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1

Sbuelz, Alessandro, and Fabio Trojani. "Asset prices with locally constrained-entropy recursive multiple-priors utility." Journal of Economic Dynamics and Control 32, no. 11 (November 2008): 3695–717. http://dx.doi.org/10.1016/j.jedc.2008.03.002.

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2

Blanchard, Romain, and Laurence Carassus. "Short Communication: Super-Replication Prices with Multiple Priors in Discrete Time." SIAM Journal on Financial Mathematics 13, no. 2 (May 16, 2022): SC53—SC65. http://dx.doi.org/10.1137/22m1470013.

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3

Epstein, Larry G., and Martin Schneider. "Recursive multiple-priors." Journal of Economic Theory 113, no. 1 (November 2003): 1–31. http://dx.doi.org/10.1016/s0022-0531(03)00097-8.

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4

Ghirardato, Paolo, Peter Klibanoff, and Massimo Marinacci. "Additivity with multiple priors." Journal of Mathematical Economics 30, no. 4 (November 1998): 405–20. http://dx.doi.org/10.1016/s0304-4068(97)00047-5.

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5

Chateauneuf, Alain, Fabio Maccheroni, Massimo Marinacci, and Jean-Marc Tallon. "Monotone continuous multiple priors." Economic Theory 26, no. 4 (November 2005): 973–82. http://dx.doi.org/10.1007/s00199-004-0540-2.

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6

D’Andrea, Amanda M. E., Vera L. D. Tomazella, Hassan M. Aljohani, Pedro L. Ramos, Marco P. Almeida, Francisco Louzada, Bruna A. W. Verssani, Amanda B. Gazon, and Ahmed Z. Afify. "Objective bayesian analysis for multiple repairable systems." PLOS ONE 16, no. 11 (November 23, 2021): e0258581. http://dx.doi.org/10.1371/journal.pone.0258581.

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This article focus on the analysis of the reliability of multiple identical systems that can have multiple failures over time. A repairable system is defined as a system that can be restored to operating state in the event of a failure. This work under minimal repair, it is assumed that the failure has a power law intensity and the Bayesian approach is used to estimate the unknown parameters. The Bayesian estimators are obtained using two objective priors know as Jeffreys and reference priors. We proved that obtained reference prior is also a matching prior for both parameters, i.e., the credibility intervals have accurate frequentist coverage, while the Jeffreys prior returns unbiased estimates for the parameters. To illustrate the applicability of our Bayesian estimators, a new data set related to the failures of Brazilian sugar cane harvesters is considered.
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7

Marinacci, Massimo. "Probabilistic Sophistication and Multiple Priors." Econometrica 70, no. 2 (March 2002): 755–64. http://dx.doi.org/10.1111/1468-0262.00303.

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8

Alon, Shiri, and Gabi Gayer. "Utilitarian Preferences With Multiple Priors." Econometrica 84, no. 3 (2016): 1181–201. http://dx.doi.org/10.3982/ecta12676.

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9

Amarante, Massimiliano. "Ambiguity, measurability and multiple priors." Economic Theory 26, no. 4 (November 2005): 995–1006. http://dx.doi.org/10.1007/s00199-004-0559-4.

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10

Madan, Dilip B., and Robert J. Elliott. "Multiple Priors and Asset Pricing." Methodology and Computing in Applied Probability 11, no. 2 (February 28, 2008): 211–29. http://dx.doi.org/10.1007/s11009-007-9051-5.

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11

Kajii, Atsushi, and Takashi Ui. "Agreeable bets with multiple priors." Journal of Economic Theory 128, no. 1 (May 2006): 299–305. http://dx.doi.org/10.1016/j.jet.2005.01.004.

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12

Kopylov, Igor. "Multiple priors and comparative ignorance." Journal of Economic Theory 191 (January 2021): 105132. http://dx.doi.org/10.1016/j.jet.2020.105132.

