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How to increase precision to handle very low P-values

3 messages · alonso_canada, Duncan Murdoch

alonso_canada
# 
Hello, Rlisters

I have to compute p-values that are on the tail of the distribution,
P-values < 10^-20.

However, my current implementations enable one to estimate P-values up to
10^-12, or so.

A typical example is found below, where t is my critical value.

########### example - code adapted from Rassoc #######################

rho01 = 0.5
rho105 = 0.5
rho005  = 0.5
t = 8
z = 2

w0=(rho005-rho01*rho105)/(1-rho01^2)
w1=(rho105-rho01*rho005)/(1-rho01^2)
  
 
 fun1=function(t,z){
 return(pnorm((t-rho01*z)/sqrt(1-rho01^2))*dnorm(z))
 }
 fun2=function(t,z){
 return(pnorm(((t-w0*z)/w1-rho01*z)/sqrt(1-rho01^2))*dnorm(z))
 }
 fun3=function(t,z){
 return(pnorm((-t-rho01*z)/sqrt(1-rho01^2))*dnorm(z))
 }
 
asy=function(t){
z1=2*integrate(function(z){fun1(t,z)},lower=0,upper=t*(1-w1)/w0,subdivisions=1000)$value
z2=2*integrate(function(z){fun2(t,z)},lower=t*(1-w1)/w0,upper=t,subdivisions=1000)$value
z3=-2*integrate(function(z){fun3(t,z)},lower=0,upper=t,subdivisions=500)$value
return(z1+z2+z3)
}
    
pvalue <-  1-asy(t)
pvalue
 ###########################################

Using this script, my critical values can achieve values up to 7.5, or so.
Above this cutoff my P-values show up as negative values. Why's that?


Grateful for any tips.

All the best,

Alonso


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Duncan Murdoch
#
On 23/11/2011 11:16 AM, alonso_canada wrote:
The p* functions (pnorm, etc.) generally have a "log" argument, so they 
can return logs of probabilities.  Together with the "lower" argument, 
they have a huge range.

To use them with integrate(), rescale them.  For example, to find the 
integral of pnorm() from z=-32 to -30 you could do:

maxval <- pnorm(-30, log=TRUE)
scaled <- function(x) exp( pnorm(x, log=TRUE) - maxval )
scaledintegral <- integrate(scaled, lower=-32, upper=-30)
# Log of the result:
log(scaledintegral$value) + maxval

(The answer is -457.7, so it is actually representable:  1.631957e-199.)

Duncan Murdoch