Advertisement

Cognitive Processing

, Volume 20, Issue 4, pp 447–457 | Cite as

The Bayesian causal inference model benefits from an informed prior to predict proprioceptive drift in the rubber foot illusion

  • Tim SchürmannEmail author
  • Joachim Vogt
  • Oliver Christ
  • Philipp Beckerle
Research Article
  • 54 Downloads

Abstract

Bayesian cognitive modeling has become a prominent tool for the cognitive sciences aiming at a deeper understanding of the human mind and applications in cognitive systems, e.g., humanoid or wearable robotics. Such approaches can capture human behavior adequately with a focus on the crossmodal processing of sensory information. The rubber foot illusion is a paradigm in which such integration is relevant. After experimental stimulation, many participants perceive their real limb closer to an artificial replicate than it actually is. A measurable effect of this recalibration on localization is called the proprioceptive drift. We investigate whether the Bayesian causal inference model can estimate the proprioceptive drift observed in empirical studies. Moreover, we juxtapose two models employing informed prior distributions on limb location against an existing model assuming uniform prior distribution. The model involving empirically informed prior information yields better predictions of the proprioceptive drift regarding the rubber foot illusion when evaluated with separate experimental data. Contrary, the uniform model produces implausibly narrow position estimates that seem due to the precision ratio between the contributing sensory channels. We conclude that an informed prior on limb localization is a plausible and necessary modification to the Bayesian causal inference model when applied to limb illusions. Future research could overcome the remaining discrepancy between model predictions and empirical observation by investigating the changes in sensory precision as a function of distance between the eyes and respective limbs.

Keywords

Rubber foot illusion Bayesian inference Crossmodal integration Cognitive modeling 

Notes

Acknowledgements

This work received support from the German Research Foundation (DFG) through the project “Users’ Body Experience and Human–Machine Interfaces in (Assistive) Robotics” (No. BE 5729/3&11). In addition, we would like to thank Mareike Flögel for providing their dataset as well as an average distance estimate between eyes and feet in an RFI experiment. Further, we would like to thank Frank Jäkel for advice on the manuscript.

Compliance with ethical standards

Conflict of interest

The authors declare no conflict of interest.