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13

Hara, Chiaki, and Atsushi Kajii. "Risk-free bond prices in incomplete markets with recursive multiple-prior utilities." International Journal of Economic Theory 2, no. 2 (June 2006): 135–57. http://dx.doi.org/10.1111/j.1742-7363.2006.00028.x.

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14

KAJII, ATSUSHI, and TAKASHI UI. "INCOMPLETE INFORMATION GAMES WITH MULTIPLE PRIORS*." Japanese Economic Review 56, no. 3 (September 2005): 332–51. http://dx.doi.org/10.1111/j.1468-5876.2005.00327.x.

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15

Wakai, Katsutoshi. "A note on recursive multiple-priors." Journal of Economic Theory 135, no. 1 (July 2007): 567–71. http://dx.doi.org/10.1016/j.jet.2005.10.008.

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16

Epstein, Larry G., and Massimo Marinacci. "Mutual absolute continuity of multiple priors." Journal of Economic Theory 137, no. 1 (November 2007): 716–20. http://dx.doi.org/10.1016/j.jet.2006.12.004.

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17

Muijs, Remco, Johan O. Robertsson, and Klaus Holliger. "Prestack depth migration of primary and surface-related multiple reflections: Part I — Imaging." GEOPHYSICS 72, no. 2 (March 2007): S59—S69. http://dx.doi.org/10.1190/1.2422796.

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Surface-related multiples (i.e., all seismic waves reflected at the free surface at least once) often severely contaminate seismic recordings. Because conventional imaging techniques require input data that consist of primary reflections only, significant processing effort is commonly dedicated to attenuating multiples prior to migration. On the other hand, surface-related multiples provide additional illumination of the subsurface and, therefore, should not be considered as noise. We present a prestack depth-migration method that allows primary and multiple reflections to be imaged simultaneously. Depth imaging using primary and multiple reflections (DIPMR) involves decomposing the datainto upgoing and downgoing wave constituents, followed by downward extrapolation. Artifacts generated by interference of upgoing and downgoing events not associated with the same subsurface reflection points (crosstalk) are attenuated by using a 2D deconvolution imaging condition. In contrast to existing methods, DIPMR does not require a priori information about the source signature or directivity, because the illuminating source wavefield is extracted directly from the data themselves via the up/down separation. Moreover, there is no need for elimination nor identification of multiples prior to migration. By including surface-related multiples in the imaging procedure, the effective source wavefield is stronger, the spatial aperture is wider, and a higher vertical resolution is enabled through the application of a deconvolution-based imaging condition.
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18

Barrera-Causil, Carlos Javier, and Juan Carlos Correa-Morales. "Elicitation of the Parameters of Multiple Linear Models." Revista Colombiana de Estadística 44, no. 1 (January 15, 2021): 159–70. http://dx.doi.org/10.15446/rce.v44n1.83525.

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Estimating the parameters of a multiple linear model is a common task in all areas of sciences. In order to obtain conjugate distributions, the Bayesian estimation of these parameters is usually carried out using noninformative priors. When informative priors are considered in the Bayesian estimation an important problem arises because techniques arerequired to extract information from experts and represent it in an informative prior distribution. Elicitation techniques can be used for suchpurpose even though they are more complex than the traditional methods. In this paper, we propose a technique to construct an informative prior distribution from expert knowledge using hypothetical samples. Our proposal involves building a mental picture of the population of responses at several specific points of the explanatory variables of a given model andindirectly eliciting the mean and the variance at each of these points. In addition, this proposal consists of two steps: the first step describes the elicitation process and the second step shows a simulation process to estimate the model parameters.
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19

Wojtowicz, S. "Multiple Sclerosis and prions." Medical Hypotheses 40, no. 1 (January 1993): 48–54. http://dx.doi.org/10.1016/0306-9877(93)90196-w.

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20

Lin, Jian, Qiurong Yan, Shang Lu, Yongjian Zheng, Shida Sun, and Zhen Wei. "A Compressed Reconstruction Network Combining Deep Image Prior and Autoencoding Priors for Single-Pixel Imaging." Photonics 9, no. 5 (May 13, 2022): 343. http://dx.doi.org/10.3390/photonics9050343.

