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Search Results: 1 - 10 of 27128 matches for " Eric-Jan Wagenmakers "
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Do the Dynamics of Prior Information Depend on Task Context? An Analysis of Optimal Performance and an Empirical Test
Don van Ravenzwaaij,Eric-Jan Wagenmakers
Frontiers in Psychology , 2012, DOI: 10.3389/fpsyg.2012.00132
Abstract: In speeded two-choice tasks, optimal performance is prescribed by the drift diffusion model. In this model, prior information or advance knowledge about the correct response can manifest itself as a shift in starting point or as a shift in drift rate criterion. These two mechanisms lead to qualitatively different choice behavior. Analyses of optimal performance (i.e., Bogacz et al., 2006; Hanks et al., 2011) have suggested that bias should manifest itself in starting point when difficulty is fixed over trials, whereas bias should (additionally) manifest itself in drift rate criterion when difficulty is variable over trials. In this article, we challenge the claim that a shift in drift criterion is necessary to perform optimally in a biased decision environment with variable stimulus difficulty. This paper consists of two parts. Firstly, we demonstrate that optimal behavior for biased decision problems is prescribed by a shift in starting point, irrespective of variability in stimulus difficulty. Secondly, we present empirical data which show that decision makers do not adopt different strategies when dealing with bias in conditions of fixed or variable across-trial stimulus difficulty. We also perform a test of specific influence for drift rate variability.
Adjusted Priors for Bayes Factors Involving Reparameterized Order Constraints
Daniel W. Heck,Eric-Jan Wagenmakers
Statistics , 2015,
Abstract: To test psychological theories, it is often desirable to evaluate informative hypotheses involving order constraints on the parameters of statistical models. To fit and test such restrictions, order constraints of the form $\theta_i \leq \theta_j$ can be reparameterized using auxiliary parameters $\eta\in [0,1]$ by replacing the original parameter by $\theta_i = \eta\cdot\theta_j$. This approach is especially common in multinomial processing tree modeling because a new MPT model is obtained by this reparameterization. Here, we discuss the importance of choosing the correct prior distributions for the auxiliary parameters of a reparameterized model. This issue is important for computing the Bayes factor, a model selection criterion that measures the evidence in favor of an order constraint by making a trade-off between model fit and complexity. We show that the naive choice of a uniform prior for the auxiliary parameters results in biased model selection compared to the common approach of using a uniform prior on the subspace of admissible original parameters. As a remedy, we derive the adjusted priors for the auxiliary parameters of the reparameterized model. The practical relevance of the problem is underscored with a concrete example using the multi-trial pair-clustering model.
Origin of the Bayes Factor
Alexander Etz,Eric-Jan Wagenmakers
Statistics , 2015,
Abstract: This article details the historical developments that gave rise to the Bayes factor for testing a point null hypothesis against a composite alternative. In line with current thinking, we find that the conceptual innovation - to assign prior mass to a general law - is due to a series of three articles by Dorothy Wrinch and Sir Harold Jeffreys (1919, 1921, 1923). However, our historical investigation also suggests that in 1932 it was J.B.S. Haldane who derived the first Bayes factor. Jeffreys was well aware of Haldane's work and it may have inspired him to pursue a more concrete statistical implementation for his conceptual ideas. It thus appears that Haldane may have had a much bigger role in the statistical development of the Bayes factor than has hitherto been assumed.
Analytic Posteriors for Pearson's Correlation Coefficient
Alexander Ly,Maarten Marsman,Eric-Jan Wagenmakers
Statistics , 2015,
Abstract: For bivariate normal data, all (marginal) posterior moments of Pearson's correlation coefficient are given in analytic form.
Testing Order Constraints: Qualitative Differences Between Bayes Factors and Normalized Maximum Likelihood
Daniel W. Heck,Eric-Jan Wagenmakers,Richard D. Morey
Statistics , 2014, DOI: 10.1016/j.spl.2015.06.014
Abstract: We compared Bayes factors to normalized maximum likelihood for the simple case of selecting between an order-constrained versus a full binomial model. This comparison revealed two qualitative differences in testing order constraints regarding data dependence and model preference.
Fitting the Cusp Catastrophe in R: A cusp Package Primer
Raoul P. P. P. Grasman,Han L. J. van der Maas,Eric-Jan Wagenmakers
Journal of Statistical Software , 2009,
Abstract: Of the seven elementary catastrophes in catastrophe theory, the “cusp” model is the most widely applied. Most applications are however qualitative. Quantitative techniques for catastrophe modeling have been developed, but so far the limited availability of flexible software has hindered quantitative assessment. We present a package that implements and extends the method of Cobb (Cobb and Watson 1980; Cobb, Koppstein, and Chen 1983), and makes it easy to quantitatively fit and compare different cusp catastrophe models in a statistically principled way. After a short introduction to the cusp catastrophe, we demonstrate the package with two instructive examples.
