A Tutorial on Fisher information

Ly, Alexander; Marsman, Maarten; Verhagen, Josine; Grasman, Raoul P. P. P.; Wagenmakers, Eric‐Jan

doi:10.1016/j.jmp.2017.05.006

Cited by 214 publications

(133 citation statements)

References 96 publications

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“…As in previous work (Keshvari, van den Berg, & Ma, 2012; van den Berg, Awh, & Ma, 2014; van den Berg, Shin, Chou, George, & Ma, 2012), we define memory precision as Fisher information, J , which provides a lower bound on the variance of any unbiased estimator of the stimulus and is a common tool in the study of theoretical limits on stimulus coding and discrimination precision (Abbott & Dayan, 1999; Cover & Thomas, 2005; Ly, A., Marsman, Verhagen, Grasman, & Wagenmakers, 2015; Paradiso, 1988). It is monotonically related to κ through the relation

J false(κ false) = κ \frac{I_{1} false(κ false)}{I_{0} false(κ false)}

(Keshvari et al, 2012), where I 1 is the modified Bessel function of the first kind of order 1.…”

Section: Model Constructionmentioning

confidence: 99%

Fechner’s law in metacognition: A quantitative model of visual working memory confidence.

Berg¹,

Yoo²,

Ji³

2017

Psychological Review

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Although visual working memory (VWM) has been studied extensively, it is unknown how people form confidence judgments about their memories. Peirce (1878) speculated that Fechner’s law – which states that sensation is proportional to the logarithm of stimulus intensity – might apply to confidence reports. Based on this idea, we hypothesize that humans map the precision of their VWM contents to a confidence rating through Fechner’s law. We incorporate this hypothesis into the best available model of VWM encoding and fit it to data from a delayed-estimation experiment. The model provides an excellent account of human confidence rating distributions as well as the relation between performance and confidence. Moreover, the best-fitting mapping in a model with a highly flexible mapping closely resembles the logarithmic mapping, suggesting that no alternative mapping exists that accounts better for the data than Fechner's law. We propose a neural implementation of the model and find that this model also fits the behavioral data well. Furthermore, we find that jointly fitting memory errors and confidence ratings boosts the power to distinguish previously proposed VWM encoding models by a factor of 5.99 compared to fitting only memory errors. Finally, we show that Fechner's law also accounts for metacognitive judgments in a word recognition memory task, which is a first indication that it may be a general law in metacognition. Our work presents the first model to jointly account for errors and confidence ratings in VWM and could lay the groundwork for understanding the computational mechanisms of metacognition.

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J false(κ false) = κ \frac{I_{1} false(κ false)}{I_{0} false(κ false)}

(Keshvari et al, 2012), where I 1 is the modified Bessel function of the first kind of order 1.…”

Section: Model Constructionmentioning

confidence: 99%

Fechner’s law in metacognition: A quantitative model of visual working memory confidence.

Berg¹,

Yoo²,

Ji³

2017

Psychological Review

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“…174-179 and 289-292). This recommendation is not the prior derived from Jeffreys's rule based on the Fisher information (e.g., Ly et al, 2017), as discussed in Berger and Sun (2008). With = 1, = = = 0, thus, a uniform prior on , Jeffreys showed that the marginal posterior for is approximately proportional to h a (n, r | ), where…”

Section: Notation and Resultsmentioning

confidence: 98%

“…174–179 and 289–292). This recommendation is not the prior derived from Jeffreys's rule based on the Fisher information (e.g., LY et al , ), as discussed in BERGER and SUN (). With α =1, β = γ = δ =0, thus, a uniform prior on ρ , Jeffreys showed that the marginal posterior for ρ is approximately proportional to h a ( n , r | ρ ), where

h_{a} (n, r | ρ) = {(1 - ρ^{2})}^{\frac{n - 1}{2}} {(1 - ρ r)}^{\frac{3 - 2 n}{2}},

represents the ρ ‐dependent part of the likelihood Equation with θ 0 =( μ 1 , μ 2 , σ 1 , σ 2 ) integrated out.…”

Section: Notation and Resultsmentioning

confidence: 99%

Analytic posteriors for Pearson's correlation coefficient

Marsman

Wagenmakers

2017

Statistica Neerlandica

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201

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“…This depends on how a change in qt is mapped onto a change in kt, which is given by the Fisher information, the variance of the first derivative of the log-likelihood function with respect to qt. For the binomial distribution with n = 1 (i.e., the Bernoulli distribution), the Fisher information is (e.g., Ly et al, 2017):…”

Section: A "Toy" Model Examplementioning

confidence: 99%

Leave-One-Trial-Out (LOTO): A general approach to link single-trial parameters of cognitive models to neural data

Gluth

Meiran

2018

Preprint

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It has become a key goal of model-based neuroscience to estimate trial-by-trial fluctuations of cognitive model parameters for linking these fluctuations to brain signals. However, previously developed methods were limited by being difficulty to implement, timeconsuming, or model-specific. Here, we propose an easy, efficient and general approach to estimating trial-wise changes in parameters: Leave-One-Trial-Out (LOTO). The rationale behind LOTO is that the difference between the parameter estimates for the complete dataset and for the dataset with one omitted trial reflects the parameter value in the omitted trial. We show that LOTO is superior to estimating parameter values from single trials and compare it to previously proposed approaches. Furthermore, the method allows distinguishing true variability in a parameter from noise and from variability in other parameters. In our view, the practicability and generality of LOTO will advance research on tracking fluctuations in latent cognitive variables and linking them to neural data.

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A Tutorial on Fisher information

Cited by 214 publications

References 96 publications

Fechner’s law in metacognition: A quantitative model of visual working memory confidence.

Fechner’s law in metacognition: A quantitative model of visual working memory confidence.

Analytic posteriors for Pearson's correlation coefficient

Leave-One-Trial-Out (LOTO): A general approach to link single-trial parameters of cognitive models to neural data

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