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About 10,000 papers for “Prior probability”

prior probability

2024

Citation: 'prior probability' in the IUPAC Compendium of Chemical Terminology, 5th ed.; International Union of Pure and Applied Chemistry; 2025. Online version 5.0.0, 2025. 10.1351/goldbook.11496 • License: The IUPAC Gold Book is licensed under Creative Commons Attribution-ShareAlike CC BY-SA 4.0 International for individual terms. Requests for commercial usage of the compendium should be directed to IUPAC.

Cited by 0

Processing of prior probability

Christina Scheibe · edoc Publication server (Humboldt University of Berlin) · 2010

Um eine Entscheidung zu treffen, muss Information interpretiert und in eine Handlung übersetzt werden. Dafür wird die a priori Wahrscheinlichkeit bezüglich der Entscheidungsalternativen in den Prozess der Entscheidungsfindung integriert und löst Mechanismen der Handlungsvorbereitung aus. In der vorliegenden Dissertation habe ich untersucht, welche Vorbereitungsprozesse aufgrund von wahrscheinlichkeitsbasierter Vorinformation stattfinden und welche Gehirnareale mit der Integration dieser Information assoziiert sind. Um diese Fragen zu beantworten, habe ich eine Verhaltensstudie, eine Studie mit Ableitung des Elektroenzephalogramms (EEG) und eine Studie mittels der funktionellen Magnetresonanztomographie (fMRT) mit simultaner Ableitung des EEGs durchgeführt. Die Versuchspersonen bearbeiteten währenddessen eine Zahlenvergleichsaufgabe mit einem Hinweisreiz, der Wahrscheinlichkeitsinformation bezüglich der erforderlichen Antwort enthielt. Die Reaktionszeit wurde durch die wahrscheinlichkeitsbasierte Vorinformation des Hinweisreizes parametrisch moduliert (Studie 1). Daraus lässt sich schlussfolgern, dass Vorbereitungsprozesse in Abhängigkeit der Wahrscheinlichkeitsinformation stattfinden. Die EEG Studie (Studie 2) ergab einen parametrischen Effekt von Wahrscheinlichkeitsinformation auf die Amplitude der Contingent Negative Variation (CNV), einer EEG-Komponente, die Vorbereitungsprozesse auf prämotorischer Ebene reflektiert. Darüber hinaus fand sich mittels einer Dipolquellenanalyse ein Dipol im anterioren Cingulum (ACC), dessen Aktivität ebenfalls durch die Wahrscheinlichkeitsinformation parametrisch moduliert war. Diese Ergebnisse lassen auf prämotorische Vorbereitungsprozesse aufgrund von Wahrscheinlichkeitsinformation schließen. In den fMRT-Ergebnissen zeigte sich eine parametrisch modulierte neuronale Aktivierung im posterioren Teil des medial-frontalen Kortex (pMFC), die auf eine Kontrollfunktion zur Handlungsanpassung dieses Areals zurückgeführt werden kann (Studie 3a). Um dynamische Fluktuationen der Wahrscheinlichkeitsverarbeitung zu untersuchen, wurde die CNV Amplitude der Einzeltrials in das Modell der fMRT-Analyse integriert (Studie 3b). Die CNV Amplitude korrelierte mit der neuronalen Aktivität in einem Netzwerk, bestehend aus frontalen, parietalen und striatalen Arealen, das mit allgemeiner wahrscheinlichkeitsunabhängiger Handlungsvorbereitung im Zusammenhang steht. Dagegen zeigten sich im dorsolateralen Präfrontalkortex (DLPFC), im inferioren frontalen Gyrus (IPG) und im inferioren Parietallappen (IPL) Aktivierungen, die sich auf die dynamische Integration von Wahrscheinlichkeitsinformation zurückführen lassen.

Cited by 0Open access

Prior probability and uncertainty

R.L. Kashyap · IEEE Transactions on Information Theory · 1971

Consider a stochastic system with output <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Y</tex> whose probability density <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(pY \mid \Lambda)</tex> is a known function of the parameter <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\Lambda</tex> whose true value is unknown. Our aim is to assign a prior probability density <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> b(\Lambda)</tex> for <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\Lambda</tex> using all the available knowledge so that we can assess the probabilistic behavior of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Y</tex> from the corresponding marginal density <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q(Y)</tex> . Usually the range of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\Lambda</tex> is known. In addition, by considering the distribution of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\Lambda</tex> in similar systems, we can define the density <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f(\Lambda)</tex> , about which we may have some knowledge such as <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">E(\Lambda _ 1 ^ {2}) \geq 1/2</tex> , etc. We derive an expression for the uncertainty functional <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\phi(\cdot)</tex> involving <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f(\Lambda) </tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b(\Lambda)</tex> to quantify the discrepancy between the actual behavior of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Y</tex> and our assessment of its behavior. We pose a two-person zero-sum game with <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\phi</tex> as the payoff function so that <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b(\Lambda)</tex> is chosen by us to minimize <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\phi</tex> , whereas <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f(\Lambda)</tex> is chosen by nature to maximize <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\phi</tex> . We derive an asymptotic expression for the prior density, work out a few examples, and discuss the advantages of this method over others.