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Single-pixel imaging (SPI) is a promising imaging scheme based on compressive sensing. However, its application in high-resolution and real-time scenarios is a great challenge due to the long sampling and reconstruction required. The Deep Learning Compressed Network (DLCNet) can avoid the long-time iterative operation required by traditional reconstruction algorithms, and can achieve fast and high-quality reconstruction; hence, Deep-Learning-based SPI has attracted much attention. DLCNets learn prior distributions of real pictures from massive datasets, while the Deep Image Prior (DIP) uses a neural network′s own structural prior to solve inverse problems without requiring a lot of training data. This paper proposes a compressed reconstruction network (DPAP) based on DIP for Single-pixel imaging. DPAP is designed as two learning stages, which enables DPAP to focus on statistical information of the image structure at different scales. In order to obtain prior information from the dataset, the measurement matrix is jointly optimized by a network and multiple autoencoders are trained as regularization terms to be added to the loss function. Extensive simulations and practical experiments demonstrate that the proposed network outperforms existing algorithms.
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21

Han, J. H., and B. Ahn. "Multiple-regime price transmission between wheat and wheat flour prices in Korea." Agricultural Economics (Zemědělská ekonomika) 61, No. 12 (June 6, 2016): 552–63. http://dx.doi.org/10.17221/47/2015-agricecon.

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22

Qiu, Jianying, and Utz Weitzel. "Experimental evidence on valuation with multiple priors." Journal of Risk and Uncertainty 53, no. 1 (August 2016): 55–74. http://dx.doi.org/10.1007/s11166-016-9244-9.

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23

Kelsey, David, and Frank Milne. "Induced Preferences, Nonadditive Beliefs, and Multiple Priors." International Economic Review 40, no. 2 (May 1999): 455–77. http://dx.doi.org/10.1111/1468-2354.00024.

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24

Gopalan, Ramanan, and Donald A. Berry. "Bayesian Multiple Comparisons Using Dirichlet Process Priors." Journal of the American Statistical Association 93, no. 443 (September 1998): 1130–39. http://dx.doi.org/10.1080/01621459.1998.10473774.

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25

Stathopoulou, Elisavet Konstantina, Roberto Battisti, Dan Cernea, Andreas Georgopoulos, and Fabio Remondino. "Multiple View Stereo with quadtree-guided priors." ISPRS Journal of Photogrammetry and Remote Sensing 196 (February 2023): 197–209. http://dx.doi.org/10.1016/j.isprsjprs.2022.12.013.

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26

Stinchcombe, Maxwell B. "Objective and subjective foundations for multiple priors." Journal of Economic Theory 165 (September 2016): 263–91. http://dx.doi.org/10.1016/j.jet.2016.04.011.

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27

Madrigal, Francisco, Jean-Bernard Hayet, and Mariano Rivera. "Motion priors for multiple target visual tracking." Machine Vision and Applications 26, no. 2-3 (March 6, 2015): 141–60. http://dx.doi.org/10.1007/s00138-015-0662-5.

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28

Fu, Chuan, Bo Du, and Xinjian Huang. "Hyperspectral image compression based on multiple priors." Journal of the Franklin Institute 361, no. 14 (September 2024): 107056. http://dx.doi.org/10.1016/j.jfranklin.2024.107056.

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29

Xu, Yingchun, Xiaohu Zheng, Wen Yao, Ning Wang, and Xiaoqian Chen. "A sequential multi-prior integration and updating method for complex multi-level system based on Bayesian melding method." Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability 235, no. 5 (March 26, 2021): 863–76. http://dx.doi.org/10.1177/1748006x211004518.

