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.
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References
Annis J, Palmeri TJ (2017) Bayesian statistical approaches to evaluating cognitive models: Bayesian statistical approaches. Cognit Sci. https://doi.org/10.1002/wcs.1458
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
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
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
Botvinick M, Cohen J (1998) Rubber hands “feel” touch that eyes see. Nature 391:756
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
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
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, Germany
Clark A (2013) Whatever next? Predictive brains, situated agents, and the future of cognitive science. Behav Brain Sci 36(3):181–204
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
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
Dayan P, Hinton GE, Neal RM, Zemel RS (1995) The helmholtz machine. Neural Comput 7(5):889–904
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
Doya K (ed) (2011) Bayesian brain: probabilistic approaches to neural coding. MIT Press, Cambridge
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
Farrell S, Lewandowsky S (2018) Computational modeling of cognition and behavior, 1st edn. Cambridge University Press, Cambridge. https://doi.org/10.1017/CBO9781316272503
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
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
Friston KJ, Stephan KE (2007) Free-energy and the brain. Synthese 159(3):417–458
Gelman A (2006) Prior distributions for variance parameters in hierarchical models (comment on article by Browne and Draper). Bayesian Anal 1(3):515–534
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
Hahn U (2014) The Bayesian boom: Good thing or bad? Front Psychol. https://doi.org/10.3389/fpsyg.2014.00765
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
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
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
Kruschke JK (2015) Doing Bayesian data analysis: a tutorial with R, JAGS, and stan, 2nd edn. Academic Press, Boston
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
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
Lee MD, Wagenmakers E-J (2013) Bayesian cognitive modeling: a practical course. Cambridge University Press, Cambridge
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
Marr D (1982) Vision: a computational investigation into the human representation and processing of visual information. MIT Press, Cambridge
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
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
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
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
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
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
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
Schürmann T, Mohler BJ, Peters J, Beckerle P (2019) How cognitive models of human body experience might push robotics. Front Neurorobot 13:14
Schwartenbeck P, Friston K (2016) Computational phenotyping in psychiatry: a worked example. ENeuro. https://doi.org/10.1523/ENEURO.0049-16.2016
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
Siciliano B, Khatib O (eds) (2008) Springer handbook of robotics: with… 84 tables. Springer, Berlin
Sun R (ed) (2008) The Cambridge handbook of computational psychology. Cambridge University Press, New York
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
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
Weiss Y, Simoncelli EP, Adelson EH (2002) Motion illusions as optimal percepts. Nat Neurosci 5(6):598–604. https://doi.org/10.1038/nn858
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 8:232
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
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.
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Schürmann, T., Vogt, J., Christ, O. et al. The Bayesian causal inference model benefits from an informed prior to predict proprioceptive drift in the rubber foot illusion. Cogn Process 20, 447–457 (2019). https://doi.org/10.1007/s10339-019-00928-9
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DOI: https://doi.org/10.1007/s10339-019-00928-9