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Estimating Dynamic Signals From Trial Data With Censored Values Cover

Estimating Dynamic Signals From Trial Data With Censored Values

Computational Psychiatry

Volume 1 (2017): Issue 0

By: Ali Yousefi, Darin D. Dougherty, Emad N. Eskandar, Alik S. Widge and Uri T. Eden

Open Access

|Oct 2017

Figures & tables

Figures & Tables

Table 1.

Exact filter procedure

Initialize: Define the prior distribution of p(x₀)

For each time k:

Run prediction step: Update the predictive distribution of x_k given the state model and previous

time posterior distribution.

p x_{k}| y_{1 : k - 1}, z_{1 : k - 1}) = \int f x_{k}| x_{k - 1}) p x_{k - 1}| y_{1 : k - 1}, z_{1 : k - 1}) d x_{k - 1} (5)

Run update step: Update the posterior distribution of x_k given the observation y_k and the

predictive distribution.

L x_{k}; y_{k}, z_{k}) = \begin{array}{l} f z_{k}| x_{k}, y_{k}) f y_{k}| x_{k}) & y_{k} \in 0 T_{k}] \\ Pr y_{k} > T_{k}| x_{k}) & y_{k} = ‘ Censored ’\} \end{array} (6)

p x_{k}| y_{1 : k}, z_{1 : k}) \propto L x_{k}; z_{k}, y_{k}) p x_{k}| y_{1 : k ‐ 1}, z_{1 : k ‐ 1}) (7)

Estimation results for a single realization. (a) One realization of the inattention-state process over 100 trials, based on Equation 8. (b) Realization of reaction time and binary decision data, based on the state process in panel a and Equations 9 and 10. Both the reaction time and binary response data are censored whenever the reaction time is longer than 0.9 s. The circles show the binary decision, either 0 or 1, and the “x” marks show the missing points. (c) Estimation results for the exact filter, based on the full likelihood in Equation 11. (d) Estimation results for data deletion, based on the likelihood in Equation 25M. (e) Estimation results for data imputation, based on the likelihood in Equation 26. (f) Estimation results for the approximate Gaussian filter, detailed in Equations 21, , –24.

Estimator accuracy summary results.(a) Root-mean square error (RMSE) values as a function of the expected fraction of censored trials, based only on reaction time data. (b) Fractions of trials in which the true state value is contained in the estimated 95% HPD region, as a function of the expected fraction of censored trials based only on reaction time data. (c) RMSE values as a function of the expected fraction of censored trials, based on both reaction time and binary decision data. (d) Fractions of trials in which the true state value is contained in the estimated 95% HPD region, as a function of the expected fraction of censored trials, based on both reaction time and binary decision data. The simulation was run for a set of threshold values marked by “o,” and the performance graphs are derived by interpolation of the corresponding marked points.

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DOI: https://doi.org/10.1162/CPSY_a_00003 | Journal eISSN: 2379-6227

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Language: English

Submitted on: Aug 3, 2016

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Accepted on: Apr 5, 2017

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Published on: Oct 1, 2017

Published by: MIT Press

In partnership with: Paradigm Publishing Services

Publication frequency: 1 issue per year

Keywords:

state-space model,

Bayesian filtering Gaussian approximation,

likelihood function,

dynamic behavioral signal

© 2017 Ali Yousefi, Darin D. Dougherty, Emad N. Eskandar, Alik S. Widge, Uri T. Eden, published by MIT Press
This work is licensed under the Creative Commons Attribution 4.0 License.

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