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Introduction

My name is Russell J. Bowater. I live in southern Mexico and I carry out research in the area of probability and statistics. I was a tenured associate professor in a private university, but now I am an independent scientist (and quite proud to be so). If you are interested, my academic and work history can be found here. Also, I have a (very new) Twitter page, which can be found here.

Details are given below of a selection of my published 
papers about the foundations of statistics, along with a description of how the papers came into being. A list of all my published papers can be found here.

My opinion about editorial decision letters can be found here (my sorry attempt at humour).

Please note that, as of 15th December 2017, I no longer have access to the email address "russell.bowater@udlap.mx" which I used in two recent papers. Therefore, please contact me using the information in my "extras about me" page, which can be found here.

Highlighted papers

Bowater, R. J. and Guzmán-Pantoja, L. E. (2019). Bayesian, classical and hybrid methods of inference when one parameter value is special. Journal of Applied Statistics, 46, 1417-1437.
Also available as: Bowater, R. J. and Guzmán-Pantoja, L. E. (2018). [same title]. arXiv.org (Cornell University), Statistics, arXiv:1809.02089.
This version of the paper can be found here.

This paper was written in late 2015 and early 2016, however, similar to the two papers published in 2017 that are discussed below, I had the idea for it many years before. In fact, this paper and these two earlier papers form a natural set of three papers, since all three were planned during my four years in Italy (2002 to 2006), and also in the sense that I did not have a clue at the time how the work in these papers could be extended or combined to form any kind of unifying theory (!) For this reason, although the paper is a largely valid piece of work that discusses some important topics, it certainly, at least from my point of view, feels a bit patched up in places. Also, to provide a balanced overview, it is sympathetic to methods, e.g. the two-step Bayesian method, that in fact I would never advocate in a million years (!)

The first journal that this paper was sent to was Statistical Methods in Medical Research, and although it was well understood and viewed largely favourably by the two anonymous referees, it was nevertheless turned down due to space priorities. I would like to thank these two referees as they gave me hope that the importance of such a controversial paper would be appreciated at least by some open-minded souls.

Bowater, R. J. (2017). A defence of subjective fiducial inference. AStA Advances in Statistical Analysis, 101, 177-197.
The author's accepted version of this paper can be found here.
The published version of this paper can be found here.

I had the essential idea that forms the basis of this paper in 1999. Much later I labelled this idea as "subjective fiducial inference". However, other projects and a need to develop a concept of probability to justify this type of inference meant that I did not complete a draft of a paper on this topic until 2004. The paper though was not submitted for publication immediately, and as time passed by I became dissatisfied with the style in which the paper was written to the extent that in 2007 I decided that it was best not to ever have it reviewed. Consequently, I began
writing another paper on the same topic in 2008, but by 2010 I also became dissatisfied with the style of this second paper meaning that despite being at an advanced writing stage it was never actually completed.

It was then in 2012 that I decided on a third way of presenting the idea of subjective fiducial inference in the form of a paper, which this time would be as a very clear defence of this type of inference against criticisms that I expected would be raised against it. This paper was submitted for publication in 2013, and was eventually accepted by AStA Advances in Statistical Analysis in 2016, that is, more than 17 years after I had realized the value of the original idea!

As I acknowledge in the paper, it was David Draper who first outlined the fiducial argument to me while in a London pub in 1998 (a year after I had obtained my PhD in statistics!), although I should clarify that he was simply satisfying my curiosity and not actually advocating it. I had the privilege of sharing many interesting conservations with David Draper on the foundations of statistics during a period of time (1996 to 1999) when, like him, my thinking was mainly Bayesian. I am very grateful to David for that. I also thank Göran Kauermann for his saintly patience as editor of AStA Advances in Statistical Analysis.

Bowater, R. J. (2017). A formulation of the concept of probability based on the use of experimental devices. Communications in Statistics: Theory and Methods46, 4774-4790.
The author's corrected original and preferred version of this paper can be found here.
The published version of this paper can be found here.

I became interested in trying to define probability using the idea of similarity in 2000. A first draft of a paper on this topic was completed in 2003 and, after being redrafted, was submitted for publication in 2006. However, the paper was rejected various times and, as a result, in 2009 I decided to no longer pursue its publication. I had not given up though on the whole project, and in 2010 I began trying to motivate the same concept of probability in a completely different way
with the goal of making it more palatable to journal editors and referees. Well, at least that is what I thought would be the case. A paper based on this new motivation was submitted for publication in 2012, and was eventually accepted by Communications in Statistics in 2015.

I would like to thank Richard Bradley (London School of Economics) for the kind remarks he made about this paper in his capacity as a editor of the journal "Economics and Philosophy" and for the encouragement he gave me to continue pursuing publication, even though he felt that the paper did not fall within the scope of his journal.

Bowater, R. J. (2004). A foundational justification for a weighted likelihood approach to inference. International Statistical Review72, 307-330.
The published version of this paper can be found here.

I had the idea for this paper in 1999 and the paper was submitted for publication in 2001. I should make it clear that, except for perhaps one or two nights in 1999, I never thought weighted likelihood inference was a good idea, but I used the paper as a vehicle to discuss the meaning of probability and to attack some important principles that underlie Bayesian theory, especially the independence axiom.

The paper was accepted for publication in 2003 by the International Statistical Review, which was the first journal that I sent it to. My thanks go to Elja Arjas who was the editor of the journal at the time. I was very honoured that the paper is followed by a commentary by Glenn Shafer, so honoured in fact that I was not too bothered by his rather negative remarks!

Papers under peer review

1) "Multivariate subjective fiducial inference."

Available as: Bowater, R. J. (2018). Multivariate subjective fiducial inference. arXiv.org (Cornell University), Statistics, arXiv:1804.09804.
First version: 25-Apr-2018. Current version: 31-Jul-2019. This version of the paper can be found here. More details to follow.

2) "On a generalized form of subjective probability."

Available as: Bowater, R. J. and Guzmán-Pantoja, L. E. (2018). On a generalized form of subjective probability. arXiv.org (Cornell University), Statistics, arXiv:1810.10972.
Published: 25-Oct-2018. This paper can be found here. More details to follow.

3) "Organic fiducial inference."

Available as: Bowater, R. J. (2019). Organic fiducial inference. arXiv.org (Cornell University), Statistics, arXiv:1901.08589.
First version: 23-Jan-2019. Current version: 01-Aug-2019. This version of the paper can be found here. More details to follow.