The problem of rigid conditional probabilities.
Posterior probabilities for each specimen are also shown.
Born probabilities are neither credences nor frequencies.
For R0 = 1.2, true probabilities greater than 0.97 are classified into bins of size 0.01.
Skyrms’s and Lewis’s calculations of expected utility dispense with causal probabilities.
Very roughly speaking, epistemic probabilities can be doxastic, decision-theoretic, or logical.
First, why should we update our subjective probabilities according to strict conditionalization?
While clashing with the symmetrical character of probabilities, the asymmetry of propensities matches that of the causal relation.
Although probabilities reflect quantitative uncertainty at one level, there can also be qualitative uncertainty about probabilities.
As a result, probabilities in causal decision theory may form a foundation for probabilities in the probabilistic theory of causation.
We have discussed how to measure and interpret subjective probabilities, and why degrees of belief should be subjective probabilities.
It has been argued that imprecise probabilities are a natural and intuitive way of overcoming some of the issues with orthodox precise probabilities.
They distinguished causal decision theory, which uses probabilities of subjunctive conditionals, from evidential decision theory, which uses conditional probabilities.
Probabilities in the histories interpretation of quantum mechanics are standard Kolmogorov probabilities, not some new invention that, for example, allows negative probabilities.
Since lower true probabilities occur infrequently, for computational efficiency we then consider true probabilities equal to 0, and true probabilities greater than zero but less than 0.3, in their own bins.
Notable exceptions are Suppes (1970), who takes probability to be a feature of a model of a scientific theory; and Skyrms (1980), who understands the relevant probabilities to be the subjective probabilities of a certain kind of rational agent.
While QBists follow de Finetti in taking all probabilities to be credences of actual agents, Healey’s pragmatist takes probabilities to exist independently of the existence of agents but not to be physical propensities or frequencies, nor even to supervene on Lewis’s Humean mosaic (see entry on David Lewis §5).
The Port Royal Logic (Arnauld, 1662) showed how utilities and probabilities together determine rational preferences; de Finetti’s betting analysis derives probabilities from utilities and rational preferences; von Neumann and Morgenstern (1944) derive utilities from probabilities and rational preferences.
Extant hidden-variables theories reproduce the quantum probabilities, and collapse theories have the intriguing feature of reproducing very close approximations to quantum probabilities for all experiments that have been performed so far but departing from the quantum probabilities for other conceivable experiments.
Although the model probabilities (i.e., the probabilities of outcomes prescribed by the states λ) are different from the corresponding quantum-mechanical probabilities of outcomes (i.e., the probabilities prescribed by the quantum-mechanical states ψ), the quantum mechanical probabilities (which have been systematically confirmed) are recovered by averaging over the model probabilities.
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Although the model probabilities ie the probabilities of outcomes prescribed by the states λ are different from the corresponding quantum-mechanical probabilities of outcomes ie the probabilities prescribed by the quantum-mechanical states ψ the quantum mechanical probabilities which have been systematically confirmed are recovered by averaging over the model probabilities