IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i17p2036-d621012.html
   My bibliography  Save this article

Quantum-Like Sampling

Author

Listed:
  • Andreas Wichert

    (Department of Informatics, INESC-ID/IST-University of Lisboa, 1000-029 Lisboa, Portugal)

Abstract

Probability theory is built around Kolmogorov’s axioms. To each event, a numerical degree of belief between 0 and 1 is assigned, which provides a way of summarizing the uncertainty. Kolmogorov’s probabilities of events are added, the sum of all possible events is one. The numerical degrees of belief can be estimated from a sample by its true fraction. The frequency of an event in a sample is counted and normalized resulting in a linear relation. We introduce quantum-like sampling. The resulting Kolmogorov’s probabilities are in a sigmoid relation. The sigmoid relation offers a better importability since it induces the bell-shaped distribution, it leads also to less uncertainty when computing the Shannon’s entropy. Additionally, we conducted 100 empirical experiments by quantum-like sampling 100 times a random training sets and validation sets out of the Titanic data set using the Naïve Bayes classifier. In the mean the accuracy increased from 78.84 % to 79.46 % .

Suggested Citation

  • Andreas Wichert, 2021. "Quantum-Like Sampling," Mathematics, MDPI, vol. 9(17), pages 1-11, August.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:17:p:2036-:d:621012
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/17/2036/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/17/2036/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. V. Yukalov & D. Sornette, 2011. "Decision theory with prospect interference and entanglement," Theory and Decision, Springer, vol. 70(3), pages 283-328, March.
    2. Jérôme Busemeyer & Ariane Lambert-Mogiliansky & Zheng Wang, 2009. "Empirical Comparison of Markov and Quantum models of decision-making," Post-Print halshs-00754332, HAL.
    3. Jérôme Busemeyer & Ariane Lambert-Mogiliansky & Zheng Wang, 2009. "Empirical Comparison of Markov and Quantum models of decision-making," PSE-Ecole d'économie de Paris (Postprint) halshs-00754332, HAL.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Boyer-Kassem, Thomas & Duchêne, Sébastien & Guerci, Eric, 2016. "Testing quantum-like models of judgment for question order effect," Mathematical Social Sciences, Elsevier, vol. 80(C), pages 33-46.
    2. Thomas Boyer-Kassem & Sébastien Duchêne & Eric Guerci, 2016. "Quantum-like models cannot account for the conjunction fallacy," Theory and Decision, Springer, vol. 81(4), pages 479-510, November.
    3. Ana Njegovanovic, 2018. "Hilbert Space / Quantum Theory of the Financial Decision and Role of the Prefrontal Cortex with a View to Emotions," International Journal of Social and Administrative Sciences, Asian Economic and Social Society, vol. 3(1), pages 42-54, March.
    4. Ashtiani, Mehrdad & Azgomi, Mohammad Abdollahi, 2015. "A survey of quantum-like approaches to decision making and cognition," Mathematical Social Sciences, Elsevier, vol. 75(C), pages 49-80.
    5. Mehrdad Ashtiani & Mohammad Abdollahi Azgomi, 2016. "A formulation of computational trust based on quantum decision theory," Information Systems Frontiers, Springer, vol. 18(4), pages 735-764, August.
    6. Hancock, Thomas O. & Broekaert, Jan & Hess, Stephane & Choudhury, Charisma F., 2020. "Quantum choice models: A flexible new approach for understanding moral decision-making," Journal of choice modelling, Elsevier, vol. 37(C).
    7. Khrennikov, Andrei, 2015. "Quantum version of Aumann’s approach to common knowledge: Sufficient conditions of impossibility to agree on disagree," Journal of Mathematical Economics, Elsevier, vol. 60(C), pages 89-104.
    8. Khrennikova, Polina, 2016. "Application of quantum master equation for long-term prognosis of asset-prices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 450(C), pages 253-263.
    9. Xiao Tan & Jianjun Zhu & Tong Wu, 2022. "Dynamic Reference Point-Oriented Consensus Mechanism in Linguistic Distribution Group Decision Making Restricted by Quantum Integration of Information," Group Decision and Negotiation, Springer, vol. 31(2), pages 491-528, April.
    10. Loretta Mastroeni & Maurizio Naldi & Pierluigi Vellucci, 2023. "Personal Finance Decisions with Untruthful Advisors: An Agent-Based Model," Computational Economics, Springer;Society for Computational Economics, vol. 61(4), pages 1477-1522, April.
    11. Hancock, Thomas O. & Broekaert, Jan & Hess, Stephane & Choudhury, Charisma F., 2020. "Quantum probability: A new method for modelling travel behaviour," Transportation Research Part B: Methodological, Elsevier, vol. 139(C), pages 165-198.
    12. Xiaoyang Xin & Mengdan Sun & Bo Liu & Ying Li & Xiaoqing Gao, 2022. "A More Realistic Markov Process Model for Explaining the Disjunction Effect in One-Shot Prisoner’s Dilemma Game," Mathematics, MDPI, vol. 10(5), pages 1-23, March.
    13. Luke Snow & Shashwat Jain & Vikram Krishnamurthy, 2022. "Lyapunov based Stochastic Stability of Human-Machine Interaction: A Quantum Decision System Approach," Papers 2204.00059, arXiv.org.
    14. Yu, Jiangbo Gabriel & Jayakrishnan, R., 2018. "A quantum cognition model for bridging stated and revealed preference," Transportation Research Part B: Methodological, Elsevier, vol. 118(C), pages 263-280.
    15. Jingmei Xiao & Mei Cai & Yu Gao, 2022. "A VIKOR-Based Linguistic Multi-Attribute Group Decision-Making Model in a Quantum Decision Scenario," Mathematics, MDPI, vol. 10(13), pages 1-23, June.
    16. Wei-Cheng Cui, 2019. "On A Logically Consistent Cosmological Model Based on Buddhist Philosophy," Annals of Social Sciences & Management studies, Juniper Publishers Inc., vol. 3(1), pages 28-32, March.
    17. Ismaël Rafaï & Sébastien Duchêne & Eric Guerci & Irina Basieva & Andrei Khrennikov, 2022. "The triple-store experiment: a first simultaneous test of classical and quantum probabilities in choice over menus," Theory and Decision, Springer, vol. 92(2), pages 387-406, March.
    18. Fellnhofer, Katharina & Sornette, Didier, 2022. "Embracing The Intuitive-Analytical Paradox? How Intuitive And Analytical Decision-Making Drive Paradoxes In Simple And Complex Environments," OSF Preprints evjd6, Center for Open Science.
    19. Maroussia Favre & Didier Sornette, 2015. "A Generic Model of Dyadic Social Relationships," PLOS ONE, Public Library of Science, vol. 10(3), pages 1-16, March.
    20. Bodo Herzog, 2015. "Anchoring of expectations: The role of credible targets in a game experiment," Journal of Economic and Financial Studies (JEFS), LAR Center Press, vol. 3(6), pages 1-15, December.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:9:y:2021:i:17:p:2036-:d:621012. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.