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```
# R FUNCTIONS FOR PERFORMING UNIVARIATE SLICE SAMPLING.
#
# Radford M. Neal, 17 March 2008.
#
# Implements, with slight modifications and extensions, the algorithm described
# in Figures 3 and 5 of the following paper:
#
# Neal, R. M (2003) "Slice sampling" (with discussion), Annals of Statistics,
# vol. 31, no. 3, pp. 705-767.
#
# See the documentation for the function uni.slice below for how to use it.
# The function uni.slice.test was used to test the uni.slice function.
# GLOBAL VARIABLES FOR RECORDING PERFORMANCE.
#uni.slice.calls <- 0 # Number of calls of the slice sampling function
#uni.slice.evals <- 0 # Number of density evaluations done in these calls
# UNIVARIATE SLICE SAMPLING WITH STEPPING OUT AND SHRINKAGE.
#
# Performs a slice sampling update from an initial point to a new point that
# leaves invariant the distribution with the specified log density function.
#
# Arguments:
#
# x0 Initial point
# g Function returning the log of the probability density (plus constant)
# w Size of the steps for creating interval (default 1)
# m Limit on steps (default infinite)
# lower Lower bound on support of the distribution (default -Inf)
# upper Upper bound on support of the distribution (default +Inf)
# gx0 Value of g(x0), if known (default is not known)
#
# The log density function may return -Inf for points outside the support
# of the distribution. If a lower and/or upper bound is specified for the
# support, the log density function will not be called outside such limits.
#
# The value of this function is the new point sampled, with an attribute
# of "log.density" giving the value of the log density function, g, at this
# point. Depending on the context, this log density might be passed as the
# gx0 argument of a future call of uni.slice.
#
# The global variable uni.slice.calls is incremented by one for each call
# of uni.slice. The global variable uni.slice.evals is incremented by the
# number of calls made to the g function passed.
#
# WARNING: If you provide a value for g(x0), it must of course be correct!
# In addition to giving wrong answers, wrong values for gx0 may result in
# the uni.slice function going into an infinite loop.
MfU.UniSlice <- function (x0, f, ..., w=1, m=Inf, lower=-Inf, upper=+Inf, gx0=NULL)
{
g <- function(x) f(x,...)
# Check the validity of the arguments.
if (!is.numeric(x0) || length(x0)!=1
|| !is.function(g)
|| !is.numeric(w) || length(w)!=1 || w<=0
|| !is.numeric(m) || !is.infinite(m) && (m<=0 || m>1e9 || floor(m)!=m)
|| !is.numeric(lower) || length(lower)!=1 || x0<lower
|| !is.numeric(upper) || length(upper)!=1 || x0>upper
|| upper<=lower
|| !is.null(gx0) && (!is.numeric(gx0) || length(gx0)!=1))
{
stop ("Invalid slice sampling argument")
}
# Keep track of the number of calls made to this function.
#uni.slice.calls <<- uni.slice.calls + 1
# Find the log density at the initial point, if not already known.
if (is.null(gx0))
{
#uni.slice.evals <<- uni.slice.evals + 1
gx0 <- g(x0)
}
# Determine the slice level, in log terms.
logy <- gx0 - rexp(1)
# Find the initial interval to sample from.
u <- runif(1,0,w)
L <- x0 - u
R <- x0 + (w-u) # should guarantee that x0 is in [L,R], even with roundoff
# Expand the interval until its ends are outside the slice, or until
# the limit on steps is reached.
if (is.infinite(m)) # no limit on number of steps
{
repeat
{ if (L<=lower) break
#uni.slice.evals <<- uni.slice.evals + 1
if (g(L)<=logy) break
L <- L - w
}
repeat
{ if (R>=upper) break
#uni.slice.evals <<- uni.slice.evals + 1
if (g(R)<=logy) break
R <- R + w
}
}
else if (m>1) # limit on steps, bigger than one
{
J <- floor(runif(1,0,m))
K <- (m-1) - J
while (J>0)
{ if (L<=lower) break
#uni.slice.evals <<- uni.slice.evals + 1
if (g(L)<=logy) break
L <- L - w
J <- J - 1
}
while (K>0)
{ if (R>=upper) break
#uni.slice.evals <<- uni.slice.evals + 1
if (g(R)<=logy) break
R <- R + w
K <- K - 1
}
}
# Shrink interval to lower and upper bounds.
if (L<lower)
{ L <- lower
}
if (R>upper)
{ R <- upper
}
# Sample from the interval, shrinking it on each rejection.
repeat
{
x1 <- runif(1,L,R)
#uni.slice.evals <<- uni.slice.evals + 1
gx1 <- g(x1)
if (gx1>=logy) break
if (x1>x0)
{ R <- x1
}
else
{ L <- x1
}
}
# Return the point sampled, with its log density attached as an attribute.
attr(x1,"log.density") <- gx1
return (x1)
}
```

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