpp 1.0 1.0 1.000000 1.0 1.0 1.00 100
```

In this example `rpost_rcpp`

is, on average, a factor of approximately 8-9 times faster than `rpost`

.

We repeat the analysis of the Port Pirie annual maximum sea level data from the Introducing revdbayes. We add to the comparison the example calculations that feature in the **evdbayes** user guide, based on the `posterior`

function.

```
mat <- diag(c(10000, 10000, 100))
pn <- set_prior(prior = "norm", model = "gev", mean = c(0,0,0), cov = mat)
# Tuning parameters from the evdbayes user guide.
t0 <- c(3.87, 0.2, -0.05)
s <- c(.06, .25, .25)
if (got_microbenchmark) {
if (got_evdbayes) {
res <- microbenchmark(
rpost = rpost(n = n, model = "gev", prior = pn, data = portpirie),
rpost_rcpp = rpost_rcpp(n = n, model = "gev", prior = pn,
data = portpirie),
evdbayes = posterior(n = n, init = t0, prior = pn, lh = "gev",
data = portpirie, psd = s, burn = 0)
)
} else {
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)
options(microbenchmark.unit = "relative")
print(res, signif = 2)
}
#> Unit: milliseconds
#> expr min lq mean median uq max neval
#> rpost 249.0 263.0 276.05224 271.0 280.0 390 100
#> rpost_rcpp 71.3 74.8 79.35369 77.3 82.2 104 100
#> evdbayes 208.0 216.0 228.92112 224.0 236.0 298 100
#> Unit: relative
#> expr min lq mean median uq max neval
#> rpost 3.5 3.5 3.478757 3.5 3.4 3.8 100
#> rpost_rcpp 1.0 1.0 1.000000 1.0 1.0 1.0 100
#> evdbayes 2.9 2.9 2.884820 2.9 2.9 2.9 100
```

This comparison is generous to `posterior`

because the burn-in has been 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 less than 50% slower than `posterior`

while `rpost_rcpp`

is faster than `posterior`

by a factor of 4.

We compare the computational efficiencies of `rpost`

, `rpost_rcpp`

and the evdbayes function `posterior`

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")
# Tuning parameters from the evdbayes user guide.
t0 <- c(43.2, 7.64, 0.32)
s <- c(2, .2, .07)
if (got_microbenchmark) {
if (got_evdbayes) {
# Informative prior set using evdbayes
pr <- prior.quant(prob = 10^-(1:3), shape = c(38.9, 7.1, 47),
scale = c(1.5, 6.3, 2.6))
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),
evdbayes = posterior(n = n, init = t0, prior = pr, "pp", data = rainfall,
thresh = 40, noy = 54, psd = s, burn = 0)
)
} else {
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)
options(microbenchmark.unit = "relative")
print(res, signif = 2)
}
#> Unit: milliseconds
#> expr min lq mean median uq max neval
#> rpost 438.0 455.0 471.23499 467.0 478.0 576 100
#> rpost_rcpp 46.3 49.3 52.94718 51.1 53.3 125 100
#> evdbayes 282.0 288.0 302.51777 295.0 309.0 388 100
#> Unit: relative
#> expr min lq mean median uq max neval
#> rpost 9.5 9.2 8.900096 9.1 9.0 4.6 100
#> rpost_rcpp 1.0 1.0 1.000000 1.0 1.0 1.0 100
#> evdbayes 6.1 5.8 5.713577 5.8 5.8 3.1 100
```

In this example `rpost`

is more than a factor of two slower than `posterior`

but `rpost_rcpp`

is 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.

```
# GP model, user-defined prior
ptr_gp_flat <- create_prior_xptr("gp_flat")
p_user <- set_prior(prior = ptr_gp_flat, model = "gp", min_xi = -1)
gpg <- rpost_rcpp(n = 1000, model = "gp", prior = p_user, thresh = u,
data = gom)
```

Eddelbuettel, D. 2013. *Seamless R and C++ Integration with Rcpp*. New York: Springer. http://www.springer.com/gb/book/9781461468677.

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://journal.r-project.org/archive/.

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