Bayesianism involves taking Bayesian statistics seriously - really seriously. Bayesians typically hold that:

  • Probability should always be used to represent uncertainty;
  • There's no uncertainty, except inside some kind of mind;
  • There's no such thing as absolute certainty: beliefs are always uncertain;
  • It is possible to make probability assessments without any evidence;
  • Bayesian statistics is an important foundation of the scientific method.

Bayes rule can be interpreted as indicating how to update probability estimates in response to observational evidence. This operation is an important part of the scientific method. It doesn't tell you which experiments to perform or how to get initial probability estimates (or "priors", as Bayesians call them), but it does specify how to update your world view in response to observations.

The idea that probability represents uncertainty goes counter to most formal education in probability theory - which holds instead that probabilities represent frequencies of occurance: the "frequentist" interpretation of probability. For frequentists, probabilities are observer independent. A coin flip might have p(heads) = 1/2 regardless of the observer. Prior probabilities don't matter. The observer's ignorance doesn't matter. p(heads) = 1/2 is an observer-independent fact. This interpretation of the term "probability" is an irritation to Bayesians. There should not be two meanings of the term "probability". Bayesianism is much more important and significant than frequentism. It should get monopoly rights over the term "probability".

Historically, prominent opponents of Bayesianism have included Karl Popper and his followers. Popper denied the validity of induction, and held that only falsification was significant. By contrast, Bayesian statistics uses the same mathematical approach to represent both falsification and confirmation. Observations that falsify a hypothesis are typically stronger evidence than observations that confirm it - but both types of observation result in probability updates via the same formula: Bayes theorem.

Another casualty of Bayesianism is David Deutsch's "Constructor Theory". This holds that we can characterize physical laws by identifying which transformations are possible and which transformations are impossible. However Bayesianism insists that we can never be certain about such things. A supposedly impossible transformation might one day turn out to be possible. Similarly a transformation we believed to be possible might turn out to not be reproducible. The initial belief in its possibility could have been due to experimental errors. Bayesianism insists that statements about "possibility" and "impossibility" be reformulated as assessments of probability - turning the world into shades of grey.

It is possible to rework "Constructor Theory" in Bayesian terms by considering instead the probabilities associated with various different transformations. However, it then sounds much more normal and much less revolutionary.

David Deutsch himself frames his ideas as conflicting with Bayesianism. He writes:

A scientific explanation is a statement of what is there in reality, and how it behaves and how that accounts for the explicanda. Neither confirmation nor credence nor ‘inductive reasoning’ (from observations to theories or to justifications of theories as true or probable) appear in this account. [...] This contradicts the ‘Bayesian’ philosophy that rational credences obey the probability calculus and that science is a process of finding theories with high rational credences, given the observations.

It's generally desirable to quantify uncertainty - as Bayesianism recommends. Without quantification, it isn't possible to update properly on incoming evidence.


Tim Tyler | Contact