Prioblems with the "Deriv" R package - r

Question

I am having two related problems with the Deriv() function from the Deriv package (from CRAN).
Problem (1): I believe that the code in the rule for differentiating dbinom() w.r.t "prob" is incorrect. Evidence for this (and my proposed correction) is shown in the following code. I would have preferred to attach text files containing the code, but as far as I can see there is no way to do this.
#
# Script demo01.R.
#
library(Deriv)
# Plot dbinom as a function of probabiity.
plot(function(p){dbinom(3,8,p)},from=0,to=1,xlab="parameter \"prob\"",
ylab="binomial probability",main="dbinom")
abline(v=3/8,col="red")
readline("Go? ")
# Plot the derivative of dbinom, with respect to prob, calculated by
# Deriv(), as a function of probability.
Ddb <- Deriv(dbinom,"prob")
plot(function(p){Ddb(3,8,p)},from=0,to=1,xlab="parameter \"prob\"",
ylab="",main="derivative of dbinom")
readline("Go? ")
# Replace what I believe to be incorrect code for the rule for
# differentiating dbinom() with what I believe to be correct code.
# This rule should, strictly speaking, be placed in a new environment
# rather than over-writing the existing rule, but this seems to
# break down when second derivatives are taken.
drule[["dbinom"]] <- alist(x=NULL,size=NULL,prob={
.e1 <- 1 - prob
.e2 <- size - 1
if (x == 0)
-(x * .e1^(x - 1))
else if (x == size)
prob^.e2 * size
else size*(dbinom(x-1,.e2,prob) - dbinom(x,.e2,prob)) *
(if (log) dbinom(x, size, prob) else 1)
})
# Plot the derivative of dbinom, with respect to prob, calculated by
# the corrected version of Deriv(), as a function of probability.
Ddb <- Deriv(dbinom,"prob")
plot(function(p){Ddb(3,8,p)},from=0,to=1,xlab="parameter \"prob\"",
ylab="",main="derivative of dbinom, corrected")
abline(v=3/8,col="red")
abline(h=0,col="blue")
You will observe that the derivative of dbinom()
should be positive for prob < 3/8 and negative for prob > 3/8. My corrected version has this property, whereas the derivative produced by the uncorrected version is negative everywhere.
Can anyone confirm that I am right about about there being a bug in the Deriv package? (I.e. that I am not making some sort of stupid mistake?)
Problem (2). I "crosschecked" the calculations performed by Deriv() by applying this function to a "roll-your-own" version of dbinom() for which no special rule is needed. I also applied the (corrected version) of Deriv() to dbinom(). The code that I used is as follows:
#
# Script demo02.
#
library(Deriv)
# Replace what I believe to be incorrect code for the rule for
# differentiating dbinom() with what I believe to be correct code.
# This rule should, strictly speaking, be placed in a new environment
# rather than over-writing the existing rule, but this seems to
# break down when second derivatives are taken.
drule[["dbinom"]] <- alist(x=NULL,size=NULL,prob={
.e1 <- 1 - prob
.e2 <- size - 1
if (x == 0)
-(x * .e1^(x - 1))
else if (x == size)
prob^.e2 * size
else size*(dbinom(x-1,.e2,prob) - dbinom(x,.e2,prob)) *
(if (log) dbinom(x, size, prob) else 1)
},log=NULL)
fooB1 <- function(x,prob,size) {
dbinom(x,size,prob)
}
fooB2 <- function(x,prob,size) {
choose(size,x)*prob^x*(1-prob)^(size-x)
}
dfooB1 <- Deriv(fooB1,"prob")
dfooB2 <- Deriv(fooB2,"prob")
d2fooB1 <- Deriv(fooB1,"prob",nderiv=2)
d2fooB2 <- Deriv(fooB2,"prob",nderiv=2)
vB1 <- fooB1(x=3,prob=0.6,size=8)
vB2 <- fooB2(x=3,prob=0.6,size=8)
dB1 <- dfooB1(x=3,prob=0.6,size=8)
dB2 <- dfooB2(x=3,prob=0.6,size=8)
d2B1 <- d2fooB1(x=3,prob=0.6,size=8)
d2B2 <- d2fooB2(x=3,prob=0.6,size=8)
If you run this code you will see that the function values (vB1 and vB2) agree, both having the value 0.123863. Likewise the first derivative values dB1 and dB2 agree: -0.9289728.
However the second derivatives disagree. The value of d2B1 is 1.769472, whereas the value of d2B2 is 2.064384. I have no idea which (if either) of these answers is correct.
Something (the chain rule?) is not working as it should.
Is there any action that I can take to resolve this discrepancy?