The neural substrate of prior information in perceptual decision making: a model-based analysis
Birte U. Forstmann,Scott Brown,Gilles Dutilh,Jane Neumann,Eric-Jan Wagenmakers
Frontiers in Human Neuroscience , 2010, DOI: 10.3389/fnhum.2010.00040
Abstract: Prior information biases the decision process: actions consistent with prior information are executed swiftly, whereas actions inconsistent with prior information are executed slowly. How is this bias implemented in the brain? To address this question we conducted an experiment in which people had to decide quickly whether a cloud of dots moved coherently to the left or to the right. Cues provided probabilistic information about the upcoming stimulus. Behavioral data were analyzed with the linear ballistic accumulator (LBA) model, confirming that people used the cue to bias their decisions. The functional magnetic resonance imaging (fMRI) data showed that presentation of the cue differentially activated orbitofrontal cortex, hippocampus, and the putamen. Directional cues selectively activated the contralateral putamen. The fMRI analysis yielded results only when the LBA bias parameter was included as a covariate, highlighting the practical benefits of formal modeling. Our results suggest that the human brain uses prior information by increasing cortico-striatal activation to selectively disinhibit preferred responses.
The role of the noradrenergic system in the exploration-exploitation trade-off: a pharmacological study
Marieke Jepma,Erik T. te Beek,Eric-Jan Wagenmakers,Joop M.A. van Gerven,Sander Nieuwenhuis
Frontiers in Human Neuroscience , 2010, DOI: 10.3389/fnhum.2010.00170
Abstract: Animal research and computational modeling have indicated an important role for the neuromodulatory locus coeruleus–norepinephrine (LC–NE) system in the control of behavior. According to the adaptive gain theory, the LC–NE system is critical for optimizing behavioral performance by regulating the balance between exploitative and exploratory control states. However, crucial direct empirical tests of this theory in human subjects have been lacking. We used a pharmacological manipulation of the LC–NE system to test predictions of this theory in humans. In a double-blind parallel-groups design (N = 52), participants received 4 mg reboxetine (a selective norepinephrine reuptake inhibitor), 30 mg citalopram (a selective serotonin reuptake inhibitor), or placebo. The adaptive gain theory predicted that the increased tonic NE levels induced by reboxetine would promote task disengagement and exploratory behavior. We assessed the effects of reboxetine on performance in two cognitive tasks designed to examine task (dis)engagement and exploitative versus exploratory behavior: a diminishing-utility task and a gambling task with a non-stationary pay-off structure. In contrast to predictions of the adaptive gain theory, we did not find differences in task (dis)engagement or exploratory behavior between the three experimental groups, despite demonstrable effects of the two drugs on non-specific central and autonomic nervous system parameters. Our findings suggest that the LC–NE system may not be involved in the regulation of the exploration–exploitation trade-off in humans, at least not within the context of a single task. It remains to be examined whether the LC–NE system is involved in random exploration exceeding the current task context.
Hidden Multiplicity in Multiway ANOVA: Prevalence and Remedies
Angelique O. J. Cramer,Don van Ravenzwaaij,Dora Matzke,Helen Steingroever,Ruud Wetzels,Raoul P. P. P. Grasman,Lourens J. Waldorp,Eric-Jan Wagenmakers
Statistics , 2014,
Abstract: Many psychologists do not realize that exploratory use of the popular multiway analysis of variance (ANOVA) harbors a multiple comparison problem. In the case of two factors, three separate null hypotheses are subject to test (i.e., two main effects and one interaction). Consequently, the probability of at least one Type I error (if all null hypotheses are true) is 14% rather than 5% if the three tests are independent. We explain the multiple comparison problem and demonstrate that researchers almost never correct for it. To mitigate the problem, we describe four remedies: the omnibus F test, the control of familywise error rate, the control of false discovery rate, and the preregistration of hypotheses.
A Rayleigh-Brillouin scattering spectrometer for ultraviolet wavelengths
Ziyu Gu,M. Ofelia Vieitez,Eric-Jan van Duijn,Wim Ubachs
Physics , 2012, DOI: 10.1063/1.4721272
Abstract: A spectrometer for the measurement of spontaneous Rayleigh-Brillouin scattering line profiles at ultraviolet wavelengths from gas phase molecules has been developed, employing a high-power frequency-stabilized UV laser with narrow bandwidth (2 MHz). The UV light from a frequency-doubled titanium:sapphire laser is further amplified in an enhancement cavity, delivering a 5 Watt UV-beam propagating through the interaction region inside a scattering cell. The design of the RB-scattering cell allows for measurements at gas pressures in the range 0-4 bar and at stably controlled temperatures from -30 to 70 degree Celsius. A scannable Fabry-Perot analyzer with instrument resolution of 232 MHz probes the Rayleigh-Brillouin profiles. Measurements on N2 and SF6 gases demonstrate the high signal-to-noise ratio achievable with the instrument, at the 1% level at the peak amplitude of the scattering profile.
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