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In engineering, there exist multiple priors about system and subsystems uncertainties, which should be integrated properly to analyze the system reliability. In the past research, an iterative updating procedure based on Bayesian Melding Method (I-BMM) was developed to merge and update multiple priors for the double-level system. However, the in-depth study in this paper shows that the original iterative procedure has no effect on the prior updating. Thus it is proposed that only a single BMM iteration process is needed following the original prior integration and updating formulation. BMM involves the sampling procedure for the probability density function (PDF) updating, wherein it is generally difficult to define the sampling number properly for obtaining accurate priors. To address this problem, a sequential prior integration and updating framework based on the original single BMM iteration process (S-BMM) is developed in this paper. In each cycle of prior updating, the sample number is sequentially added, and the difference between prior distributions obtained in the two consecutive cycles is measured with the symmetric Kullback-Leibler Divergence (SKLD). The sequential procedure is continued until the convergence to the accurate updated prior. The S-BMM framework for double-level systems is further extended for multi-level systems. Situations with some missing subsystem or component priors are also discussed. Finally, two numerical examples and one satellite engineering case are used to demonstrate and verify the proposed algorithms.
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30

Jacobs, B. "A channel-based perspective on conjugate priors." Mathematical Structures in Computer Science 30, no. 1 (January 2020): 44–61. http://dx.doi.org/10.1017/s0960129519000082.

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AbstractA desired closure property in Bayesian probability is that an updated posterior distribution be in the same class of distributions – say Gaussians – as the prior distribution. When the updating takes place via a statistical model, one calls the class of prior distributions the ‘conjugate priors’ of the model. This paper gives (1) an abstract formulation of this notion of conjugate prior, using channels, in a graphical language, (2) a simple abstract proof that such conjugate priors yield Bayesian inversions and (3) an extension to multiple updates. The theory is illustrated with several standard examples.
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31

Guan, Lei, Jiawei Dong, Qianxi Li, Jijiang Huang, Weining Chen, and Hao Wang. "Dark Light Image-Enhancement Method Based on Multiple Self-Encoding Prior Collaborative Constraints." Photonics 11, no. 2 (February 19, 2024): 190. http://dx.doi.org/10.3390/photonics11020190.

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The purpose of dark image enhancement is to restore dark images to visual images under normal lighting conditions. Due to the ill-posedness of the enhancement process, previous enhancement algorithms often have overexposure, underexposure, noise increases and artifacts when dealing with complex and changeable images, and the robustness is poor. This article proposes a new enhancement approach consisting in constructing a dim light enhancement network with more robustness and rich detail features through the collaborative constraint of multiple self-coding priors (CCMP). Specifically, our model consists of two prior modules and an enhancement module. The former learns the feature distribution of the dark light image under normal exposure as an a priori term of the enhancement process through multiple specific autoencoders, implicitly measures the enhancement quality and drives the network to approach the truth value. The latter fits the curve mapping of the enhancement process as a fidelity term to restore global illumination and local details. Through experiments, we concluded that the new method proposed in this article can achieve more excellent quantitative and qualitative results, improve detail contrast, reduce artifacts and noise, and is suitable for dark light enhancement in multiple scenes.
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32

Mohite, Siddharth R., Priyadarshini Rajkumar, Shreya Anand, David L. Kaplan, Michael W. Coughlin, Ana Sagués-Carracedo, Muhammed Saleem, et al. "Inferring Kilonova Population Properties with a Hierarchical Bayesian Framework. I. Nondetection Methodology and Single-event Analyses." Astrophysical Journal 925, no. 1 (January 1, 2022): 58. http://dx.doi.org/10.3847/1538-4357/ac3981.

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Abstract We present nimbus: a hierarchical Bayesian framework to infer the intrinsic luminosity parameters of kilonovae (KNe) associated with gravitational-wave (GW) events, based purely on nondetections. This framework makes use of GW 3D distance information and electromagnetic upper limits from multiple surveys for multiple events and self-consistently accounts for the finite sky coverage and probability of astrophysical origin. The framework is agnostic to the brightness evolution assumed and can account for multiple electromagnetic passbands simultaneously. Our analyses highlight the importance of accounting for model selection effects, especially in the context of nondetections. We show our methodology using a simple, two-parameter linear brightness model, taking the follow-up of GW190425 with the Zwicky Transient Facility as a single-event test case for two different prior choices of model parameters: (i) uniform/uninformative priors and (ii) astrophysical priors based on surrogate models of Monte Carlo radiative-transfer simulations of KNe. We present results under the assumption that the KN is within the searched region to demonstrate functionality and the importance of prior choice. Our results show consistency with simsurvey—an astronomical survey simulation tool used previously in the literature to constrain the population of KNe. While our results based on uniform priors strongly constrain the parameter space, those based on astrophysical priors are largely uninformative, highlighting the need for deeper constraints. Future studies with multiple events having electromagnetic follow-up from multiple surveys should make it possible to constrain the KN population further.
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33