References

  1. Annis J, Palmeri TJ (2017) Bayesian statistical approaches to evaluating cognitive models: Bayesian statistical approaches. Cognit Sci.  https://doi.org/10.1002/wcs.1458 CrossRefGoogle Scholar
  2. Beckerle P, De Beir A, Schurmann T, Caspar EA (2016) Human body schema exploration: analyzing design requirements of robotic hand and leg illusions, pp 763–768.  https://doi.org/10.1109/ROMAN.2016.7745205
  3. Beckerle P, Salvietti G, Unal R, Prattichizzo D, Rossi S, Castellini C, Bianchi M (2017) A human–robot interaction perspective on assistive and rehabilitation robotics. Front Neurorobotics.  https://doi.org/10.3389/fnbot.2017.00024 CrossRefGoogle Scholar
  4. Berniker M, Kording K (2011) Bayesian approaches to sensory integration for motor control. Cognit Sci 2(4):419–428.  https://doi.org/10.1002/wcs.125 CrossRefGoogle Scholar
  5. Botvinick M, Cohen J (1998) Rubber hands “feel” touch that eyes see. Nature 391:756CrossRefGoogle Scholar
  6. Caspar EA, De Beir A, De Saldanha M, Da Gama PA, Yernaux F, Cleeremans A, Vanderborght B (2015) New frontiers in the rubber hand experiment: when a robotic hand becomes one’s own. Behav Res Methods 47(3):744–755.  https://doi.org/10.3758/s13428-014-0498-3 CrossRefPubMedGoogle Scholar
  7. Christ O, Reiner M (2014) Perspectives and possible applications of the rubber hand and virtual hand illusion in non-invasive rehabilitation: technological improvements and their consequences. Neurosci Biobehav Rev 44:33–44.  https://doi.org/10.1016/j.neubiorev.2014.02.013 CrossRefPubMedGoogle Scholar
  8. Christ O, Elger A, Schneider K, Rapp A, Beckerle P (2013) Identification of haptic paths with different resolution and their effect on body scheme illusion in lower limbs. Presented at the European conference on technically assisted rehabilitation (TAR-2013), Berlin, GermanyGoogle Scholar
  9. Clark A (2013) Whatever next? Predictive brains, situated agents, and the future of cognitive science. Behav Brain Sci 36(3):181–204CrossRefGoogle Scholar
  10. Crea S, D’Alonzo M, Vitiello N, Cipriani C (2015) The rubber foot illusion. J NeuroEng Rehabil.  https://doi.org/10.1186/s12984-015-0069-6 CrossRefPubMedPubMedCentralGoogle Scholar
  11. Daunizeau J, den Ouden HEM, Pessiglione M, Kiebel SJ, Stephan KE, Friston KJ (2010) Observing the observer (I): meta-Bayesian models of learning and decision-making. PLoS ONE 5(12):e15554.  https://doi.org/10.1371/journal.pone.0015554 CrossRefPubMedPubMedCentralGoogle Scholar
  12. Dayan P, Hinton GE, Neal RM, Zemel RS (1995) The helmholtz machine. Neural Comput 7(5):889–904CrossRefGoogle Scholar
  13. Deneve S, Pouget A (2004) Bayesian multisensory integration and cross-modal spatial links. J Physiol Paris 98(1–3):249–258.  https://doi.org/10.1016/j.jphysparis.2004.03.011 CrossRefPubMedGoogle Scholar
  14. Doya K (ed) (2011) Bayesian brain: probabilistic approaches to neural coding. MIT Press, CambridgeGoogle Scholar
  15. Ehrsson HH, Rosen B, Stockselius A, Ragno C, Kohler P, Lundborg G (2008) Upper limb amputees can be induced to experience a rubber hand as their own. Brain 131(12):3443–3452.  https://doi.org/10.1093/brain/awn297 CrossRefPubMedPubMedCentralGoogle Scholar
  16. Farrell S, Lewandowsky S (2018) Computational modeling of cognition and behavior, 1st edn. Cambridge University Press, Cambridge.  https://doi.org/10.1017/CBO9781316272503 CrossRefGoogle Scholar
  17. Flögel M, Beckerle P, Christ O (2014) Rubber hand and rubber foot illusion: a comparison and perspective in rehabilitation. Clin Neurophysiol 125:S113.  https://doi.org/10.1016/S1388-2457(14)50371-9 CrossRefGoogle Scholar
  18. Flögel M, Kalveram K, Christ O, Vogt J (2015) Application of the rubber hand illusion paradigm: comparison between upper and lower limbs. Psychol Res.  https://doi.org/10.1007/s00426-015-0650-4 CrossRefPubMedGoogle Scholar
  19. Friston KJ, Stephan KE (2007) Free-energy and the brain. Synthese 159(3):417–458CrossRefGoogle Scholar
  20. Gelman A (2006) Prior distributions for variance parameters in hierarchical models (comment on article by Browne and Draper). Bayesian Anal 1(3):515–534CrossRefGoogle Scholar
  21. Giummarra MJ, Gibson SJ, Georgiou-Karistianis N, Bradshaw JL (2008) Mechanisms underlying embodiment, disembodiment and loss of embodiment. Neurosci Biobehav Rev 32(1):143–160.  https://doi.org/10.1016/j.neubiorev.2007.07.001 CrossRefPubMedGoogle Scholar
  22. Hahn U (2014) The Bayesian boom: Good thing or bad? Front Psychol.  https://doi.org/10.3389/fpsyg.2014.00765 CrossRefPubMedPubMedCentralGoogle Scholar
  23. Hirsh IJ, Sherrick CE Jr (1961) Perceived order in different sense modalities. J Exp Psychol 62(5):423–432.  https://doi.org/10.1037/h0045283 CrossRefPubMedGoogle Scholar
  24. Jones S, Cressman EK, Henriques DYP (2010) Proprioceptive localization of the left and right hands. Exp Brain Res 204(3):373–383.  https://doi.org/10.1007/s00221-009-2079-8 CrossRefPubMedGoogle Scholar
  25. Körding KP, Beierholm U, Ma WJ, Quartz S, Tenenbaum JB, Shams L (2007) Causal inference in multisensory perception. PLoS ONE 2(9):e943.  https://doi.org/10.1371/journal.pone.0000943 CrossRefPubMedPubMedCentralGoogle Scholar
