Related papers: Generalized Qualitative Probability: Savage revisi…
A distinction is sometimes made between "statistical" and "subjective" probabilities. This is based on a distinction between "unique" events and "repeatable" events. We argue that this distinction is untenable, since all events are "unique"…
I present a proof of the quantum probability rule from decision-theoretic assumptions, in the context of the Everett interpretation. The basic ideas behind the proof are those presented in Deutsch's recent proof of the probability rule, but…
The framework of generalized probabilistic theories is a powerful tool for studying the foundations of quantum physics. It provides the basis for a variety of recent findings that significantly improve our understanding of the rich physical…
According to the probability ranking principle, the document set with the highest values of probability of relevance optimizes information retrieval effectiveness given the probabilities are estimated as accurately as possible. The key…
In this paper we extend Savage's theory of decision-making under uncertainty from a classical environment into a non-classical one. We formulate the corresponding axioms and provide representation theorems for qualitative measures and…
Quantification is well known to be a major obstacle in the construction of a probabilistic network, especially when relying on human experts for this purpose. The construction of a qualitative probabilistic network has been proposed as an…
An approach is presented treating decision theory as a probabilistic theory based on quantum techniques. Accurate definitions are given and thorough analysis is accomplished for the quantum probabilities describing the choice between…
We view sorites in terms of stimuli acting upon a system and evoking this system's responses. Supervenience of responses on stimuli implies that they either lack tolerance (i.e., they change in every vicinity of some of the stimuli), or…
We introduce a novel notion of probability within quantum history theories and give a Gleasonesque proof for these assignments. This involves introducing a tentative novel axiom of probability. We also discuss how we are to interpret these…
For the classical mind, quantum mechanics is boggling enough; nevertheless more bizarre behavior could be imagined, thereby concentrating on propositional structures (empirical logics) that transcend the quantum domain. One can also…
We introduce a generalization to the lottery ticket hypothesis in which the notion of "sparsity" is relaxed by choosing an arbitrary basis in the space of parameters. We present evidence that the original results reported for the canonical…
Making a decision is often a matter of listing and comparing positive and negative arguments. In such cases, the evaluation scale for decisions should be considered bipolar, that is, negative and positive values should be explicitly…
Bayesian networks provide a probabilistic semantics for qualitative assertions about likelihood. A qualitative reasoner based on an algebra over these assertions can derive further conclusions about the influence of actions. While the…
In this paper ideas of different types of convergence of a sequence of random variables in probability, namely, statistical convergence of order $\alpha$ in probability, strong $p$-Ces$\grave{\mbox{a}}$ro summability of order $\alpha$ in…
We defend a new theory of statistical evidence, which we call Robust Bayesianism (RB). We prove that, under widely accepted assumptions, RB entails the law of likelihood [Royall, 1997], the likelihood principle [Berger and Wolpert, 1988],…
Theoretically as well as experimentally it is investigated how people represent their knowledge in order to make decisions or to share their knowledge with others. Experiment 1 probes into the ways how people 6ather information about the…
In this article we demonstrate how algorithmic probability theory is applied to situations that involve uncertainty. When people are unsure of their model of reality, then the outcome they observe will cause them to update their beliefs. We…
The law of likelihood underlies a general framework, known as the likelihood paradigm, for representing and interpreting statistical evidence. As stated, the law applies only to simple hypotheses, and there have been reservations about…
In this paper I discuss both syntax and semantics of subjective probability. The semantics determines ways of testing probability statements. Among important varieties of subjective probabilities are intersubjective probabilities and…
Bayesian probability theory is used to analyze the oft-made assumption that humans are typical observers in the universe. Some theoretical calculations make the {\it selection fallacy} that we are randomly chosen from a class of objects by…