Bland, James R., and Yaroslav Rosokha. "Learning under uncertainty with multiple priors: experimental investigation." Journal of Risk and Uncertainty 62, no. 2 (April 2021): 157–76. http://dx.doi.org/10.1007/s11166-021-09351-y.

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34

Westfall, Peter H., and Keith A. Soper. "Using Priors to Improve Multiple Animal Carcinogenicity Tests." Journal of the American Statistical Association 96, no. 455 (September 2001): 827–34. http://dx.doi.org/10.1198/016214501753208852.

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35

Blanchard, Romain, and Laurence Carassus. "No-arbitrage with multiple-priors in discrete time." Stochastic Processes and their Applications 130, no. 11 (November 2020): 6657–88. http://dx.doi.org/10.1016/j.spa.2020.06.006.

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36

Li, Jian. "The K-armed bandit problem with multiple priors." Journal of Mathematical Economics 80 (January 2019): 22–38. http://dx.doi.org/10.1016/j.jmateco.2018.10.002.

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37

Qi Mao, Ivor W. Tsang, Shenghua Gao, and Li Wang. "Generalized Multiple Kernel Learning With Data-Dependent Priors." IEEE Transactions on Neural Networks and Learning Systems 26, no. 6 (June 2015): 1134–48. http://dx.doi.org/10.1109/tnnls.2014.2334137.

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38

Ortoleva, Pietro. "Status quo bias, multiple priors and uncertainty aversion." Games and Economic Behavior 69, no. 2 (July 2010): 411–24. http://dx.doi.org/10.1016/j.geb.2009.11.007.

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39

Zimper, Alexander, and Wei Ma. "Bayesian learning with multiple priors and nonvanishing ambiguity." Economic Theory 64, no. 3 (October 26, 2016): 409–47. http://dx.doi.org/10.1007/s00199-016-1007-y.

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40

Ueno, Kimio, and Michitomo Nishizawa. "Multiple gamma functions and multiple {$q$}-gamma functions." Publications of the Research Institute for Mathematical Sciences 33, no. 5 (1997): 813–38. http://dx.doi.org/10.2977/prims/1195145019.

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41

Verret, D. "Multiple Submissions and Prior Publication." IEEE Transactions on Electron Devices 52, no. 3 (March 2005): 297–98. http://dx.doi.org/10.1109/ted.2005.844646.

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42

Crès, Hervé, Itzhak Gilboa, and Nicolas Vieille. "Aggregation of multiple prior opinions." Journal of Economic Theory 146, no. 6 (November 2011): 2563–82. http://dx.doi.org/10.1016/j.jet.2011.06.018.

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43

Oi, Shu. "Gauss hypergeometric functions, multiple polylogarithms, and multiple zeta values." Publications of the Research Institute for Mathematical Sciences 45, no. 4 (2009): 981–1009. http://dx.doi.org/10.2977/prims/1260476650.

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44

Roach, Neil W., Paul V. McGraw, David J. Whitaker, and James Heron. "Generalization of prior information for rapid Bayesian time estimation." Proceedings of the National Academy of Sciences 114, no. 2 (December 22, 2016): 412–17. http://dx.doi.org/10.1073/pnas.1610706114.

