317,062 research outputs found
The completeness of quantum theory for predicting measurement outcomes
The predictions that quantum theory makes about the outcomes of measurements
are generally probabilistic. This has raised the question whether quantum
theory can be considered complete, or whether there could exist alternative
theories that provide improved predictions. Here we review recent work that
considers arbitrary alternative theories, constrained only by the requirement
that they are compatible with a notion of "free choice" (defined with respect
to a natural causal order). It is shown that quantum theory is "maximally
informative", i.e., there is no other compatible theory that gives improved
predictions. Furthermore, any alternative maximally informative theory is
necessarily equivalent to quantum theory. This means that the state a system
has in such a theory is in one-to-one correspondence with its
quantum-mechanical state (the wave function). In this sense, quantum theory is
complete.Comment: 15 pages, 4 figures. This is an expanded and more pedagogical version
of arXiv:1005.5173 and arXiv:1111.6597 that discusses in detail the relation
to other result
Objective Bayesian analysis of neutrino masses and hierarchy
Given the precision of current neutrino data, priors still impact noticeably
the constraints on neutrino masses and their hierarchy. To avoid our
understanding of neutrinos being driven by prior assumptions, we construct a
prior that is mathematically minimally informative. Using the constructed
uninformative prior, we find that the normal hierarchy is favoured but with
inconclusive posterior odds of 5.1:1. Better data is hence needed before the
neutrino masses and their hierarchy can be well constrained. We find that the
next decade of cosmological data should provide conclusive evidence if the
normal hierarchy with negligible minimum mass is correct, and if the
uncertainty in the sum of neutrino masses drops below 0.025 eV. On the other
hand, if neutrinos obey the inverted hierarchy, achieving strong evidence will
be difficult with the same uncertainties. Our uninformative prior was
constructed from principles of the Objective Bayesian approach. The prior is
called a reference prior and is minimally informative in the specific sense
that the information gain after collection of data is maximised. The prior is
computed for the combination of neutrino oscillation data and cosmological data
and still applies if the data improve.Comment: 15 pages. Minor changes to match accepted version in JCA
Rhetoric in legislative bargaining with asymmetric information
We analyze a three-player legislative bargaining game over an ideological and a distributive decision. Legislators are privately informed about their ideological intensities, i.e., the weight placed on the ideological decision relative to the weight placed on the distributive decision. Communication takes place before a proposal is offered and majority rule voting determines the outcome. We show that it is not possible for all legislators to communicate informatively. In particular, the legislator who is ideologically more distant from the proposer cannot communicate informatively, but the closer legislator may communicate whether he would \compromise "or flight" on ideology. Surprisingly, the proposer may be worse off when bargaining with two legislators (under majority rule) than with one (who has veto power), because competition between the legislators may result in less information conveyed in equilibrium. Despite separable preferences, the proposer is always better off making proposals for the two dimensions together
Restricted Value Iteration: Theory and Algorithms
Value iteration is a popular algorithm for finding near optimal policies for
POMDPs. It is inefficient due to the need to account for the entire belief
space, which necessitates the solution of large numbers of linear programs. In
this paper, we study value iteration restricted to belief subsets. We show
that, together with properly chosen belief subsets, restricted value iteration
yields near-optimal policies and we give a condition for determining whether a
given belief subset would bring about savings in space and time. We also apply
restricted value iteration to two interesting classes of POMDPs, namely
informative POMDPs and near-discernible POMDPs
Experimental effects and causal representations
In experimental settings, scientists often âmakeâ new things, in which case the aim is to intervene in order to produce experimental objects and processesâcharacterized as âeffectsâ. In this discussion, I illuminate an important performative function in measurement and experimentation in general: intervention-based experimental production (IEP). I argue that even though the goal of IEP is the production of new effects, it can be informative for causal details in scientific representations. Specifically, IEP can be informative about causal relations in: regularities under study; âintervention systemsâ, which are measurement/experimental systems; and new technological systems
Quadratic Multi-Dimensional Signaling Games and Affine Equilibria
This paper studies the decentralized quadratic cheap talk and signaling game
problems when an encoder and a decoder, viewed as two decision makers, have
misaligned objective functions. The main contributions of this study are the
extension of Crawford and Sobel's cheap talk formulation to multi-dimensional
sources and to noisy channel setups. We consider both (simultaneous) Nash
equilibria and (sequential) Stackelberg equilibria. We show that for arbitrary
scalar sources, in the presence of misalignment, the quantized nature of all
equilibrium policies holds for Nash equilibria in the sense that all Nash
equilibria are equivalent to those achieved by quantized encoder policies. On
the other hand, all Stackelberg equilibria policies are fully informative. For
multi-dimensional setups, unlike the scalar case, Nash equilibrium policies may
be of non-quantized nature, and even linear. In the noisy setup, a Gaussian
source is to be transmitted over an additive Gaussian channel. The goals of the
encoder and the decoder are misaligned by a bias term and encoder's cost also
includes a penalty term on signal power. Conditions for the existence of affine
Nash equilibria as well as general informative equilibria are presented. For
the noisy setup, the only Stackelberg equilibrium is the linear equilibrium
when the variables are scalar. Our findings provide further conditions on when
affine policies may be optimal in decentralized multi-criteria control problems
and lead to conditions for the presence of active information transmission in
strategic environments.Comment: 15 pages, 4 figure
Bayesian inference in a cointegrating panel data model
This paper develops methods of Bayesian inference in a cointegrating panel data model. This model involves each cross-sectional unit having a vector error correction representation. It is flexible in the sense that different cross-sectional units can have different cointegration ranks and cointegration spaces. Furthermore, the parameters which characterize short-run dynamics and deterministic components are allowed to vary over cross-sectional units. In addition to a noninformative prior, we introduce an informative prior which allows for information about the likely location of the cointegration space and about the degree of similarity in coefficients in different cross-sectional units. A collapsed Gibbs sampling algorithm is developed which allows for efficient posterior inference. Our methods are illustrated using real and artificial data
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Retrospective model-based inference guides model-free credit assignment
An extensive reinforcement learning literature shows that organisms assign credit efficiently, even under conditions of state uncertainty. However, little is known about credit-assignment when state uncertainty is subsequently resolved. Here, we address this problem within the framework of an interaction between model-free (MF) and model-based (MB) control systems. We present and support experimentally a theory of MB retrospective-inference. Within this framework, a MB system resolves uncertainty that prevailed when actions were taken thus guiding an MF credit-assignment. Using a task in which there was initial uncertainty about the lotteries that were chosen, we found that when participantsâ momentary uncertainty about which lottery had generated an outcome was resolved by provision of subsequent information, participants preferentially assigned credit within a MF system to the lottery they retrospectively inferred was responsible for this outcome. These findings extend our knowledge about the range of MB functions and the scope of system interactions
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