  26. Kruschke JK (2015) Doing Bayesian data analysis: a tutorial with R, JAGS, and stan, 2nd edn. Academic Press, BostonGoogle Scholar
  27. Kruschke JK, Aguinis H, Joo H (2012) The time has come: Bayesian methods for data analysis in the organizational sciences. Organ Res Methods 15(4):722–752.  https://doi.org/10.1177/1094428112457829 CrossRefGoogle Scholar
  28. Lanillos P, Dean-Leon E, Cheng G (2017) Yielding self-perception in robots through sensorimotor contingencies. IEEE Trans Cognit Dev Syst 9(2):100–112.  https://doi.org/10.1109/TCDS.2016.2627820 CrossRefGoogle Scholar
  29. Lee MD, Wagenmakers E-J (2013) Bayesian cognitive modeling: a practical course. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  30. Lenggenhager B, Hilti L, Brugger P (2015) Disturbed body integrity and the “rubber foot illusion”. Neuropsychology 29(2):205–211.  https://doi.org/10.1037/neu0000143 CrossRefPubMedGoogle Scholar
  31. Marr D (1982) Vision: a computational investigation into the human representation and processing of visual information. MIT Press, CambridgeGoogle Scholar
  32. Moseley GL, Gallace A, Spence C (2012) Bodily illusions in health and disease: physiological and clinical perspectives and the concept of a cortical ‘body matrix’. Neurosci Biobehav Rev 36(1):34–46.  https://doi.org/10.1016/j.neubiorev.2011.03.013 CrossRefPubMedGoogle Scholar
  33. Orbán G, Wolpert DM (2011) Representations of uncertainty in sensorimotor control. Curr Opin Neurobiol 21(4):629–635.  https://doi.org/10.1016/j.conb.2011.05.026 CrossRefPubMedGoogle Scholar
  34. Robbins S, Waked E, Mcclaran J (1995) Proprioception and stability: foot position awareness as a function of age and footware. Age Ageing 24(1):67–72.  https://doi.org/10.1093/ageing/24.1.67 CrossRefPubMedGoogle Scholar
  35. Robbins S, Waked E, Allard P, McClaran J, Krouglicof N (1997) Foot position awareness in younger and older men: the influence of footwear sole properties. J Am Geriatr Soc 45(1):61–66.  https://doi.org/10.1111/j.1532-5415.1997.tb00979.x CrossRefPubMedGoogle Scholar
  36. Roncone A, Hoffmann M, Pattacini U, Fadiga L, Metta G (2016) Peripersonal space and margin of safety around the body: learning visuo-tactile associations in a humanoid robot with artificial skin. PLoS ONE 11(10):e0163713.  https://doi.org/10.1371/journal.pone.0163713 CrossRefPubMedPubMedCentralGoogle Scholar
  37. Samad M, Chung AJ, Shams L (2015) Perception of body ownership is driven by Bayesian sensory inference. PLoS ONE 10(2):e0117178.  https://doi.org/10.1371/journal.pone.0117178 CrossRefPubMedPubMedCentralGoogle Scholar
  38. Schürmann T, Overath P, Christ O, Vogt J, Beckerle P (2015) Exploration of lower limb body schema integration with respect to body-proximal robotics, pp 61–65.  https://doi.org/10.1109/RTSI.2015.7325072
  39. Schürmann T, Mohler BJ, Peters J, Beckerle P (2019) How cognitive models of human body experience might push robotics. Front Neurorobot 13:14CrossRefGoogle Scholar
  40. Schwartenbeck P, Friston K (2016) Computational phenotyping in psychiatry: a worked example. ENeuro.  https://doi.org/10.1523/ENEURO.0049-16.2016 CrossRefPubMedPubMedCentralGoogle Scholar
  41. Shimada S, Fukuda K, Hiraki K (2009) Rubber hand illusion under delayed visual feedback. PLoS ONE 4(7):e6185.  https://doi.org/10.1371/journal.pone.0006185 CrossRefPubMedPubMedCentralGoogle Scholar
  42. Siciliano B, Khatib O (eds) (2008) Springer handbook of robotics: with… 84 tables. Springer, BerlinGoogle Scholar
  43. Sun R (ed) (2008) The Cambridge handbook of computational psychology. Cambridge University Press, New YorkGoogle Scholar
  44. Tsakiris M, Haggard P (2005) The rubber hand illusion revisited: visuotactile integration and self-attribution. J Exp Psychol Hum Percept Perform 31(1):80–91.  https://doi.org/10.1037/0096-1523.31.1.80 CrossRefPubMedGoogle Scholar
  45. van Beers RJ, Sittig AC, Denier van der Gon JJ (1998) The precision of proprioceptive position sense. Exp Brain Res 122(4):367–377.  https://doi.org/10.1007/s002210050525 CrossRefPubMedGoogle Scholar
  46. Weiss Y, Simoncelli EP, Adelson EH (2002) Motion illusions as optimal percepts. Nat Neurosci 5(6):598–604.  https://doi.org/10.1038/nn858 CrossRefPubMedGoogle Scholar
  47. Wolpe N, Wolpert DM, Rowe JB (2014) Seeing what you want to see: priors for one’s own actions represent exaggerated expectations of success. Front Behav Neurosci 8:232CrossRefGoogle Scholar
  48. Xu F, Tenenbaum JB (2007) Word learning as Bayesian inference. Psychol Rev 114(2):245–272.  https://doi.org/10.1037/0033-295X.114.2.245 CrossRefPubMedGoogle Scholar

Copyright information

© Marta Olivetti Belardinelli and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Work and Engineering Psychology, Institut für PsychologieTechnische Universität DarmstadtDarmstadtGermany
  2. 2.Institute Humans in Complex Systems, School of PsychologyUniversity of Applied Arts and Sciences Northwestern SwitzerlandOltenSwitzerland
  3. 3.Elastic Lightweight Robotics Group, Robotics Research InstituteTechnische Universität DortmundDortmundGermany
  4. 4.Institute for Mechatronic Systems in Mechanical EngineeringTechnische Universität DarmstadtDarmstadtGermany

Personalised recommendations