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To enable effective interaction with the environment, the brain combines noisy sensory information with expectations based on prior experience. There is ample evidence showing that humans can learn statistical regularities in sensory input and exploit this knowledge to improve perceptual decisions and actions. However, fundamental questions remain regarding how priors are learned and how they generalize to different sensory and behavioral contexts. In principle, maintaining a large set of highly specific priors may be inefficient and restrict the speed at which expectations can be formed and updated in response to changes in the environment. However, priors formed by generalizing across varying contexts may not be accurate. Here, we exploit rapidly induced contextual biases in duration reproduction to reveal how these competing demands are resolved during the early stages of prior acquisition. We show that observers initially form a single prior by generalizing across duration distributions coupled with distinct sensory signals. In contrast, they form multiple priors if distributions are coupled with distinct motor outputs. Together, our findings suggest that rapid prior acquisition is facilitated by generalization across experiences of different sensory inputs but organized according to how that sensory information is acted on.
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45

Woerman, Amanda L., Joel C. Watts, Atsushi Aoyagi, Kurt Giles, Lefkos T. Middleton, and Stanley B. Prusiner. "α-Synuclein: Multiple System Atrophy Prions." Cold Spring Harbor Perspectives in Medicine 8, no. 7 (February 17, 2017): a024588. http://dx.doi.org/10.1101/cshperspect.a024588.

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46

Pahlke, Marieke. "Dynamic consistency in incomplete information games with multiple priors." Games and Economic Behavior 133 (May 2022): 85–108. http://dx.doi.org/10.1016/j.geb.2022.02.004.

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47

Baugh, Lee A., Amelie Yak, Roland S. Johansson, and J. Randall Flanagan. "Representing multiple object weights: competing priors and sensorimotor memories." Journal of Neurophysiology 116, no. 4 (October 1, 2016): 1615–25. http://dx.doi.org/10.1152/jn.00282.2016.

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When lifting an object, individuals scale lifting forces based on long-term priors relating external object properties (such as material and size) to object weight. When experiencing objects that are poorly predicted by priors, people rapidly form and update sensorimotor memories that can be used to predict an object's atypical size-weight relation in support of predictively scaling lift forces. With extensive experience in lifting such objects, long-term priors, assessed with weight judgments, are gradually updated. The aim of the present study was to understand the formation and updating of these memory processes. Participants lifted, over multiple days, a set of black cubes with a normal size-weight mapping and green cubes with an inverse size-weight mapping. Sensorimotor memory was assessed with lifting forces, and priors associated with the black and green cubes were assessed with the size-weight illusion (SWI). Interference was observed in terms of adaptation of the SWI, indicating that priors were not independently adjusted. Half of the participants rapidly learned to scale lift forces appropriately, whereas reduced learning was observed in the others, suggesting that individual differences may be affecting sensorimotor memory abilities. A follow-up experiment showed that lifting forces are not accurately scaled to objects when concurrently performing a visuomotor association task, suggesting that sensorimotor memory formation involves cognitive resources to instantiate the mapping between object identity and weight, potentially explaining the results of experiment 1. These results provide novel insight into the formation and updating of sensorimotor memories and provide support for the independent adjustment of sensorimotor memory and priors.
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48

Csiszar, Imre, and Thomas Breuer. "Expected Value Minimization in Information Theoretic Multiple Priors Models." IEEE Transactions on Information Theory 64, no. 6 (June 2018): 3957–74. http://dx.doi.org/10.1109/tit.2018.2827364.

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49

Strobbe, Gregor, Pieter van Mierlo, Maarten De Vos, Bogdan Mijović, Hans Hallez, Sabine Van Huffel, José David López, and Stefaan Vandenberghe. "Multiple sparse volumetric priors for distributed EEG source reconstruction." NeuroImage 100 (October 2014): 715–24. http://dx.doi.org/10.1016/j.neuroimage.2014.06.076.

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50

Friston, Karl, Lee Harrison, Jean Daunizeau, Stefan Kiebel, Christophe Phillips, Nelson Trujillo-Barreto, Richard Henson, Guillaume Flandin, and Jérémie Mattout. "Multiple sparse priors for the M/EEG inverse problem." NeuroImage 39, no. 3 (February 2008): 1104–20. http://dx.doi.org/10.1016/j.neuroimage.2007.09.048.

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