CSIRO - Mathematical and Information Sciences - Staff Look-up - Geoff Robinson
Staff Profile
Geoff Robinson
Professional Interests
Continuous-time Brownian motion
I have submitted a paper titled "Simple procedures for data analysis based on continuous-time Brownian motion" to Series C of the Journal of the Royal Statistical Society. A recent draft is in a file called WBH15.pdf. The figures and many of the calculations presented in that paper can be produced using the R code in a file called WBH15.R. This R code makes use of some R functions in a file called Preliminaries15.R and it should be noted that some checks of these functions are given in the file called Checks.R. The R code in WBH15.R also makes use of some functions written in C. The source code for these functions is in a file called myc.c; a dynamic linked library for calling these functions from R under Windows operating systems is in a file called MyC.dll; the R interfaces to those functions are in a file called MyC.R; and R code for checking that these functions are operating correctly is in a file called MyC.checks.R.
I have a general intention of either producing an R package that covers the most useful of these facilities or supporting the code as listed above for a few years and slowly improving the documentation. However, this is not guaranteed.
Maximally skew stable distributions
In September 2005 I completed a report about rapid calculation of the probability density and distribution function for maximally skew stable distributions. This report is in a file called combined.pdf. The rapid calculations are achieved by using interpolation formulae and some transformations of variables based on asymptotic formulae given by Zolotarev.
I am making some of these calculations available through this web page for research purposes, but not for commercial purposes. File selfcontained.S gives commands in Splus or R for reasonably accurate calculation of the distribution function for stable distributions. Its style of calculation illustrates many of the principles discussed in the report.
File test.c gives C code for a number of functions concerned with maximally skew stable distributions, including the calculation of the value of call options. This needs to be compiled and loaded into Splus with the Splus functions in the file functions.S and the set of commands test.S in order to produce the graphs which are given in the report. The interpolation code also needs to be able to read the file interpolationdata.keep. The other file which is needed for two of the graphs in the report is called modes.keep. It has some data about the modes of maximally skew stable distributions for various values of the parameter alpha.
Foundations of statistics
University postgraduate work.
My Ph.D. degree from University College London in 1975 was for a thesis entitled
"Conservative statistical inference" which looked at the conditional properties
of statistical procedures. That is, it considered the question ``Can you bet against the
conclusions of a statistical procedure and be reasonably sure of winning?'' Papers 1, 2,
4, 5, 7 and 8 arose out of my university research work.
Confidence intervals.
Paper 1 gave a sequence of three examples of simple situations for which Neyman's theory
of Confidence intervals gives
intuitively unreasonable results. It is regarded as a landmark paper by some Bayesian
statisticians and is ignored by most
Classical statisticians.
The two means problem.
I support the Behrens-Fisher solution to the two means problem, as explained in papers 2
and 9.
Fixed and random effects.
Paper number 13 explains my views on the estimation of fixed and random effects. I believe
this to have been a fairly
influential paper. I believe that the value judgements which it espouses are now fairly
generally accepted.
My view on the foundations of statistical inference.
Paper 4 summarizes my views on on the foundations of statistical inference. I believe that
statistical procedures should be be selected to have both conservative coverage properties
and conservative conditional properties. The simplest situation where this approach leads
to procedures which are radically different from conventional procedures is for testing
between two simple hypotheses.
For instance, the most stringent possible ``conservative'' test between the hypotheses H0:
X is normally distributed with mean zero and variance 1 and H1: X is normally distributed
with mean 4 and variance 1 on the basis of a single observation is as follows.
Accept H0 at confidence level 0.9184 if X<1.395.
Accept H1 at confidence level 0.9184 if X>2.605.
Make no decision if 1.395<X<2.605.
This has the properties that the probability of accepting a true hypothesis is at least
the nominal confidence level, 0.9184, and there are no subsets of possible outcomes
such that the conditional probability of accepting incorrect hypotheses, given that the
outcome is in a specified subset, exceed the nominal error rate of 1-0.9184=0.0816.
probability. The second of these properties follows from the fact that the
likelihood ratio is (1-0.9184)/0.9184 at one of the cut-off points, and its reciprocal at
the other.
In contrast, a Neyman-Pearson test between these two hypotheses with cut-off point 2 would
claim that the probabilities of type I and type II error are both 0.0228, and fails to
recognise that these probabilities are of little relevance once the data (say, X=1.9)
becomes known.
1. ROBINSON, G.K. (1975). Some counterexamples to the theory of confidence intervals.
Biometrika 62 155-161.
2. ROBINSON, G.K. (1976). Properties of Student's t and of the Behrens-Fisher solution to
the two means problem. Annals of Statistics 4 963-971.
3. ROBINSON, G.K. (1977). Confidence intervals. Royal Statistical Society News &
Notes. (February 1977) 2-3.
4. ROBINSON, G.K. (1977). Conservative statistical inference. J. Roy. Statist. Soc. B 39
381-386.
5. ROBINSON, G.K. (1978). On the necessity of Bayesian inference and the construction of
measures of nearness to
Bayesian form. Biometrika 65 49-52.
6. ROBINSON, G.K. (1978). Comments on paper by Efron and Hinkley. Biometrika 65 485.
7. ROBINSON, G.K. (1979). Conditional properties of statistical procedures. Annals of
Statistics 7 742-755.
8. ROBINSON, G.K. (1979). Conditional properties of statistical procedures for location
and scale parameters. Annals of Statistics 7 756-771.
9. ROBINSON, G.K. (1982). The Behrens-Fisher Problem. Encyclopedia of Statistical
Sciences, Volume 1 205-209.
Wiley.
10. ROBINSON, G.K. (1982). Confidence intervals and regions. Encyclopedia of Statistical
Sciences, Volume 2 120-127. Wiley.
11. ROBINSON, G.K. (1987). Barnard's hypothesis testing paradox. Royal Statistical Society
News & Notes. (December 1987) 2.
12. ROBINSON, G.K. (1987). Instructions to referees -- Do we need some? Aust. J.
Statistics, 29 220-221. (Letter to the
editor).
13. ROBINSON, G.K. (1991). That BLUP is a good thing -- The estimation of random effects.
Statistical Science, 6 No. 115-51.
14. G.M. LASLETT, C.J. Lloyd & G.K. ROBINSON. (1994). Encounters with statistical
inference -- An interview with Evan Williams. The Australian Journal of Statistics, 36 No.
2 133-152.
Geoff Robinson
1998-11-16
Back to Geoff Robinson Home Page
last updated
23/03/09
Geoff.Robinson@cmis.csiro.au