Some Comments on C. S. Wallace's Random Number Generators

Abstract

We outline some of Chris Wallace's contributions to pseudo-random number generation. In particular, we consider his recent idea for generating normally distributed variates without relying on a source of uniform random numbers, and compare it with more conventional methods for generating normal random numbers. Implementations of Wallace's idea can be very fast (approximately as fast as good uniform generators). We discuss the statistical quality of the output, and mention how certain pitfalls can be avoided.

Universal psychometrics: Measuring cognitive abilities in the machine kingdom

“…The physical Church-Turing thesis states that "every finitely realizable physical system can be perfectly simulated by a universal model computing machine operating by finite means" (Deutsch, 1985), i.e., a resource-bounded Turing machine 4 . This is compatible with considering animals non-deterministic, since physical machines can be made non-deterministic by any external (physical) source of randomness, such as physically random number generators (Wallace, 1990;Brent, 2008). On some occasions, we explain with non-determinism some effects which can easily be explained with deterministic machines.…”

MML, Hybrid Bayesian Network Graphical Models, Statistical Consistency, Invariance and Uniqueness

“…But better still, 'Poor, yet delighting in the Way; rich, yet a student of ritual.' " I thank Chris Wallace [Gupta et al, 2004;Dowe, 2008a, footnote 218] (for a variety of matters -such as, e.g., the letter referred to in [Dowe, 2008a, footnote 218] and all the training he gave me over the years), for whose Christopher Stewart WALLACE memorial special issue of the Computer Journal Brennan, 2008;Solomonoff, 2008;Jorgensen and McLachlan, 2008;Brent, 2008;Colon-Bonet and Winterrowd, 2008;Castro et al, 2008] it was an honour to be guest editor. (For other mention and examples of the range and importance of his work, see, e.g., [Parry, 2005] and [Clark and Wallace, 1970].)…”

Foreword re C. S. Wallace

“…30 who subsequently wrote [180] 31 after finishing this sentence, the reader is at liberty to skip to sec. 0.3.1 re this issue's authors and their contributed articles [40,228,143,47,63,49]. 32 I will say that there have been quite a few people who have been anything from sceptical to downright categorically dismissive [and not always politely] upon first hearing about MML, and yet at least two such people that I can immediately think of have gone on to embrace MML (not always with the most complete memory).…”

“…0.2.2 and in footnotes 82 and 185) wrote shortly after Chris's death: "I feel very privileged to have had the opportunity to assist Chris in his work -he had an amazing brain and memory for facts and figures (one member of staff said to me once "I will ask Chris -he knows everything.")." 45 already the author of [263,269,272] 46 for a discussion of this work, see Richard P. Brent's paper in this issue [47] 47 Dr Peter E. Tischer tells me that he once asked Chris about applying MML to images (and compression thereof) and that Chris seemed to respond to such comments as (invitations or) challenges. Peter says that his comment is what led to [283].…”

“…Another example is fastnorm3 from (sec. 0.3.1 [Brent] and) [47]. 138 Following on from footnote 137 immediately above, I am fairly regularly asked about schemes for (MDL or) MML cut-points.…”