Abstract
In this chapter, we provide an overview of various approaches for performing inference on cognitive models. Namely, we discuss the connections between approximate least squares, maximum likelihood estimate, and Bayesian statistics. We then use the comparisons across these methods to motivate the concept of approximate Bayesian computation. We close with an overview and plan for the remainder of the book.
What I cannot create, I do not understand.
Richard Feynman
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
We will use the notational convention that a variable name without subscripts such as y or x may be either vector or scalar valued; context should make clear which. If a variable is subscripted, such as y i or x i , it represents either an element of a vector or a scalar.
- 2.
Don’t confuse the probability (or density) function f Y (y | θ) with the model structure f(x, θ). The predictions of the model, described by f(x, θ) are not necessarily the same as the probability of the data given by f Y (y | θ), though they were the same for the high-threshold model above. For the simple regression model, however, f(x, {m, b}) = mx + b, while most applications of regression state that y is normally distributed with mean mx + b and some standard deviation σ. In this case, f Y (y | x, m, b, σ) is the normal density function that sketches out the bell curve.
References
S. Lewandowsky, S. Farrell, Computational Modeling in Cognition: Principles and Practice (SAGE Publications, Thousand Oaks, CA, 2010)
W.H. Batchelder, D.M. Riefer, Psychol. Rev. 97, 548 (1990)
W.H. Batchelder, D.M. Riefer, Psychon. Bull. Rev. 6, 57 (1999)
S. Dennis, M. Lee, A. Kinnell, J. Math. Psychol. 59, 361 (2008)
I. Klugkist, O. Laudy, H. Hoijtink, Psychol. Methods 15, 281 (2010)
P.S. Laplace, Stat. Sci. 1(3), 364 (1774/1986). http://dx.doi.org/10.1214/ss/1177013621
J.O. Berger, J.M. Bernardo, D. Sun, Bayesian Anal. 10(1), 189 (2015). http://dx.doi.org/10.1214/14-BA915
M.W. Howard, M.J. Kahana, J. Math. Psychol. 46, 269 (2002)
P.B. Sederberg, M.W. Howard, M.J. Kahana, Psychol. Rev. 115, 893 (2008)
A.H. Criss, J.L. McClelland, J. Mem. Lang. 55, 447 (2006)
K.J. Malmberg, R. Zeelenberg, R. Shiffrin, J. Exp. Psychol. Learn. Mem. Cogn. 30, 540 (2004)
J.K. Pritchard, M.T. Seielstad, A. Perez-Lezaun, M.W. Feldman, Mol. Biol. Evol. 16, 1791 (1999)
M.A. Beaumont, Annu. Rev. Ecol. Evol. Syst. 41, 379 (2010)
D. Wegmann, C. Leuenberger, L. Excoffier, Genetics 182, 1207 (2009)
D.L. Hintzman, Behav. Res. Methods Instrum. Comput. 16, 96–101 (1984)
C.F. Sheu, J. Math. Psychol. 36, 592 (1992)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG
About this chapter
Cite this chapter
Palestro, J.J., Sederberg, P.B., Osth, A.F., Zandt, T.V., Turner, B.M. (2018). Motivation. In: Likelihood-Free Methods for Cognitive Science. Computational Approaches to Cognition and Perception. Springer, Cham. https://doi.org/10.1007/978-3-319-72425-6_1
Download citation
DOI: https://doi.org/10.1007/978-3-319-72425-6_1
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-72424-9
Online ISBN: 978-3-319-72425-6
eBook Packages: Behavioral Science and PsychologyBehavioral Science and Psychology (R0)