On the Consistency of Jeffreys's Simplicity Postulate, and Its Role in Bayesian Inference
Bibliographic Data
| ID | 3202996 |
|---|---|
| Authors | Colin Howson (London School of Economics and Political Science, corresponding author) |
| Year | 1988 |
| Volume | 38 |
| Issue | 150 |
| Pages | 68 |
| Publication date | 1988-01-01 |
| Peer Reviewed | Yes |
| Open Access | No |
| Type | ARTICLE |
| Venue | The Philosophical Quarterly (JOURNAL) |
| Journal identifiers | ISSN: 0031-8094 • E-ISSN: 1467-9213 |
| Publisher | Oxford University Press (OUP) (PUBLISHER) |
| DOI | 10.2307/2220268 |
| OpenAlex | W2329247206 |
| Language | EN |
| Citations received | 5 |
| References cited | 2 |
This paper is about the Bayesian theory of inductive inference, and in particular about the status of a condition, called by him the Simplicity Postulate, imposed by Jeffreys [1948] and [1961] on the so-called prior probability distributions. I shall explain what the Simplicity Postulate says presently: first, some background. The context of the discussion will be a set of possible laws hi, ostensibly governing some given domain of phenomena, and a test designed to discriminate between them. The prior probabilities of the hi are here simply their pre-test probabilities; the posterior, or post-test, probability distribution is obtained by combining likelihoods with prior probabilities according to Bayes's Theorem. Posterior probability oc prior probability x likelihood, where the coefficient of proportionality is the prior probability of the test outcome e. The likelihood of hi given e is equal to the probability of e, conditional on hi, and in those cases where hi describes a well-defined statistical model which determines a probability distribution over a set of data-points of which e is one, the likelihood of hi on e, is just the probability assigned e by hi. The prior, and hence also the posterior probabilities, are understood to be relativised to a stock of well-confirmed background theories about the structure of the test, presumed to be neutral between the hi. These probabilities are interpreted by Jeffreys as reasonable degrees of belief. In such circumstances it might seem natural to make the prior probabilities of the hi equal. For reasons which will become apparent shortly, Jeffreys instead stipulates that they should be a decreasing function of the complexity of the hi, where the complexity of a hypothesis is measured by its number of independent adjustable parameters, i.e., the
Bayes' theorem · Bayesian inference · Bayesian probability · Bayesian statistics · Conditional probability · Conditional probability distribution · Consistency (knowledge bases) · Context (archaeology) · Discrete mathematics · Inference · Law of total probability · Likelihood function · Likelihood principle · Maximum likelihood · Posterior probability · Prior probability · Probability distribution · Quasi-maximum likelihood · Simplicity · Statistics · Artificial Intelligence · Bayesian Modeling and Causal Inference · Computer Science · Mathematics · Philosophy and History of Science · Statistical Mechanics and Entropy
| Unique citing works | 5 |
|---|---|
| Citations per year | 0,19 |
| Citation span | 2000 - 2025 (26) |
| Citation velocity | recent |
| Highly cited | No |
| Citation types | Neutral: 5 |