Accuracy and Credal Imprecision

Many have claimed that epistemic rationality sometimes requires us to have imprecise credal states (i.e. credal states representable only by sets of credence functions) rather than precise ones (i.e. credal states representable by single credence functions). Some writers have recently argued that this claim conflicts with accuracy-centered epistemology, i.e., the project of justifying epistemic norms by appealing solely to the overall accuracy of the doxastic states they recommend. But these arguments are far from decisive. In this essay, we prove some new results, which show that there is little hope for reconciling the rationality of credal imprecision with accuracy-centered epistemology

Testing axioms for Quantum Mechanics on Probabilistic toy-theories

In Ref. [1] one of the authors proposed postulates for axiomatizing Quantum Mechanics as a "fair operational framework", namely regarding the theory as a set of rules that allow the experimenter to predict future events on the basis of suitable tests, having local control and low experimental complexity. In addition to causality, the following postulates have been considered: PFAITH (existence of a pure preparationally faithful state), and FAITHE (existence of a faithful effect). These postulates have exhibited an unexpected theoretical power, excluding all known nonquantum probabilistic theories. Later in Ref. [2] in addition to causality and PFAITH, postulate LDISCR (local discriminability) and PURIFY (purifiability of all states) have been considered, narrowing the probabilistic theory to something very close to Quantum Mechanics. In the present paper we test the above postulates on some nonquantum probabilistic models. The first model, "the two-box world" is an extension of the Popescu-Rohrlich model, which achieves the greatest violation of the CHSH inequality compatible with the no-signaling principle. The second model "the two-clock world" is actually a full class of models, all having a disk as convex set of states for the local system. One of them corresponds to the "the two-rebit world", namely qubits with real Hilbert space. The third model--"the spin-factor"--is a sort of n-dimensional generalization of the clock. Finally the last model is "the classical probabilistic theory". We see how each model violates some of the proposed postulates, when and how teleportation can be achieved, and we analyze other interesting connections between these postulate violations, along with deep relations between the local and the non-local structures of the probabilistic theory.Comment: Submitted to QIP Special Issue on Foundations of Quantum Informatio

A Stronger Bell Argument for Quantum Non-Locality

It is widely accepted that the violation of Bell inequalities excludes local theories of the quantum realm. This paper presents a stronger Bell argument which even forbids certain non-local theories. The remaining non-local theories, which can violate Bell inequalities, are characterised by the fact that at least one of the outcomes in some sense probabilistically depends both on its distant as well as on its local parameter. While this is not to say that parameter dependence in the usual sense necessarily holds, it shows that the received analysis of quantum non-locality as “outcome dependence or parameter dependence” is deeply misleading about what the violation of Bell inequalities implies

Application of probabilistic PCR5 Fusion Rule for Multisensor Target Tracking

This paper defines and implements a non-Bayesian fusion rule for combining densities of probabilities estimated by local (non-linear) filters for tracking a moving target by passive sensors. This rule is the restriction to a strict probabilistic paradigm of the recent and efficient Proportional Conflict Redistribution rule no 5 (PCR5) developed in the DSmT framework for fusing basic belief assignments. A sampling method for probabilistic PCR5 (p-PCR5) is defined. It is shown that p-PCR5 is more robust to an erroneous modeling and allows to keep the modes of local densities and preserve as much as possible the whole information inherent to each densities to combine. In particular, p-PCR5 is able of maintaining multiple hypotheses/modes after fusion, when the hypotheses are too distant in regards to their deviations. This new p-PCR5 rule has been tested on a simple example of distributed non-linear filtering application to show the interest of such approach for future developments. The non-linear distributed filter is implemented through a basic particles filtering technique. The results obtained in our simulations show the ability of this p-PCR5-based filter to track the target even when the models are not well consistent in regards to the initialization and real cinematic