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Why is sets of probabilities the right level to stop the regress at?
Obviously, different sets of probabilities may match the same macroscopic features.
Sets of probabilities representing reactions participating in ATRP or overall ATRP reaction probability were implemented in the simulation model.
Perhaps we should have a set of sets of probabilities… Similar problems arise for theories of vagueness (Sorensen 2012).
Levi (1986, 1999) has argued that representation of such conflict is better handled with sets of probabilities than with precise probabilities.
The standard assumption about updating for sets of probabilities is that your degree of belief in $X$ after learning $E$ is given by $P(X\pvert E) = \{p(X\pvert E), p\in P, p(E) > 0\}$.
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So in what follows the discussion will be in terms of sets of probability functions.
A credal network admits several extensions several sets of probability measures comply with the constraints represented by a network.
The intervals aren't necessarily interpretable as sets of probability functions: that is, they can violate some of the properties of credal sets discussed in the formal appendix.
In order to perform exact inference, imprecise probabilities are taken as a starting point, i.e. we deal with sets of probability distributions rather than a single one.
The theory imposes probabilistic constraints upon possible causal relations, and there will be some sets of probability relations that are compatible with only one set of causal relations.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com