Cited by 42

Posterior and prior probability densities.

Isaac J. Stopard (10151370), Thomas S. Churcher (6906767), Ben Lambert (5060288) · Figshare · 2021

&lt;p&gt;The posterior distributions are estimated by kernel density estimation with a gaussian smoothing kernel.&lt;/p&gt; &lt;p&gt;(TIF)&lt;/p&gt;

Cited by 0Open access

Prior probability weighted KNN classifier.

Edward J. Kendall (535906), Matthew T. Flynn (535907) · Figshare · 2015

&lt;p&gt;Sensitivity (Sen, solid lines) and specificity (Sp, dashed lines) versus Number of Neighbors for all three datasets. MIAS (red), DDSM MLO (green), DDSM CC (black).&lt;/p&gt;

Cited by 0Open access

Fisher consistency for prior probability shift

Dirk Tasche · arXiv (Cornell University) · 2017

We introduce Fisher consistency in the sense of unbiasedness as a desirable property for estimators of class prior probabilities. Lack of Fisher consistency could be used as a criterion to dismiss estimators that are unlikely to deliver precise estimates in test datasets under prior probability and more general dataset shift. The usefulness of this unbiasedness concept is demonstrated with three examples of classifiers used for quantification: Adjusted Classify &amp; Count, EM-algorithm and CDE-Iterate. We find that Adjusted Classify &amp; Count and EM-algorithm are Fisher consistent. A counter-example shows that CDE-Iterate is not Fisher consistent and, therefore, cannot be trusted to deliver reliable estimates of class probabilities.

Cited by 1Open access

Ensuring Fairness under Prior Probability Shifts

Arpita Biswas, Suvam Mukherjee · arXiv (Cornell University) · 2021

Prior probability shift is a phenomenon where the training and test datasets differ structurally within population subgroups. This phenomenon can be observed in the yearly records of several real-world datasets, for example, recidivism records and medical expenditure surveys. If unaccounted for, such shifts can cause the predictions of a classifier to become unfair towards specific population subgroups. While the fairness notion called Proportional Equality (PE) accounts for such shifts, a procedure to ensure PE-fairness was unknown. In this work, we design an algorithm, called CAPE, that ensures fair classification under such shifts. We introduce a metric, called prevalence difference, which CAPE attempts to minimize in order to achieve fairness under prior probability shifts. We theoretically establish that this metric exhibits several properties that are desirable for a fair classifier. We evaluate the efficacy of CAPE via a thorough empirical evaluation on synthetic datasets. We also compare the performance of CAPE with several state-of-the-art fair classifiers on real-world datasets like COMPAS (criminal risk assessment) and MEPS (medical expenditure panel survey). The results indicate that CAPE ensures a high degree of PE-fairness in its predictions, while performing well on other important metrics.

Cited by 2Open access

Repetition Probability Effects Depend on Prior Experiences

Mareike Grotheer, Gyula Kovács · Journal of Neuroscience · 2014

The magnitude of repetition suppression (RS) in the Fusiform Face Area is influenced by the probability of repetitions of faces (Summerfield et al., 2008), implying that perceptual expectations affect repetition-related processes. Surprisingly, however, macaque single-cell (Kaliukhovich and Vogels, 2011) and human fMRI (Kovács et al., 2013) studies have failed to find repetition probability [P(rep)] modulations of RS with nonface stimuli in the occipitotemporal cortex, suggesting that the effect is face specific. One possible explanation of this category selectivity is that the extensive experience humans have with faces affects the neural mechanisms of RS specifically, creating P(rep) modulatory effects. To address this question, we used fMRI to test the P(rep) effects for another well trained stimulus category, upright letters of the roman alphabet as well as for unfamiliar false fonts. We observed significant RS for both stimulus sets in the Letter Form Area as well as in the caudodorsal part of the lateral occipital complex. Interestingly, the influence of P(rep) on RS was dependent on the stimulus: while we observed P(rep) modulations for the roman letters, no such effects were found for the unfamiliar false fonts in either area. Our findings suggest that P(rep) effects on RS are manifest for nonface stimuli as well, but that they depend on the experience of the subjects with the stimulus category. This shows, for the first time, that prior experience affects the influence of contextual predictive information on RS in the human occipitotemporal cortex.

Cited by 94Open access

Bayesian Prior Probability Distributions for Internal Dosimetry

Guthrie Miller, W.C. Inkret, T. Little et al. · Radiation Protection Dosimetry · 2001

The problem of choosing a prior distribution for the Bayesian interpretation of measurements (specifically internal dosimetry measurements) is considered using a theoretical analysis and by examining historical tritium and plutonium urine bioassay data from Los Alamos. Two models for the prior probability distribution are proposed: (1) the log-normal distribution, when there is some additional information to determine the scale of the true result, and (2) the 'alpha' distribution (a simplified variant of the gamma distribution) when there is not. These models have been incorporated into version 3 of the Bayesian internal dosimetry code in use at Los Alamos (downloadable from our web site). Plutonium internal dosimetry at Los Alamos is now being done using prior probability distribution parameters determined self-consistently from population averages of Los Alamos data.

Cited by 50