The root of the name "The General Updating of Probabilistic Knowledge" (TGUPK) can be thought of as being found in the name "The Bayesian Updating of Probabilistic Knowledge". This latter name effectively implies nothing more than Bayesian inference. In the field of TGUPK, we therefore consider both Bayesian and non-Bayesian inference.
By probabilistic knowledge we mean knowledge about a given quantity, which is in general assumed to be a fixed but unknown quantity, that is expressed in the form of a probability distribution over that quantity. In the theory of TGUPK, these probability distributions are regarded as being precise. However, in the practical application of TGUPK, we may sometimes need to take account of the fact that the expression of probabilistic knowledge may be somewhat imprecise. This is generally done by means of a simple sensitivity analysis and is treated as being a relatively minor issue.
There are many ways in which we may informally update probabilistic knowledge on the basis of data, but with regard to formal methods we have the following options:
1) Organic fiducial inference
2) Bayesian inference
3) A combination of organic fiducial inference and Bayesian inference
Therefore, methods of inference falling into these three categories form the basis of the field of TGUPK.
The rest of this page constitutes a list of all my papers in the field of TGUPK (in reverse chronological order) with a description of how some of them came into being.
Bowater, R. J. (2023). The fiducial-Bayes fusion: A general theory of statistical inference. arXiv.org (Cornell University), Statistics, arXiv:2310.01533.
Published: 02-Oct-2023. This paper can be found here.
Bowater, R. J. (2022). Sharp hypotheses and organic fiducial inference. arXiv.org (Cornell University), Statistics, arXiv:2207.08882.
First version: 18-July-2022. Current version:14-Sep-2023. This paper can be found here.
Bowater, R. J. (2022). Physical, subjective and analogical probability. arXiv.org (Cornell University), Statistics, arXiv:2204.10159.
Published: 20-Apr-2022. This paper can be found here.
Bowater, R. J. (2021). A revision to the theory of organic fiducial inference. arXiv.org (Cornell University), Statistics, arXiv:2111.09279.
Published: 17-Nov-2021. This paper can be found here.
Bowater, R. J. (2020). Integrated organic inference (IOI): a reconciliation of statistical paradigms. arXiv.org (Cornell University), Statistics, arXiv:2002.07966.
First version: 19-Feb-2020. Current version: 15-Apr-2021 (Final version with corrections). This version of the paper can be found here.
Bowater, R. J. (2019). Organic fiducial inference. arXiv.org (Cornell University), Statistics, arXiv:1901.08589.
First version: 23-Jan-2019. Current version: 08-Apr-2021 (Final version with corrections). This version of the paper can be found here.
Bowater, R. J. (2018). On a generalised form of subjective probability. arXiv.org (Cornell University), Statistics, arXiv:1810.10972.
First version: 25-Oct-2018. Current version: 24-Mar-2022 (Final version with minor corrections). This version of the paper can be found here.
Bowater, R. J. (2018). Multivariate subjective fiducial inference. arXiv.org (Cornell University), Statistics, arXiv:1804.09804.
First version: 25-Apr-2018. Current version: 07-Apr-2021 (Final version with corrections). This version of the paper can be found here.
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 Methods, 46, 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.