Negative Probabilities and the Uses of Signed Probability Theory

Allen, Edward Heron

doi:10.1086/288669

Cited by 18 publications

(11 citation statements)

References 5 publications

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“…During the opinion combination step, forms which in view of can take negative values and hence is a signed measure. Signed measures have all formal features of probability besides positivity [6] , [14] , [19] , [65] ; see section V of File S1 for details. There is no generally accepted probabilistic interpretation of signed measures, but in section V of File S1 we make a step towards such an interpretaion.…”

Section: Boomerang (Backfire) Effectmentioning

confidence: 99%

Opinion Dynamics with Confirmation Bias

Allahverdyan

Galstyan

2014

PLoS ONE

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BackgroundConfirmation bias is the tendency to acquire or evaluate new information in a way that is consistent with one's preexisting beliefs. It is omnipresent in psychology, economics, and even scientific practices. Prior theoretical research of this phenomenon has mainly focused on its economic implications possibly missing its potential connections with broader notions of cognitive science.Methodology/Principal FindingsWe formulate a (non-Bayesian) model for revising subjective probabilistic opinion of a confirmationally-biased agent in the light of a persuasive opinion. The revision rule ensures that the agent does not react to persuasion that is either far from his current opinion or coincides with it. We demonstrate that the model accounts for the basic phenomenology of the social judgment theory, and allows to study various phenomena such as cognitive dissonance and boomerang effect. The model also displays the order of presentation effect–when consecutively exposed to two opinions, the preference is given to the last opinion (recency) or the first opinion (primacy) –and relates recency to confirmation bias. Finally, we study the model in the case of repeated persuasion and analyze its convergence properties.ConclusionsThe standard Bayesian approach to probabilistic opinion revision is inadequate for describing the observed phenomenology of persuasion process. The simple non-Bayesian model proposed here does agree with this phenomenology and is capable of reproducing a spectrum of effects observed in psychology: primacy-recency phenomenon, boomerang effect and cognitive dissonance. We point out several limitations of the model that should motivate its future development.

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Section: Boomerang (Backfire) Effectmentioning

confidence: 99%

Opinion Dynamics with Confirmation Bias

Allahverdyan

Galstyan

2014

PLoS ONE

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“…As

W (x, p)

can assume negative values,

s_{w}

is a complex‐valued quantity . It can be split into regions where the Wigner function is positive (W + ) and negative (W − ),

\begin{matrix} true \\ right s_{w} = & - & left \int d x d p W^{+} (x, p) prefixln W^{+} (x, p) \\ - & left \int d x d p W^{-} (x, p) prefixln | W^{-} (x, p) | \\ - & left i π \int d x d p W^{-} (x, p) . \end{matrix}

…”

Section: Delocalization Of Wigner Phase‐spacementioning

confidence: 99%

Quantum uncertainties of the confined Harmonic Oscillator in position, momentum and phase‐space

Laguna

Sagar

2014

Annalen der Physik

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Quantum uncertainties in position, momentum and phasespace are studied in the confined Harmonic Oscillator. Standard deviations and Shannon entropies are used to quantify these uncertainties and their behaviors are compared and contrasted. We observe a minimum in the momentum space Shannon entropy as the box length is increased, a feature that is not present in the momentum space standard deviation. The behaviors of the standard deviation product and the Shannon entropy sum, which form the basis of uncertainty relationships, are also analyzed. Maxima are observed in the product as the box length increases in sharp contrast to the entropy sum. The relationship between these behaviors and that of the Shannon entropy of the phase-space Wigner function is analyzed and discussed. An analysis of the energetic components is also performed. The results reinforce the idea that the confined Harmonic Oscillator can be considered as an intermediate model which interpolates between the Particle in a Box Model and the Harmonic Oscillator and thus contains characteristics of both models.

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“…Of course, they have been extensively studied in mathematics (see e.g. [2] and [3] for early works, and [7] and [27] for more recent ones). A complete account is given in [6].…”

Section: Introductionmentioning

confidence: 99%

Extended probabilities and their application to statistical inference

Caprio¹,

Mukherjee²

2021

Preprint

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We propose a new, more general definition of extended probability measures. We study their properties and provide a behavioral interpretation. We use them in an inference procedure, whose environment is canonically represented by the probability space pΩ, F , P q, when both P and the composition of Ω are unknown. We develop an ex ante analysis -taking place before the statistical analysis requiring knowledge of Ω -in which we progressively learn the true composition of Ω. We describe how to update extended probabilities in this setting, and introduce the concept of lower extended probabilities. We provide two examples in the fields of ecology and opinion dynamics.

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Negative Probabilities and the Uses of Signed Probability Theory

Cited by 18 publications

References 5 publications

Opinion Dynamics with Confirmation Bias

Opinion Dynamics with Confirmation Bias

Quantum uncertainties of the confined Harmonic Oscillator in position, momentum and phase‐space

Extended probabilities and their application to statistical inference

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