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1.
Figure 2

Figure 2. From: Identifying fMRI Model Violations with Lagrange Multiplier Tests.

HRF for simulating fMRI data, defined using a combination of sigmoid functions.

Ben Cassidy, et al. IEEE Trans Med Imaging. 2012 July;31(7):1481-1492.
2.
Figure 9

Figure 9. From: Identifying fMRI Model Violations with Lagrange Multiplier Tests.

Cumulative distributionn of anomaly voxel detection rate within fMRI data set −1198T.

Ben Cassidy, et al. IEEE Trans Med Imaging. 2012 July;31(7):1481-1492.
3.
Figure 3

Figure 3. From: Identifying fMRI Model Violations with Lagrange Multiplier Tests.

Statistical power as a function of the number of basis functions tested in addition to the fitted Double Gamma Laguerre basis set.

Ben Cassidy, et al. IEEE Trans Med Imaging. 2012 July;31(7):1481-1492.
4.
Figure 5

Figure 5. From: Identifying fMRI Model Violations with Lagrange Multiplier Tests.

ROC curves for the detection of non-linear component of fMRI signal. False positive rate is negligible for threshold α = 0.01. Simulated SNR range is comparable to real data. Plot axes are scaled in (b).

Ben Cassidy, et al. IEEE Trans Med Imaging. 2012 July;31(7):1481-1492.
5.
Figure 8

Figure 8. From: Identifying fMRI Model Violations with Lagrange Multiplier Tests.

LM-anomaly map for the presence of Non-Linear component in fMRI signal (a), in conjunction with a linear BOLD activation test statistic of the same slice (b). Colours represent significance levels above a detection threshold of α = 0.01 for both plots.

Ben Cassidy, et al. IEEE Trans Med Imaging. 2012 July;31(7):1481-1492.
6.
Figure 4

Figure 4. From: Identifying fMRI Model Violations with Lagrange Multiplier Tests.

ROC curves of simulation results for the algorithm testing for presence of Time-Varying (non-stationary) Hemodynamic Response in the SNR range of [0.5,2], equating to real data; see (14). These results from an event-type stimulus pattern are consistent with those from an extended block-style stimulus.

Ben Cassidy, et al. IEEE Trans Med Imaging. 2012 July;31(7):1481-1492.
7.
Figure 1

Figure 1. From: Identifying fMRI Model Violations with Lagrange Multiplier Tests.

Parameter spaces of the restricted and full models are the intersection curve and parabolic surface respectively. The Likelihood Ratio test gets LR from likelihoods at both maxima. The Lagrange Multiplier method approximates LR by calculating likelihood and curvature at only the restricted parameter estimate.

Ben Cassidy, et al. IEEE Trans Med Imaging. 2012 July;31(7):1481-1492.
8.
Figure 7

Figure 7. From: Identifying fMRI Model Violations with Lagrange Multiplier Tests.

LM-anomaly map for the presence of Time-Varying HR in real data (a), in conjunction with the typical Least-Squares test statistic for BOLD activation (b) of the same data slice calculated using the nonparametric Laguerre HRF specification. Colours represent significance levels above a detection threshold of α = 0.01.

Ben Cassidy, et al. IEEE Trans Med Imaging. 2012 July;31(7):1481-1492.
9.
Figure 6

Figure 6. From: Identifying fMRI Model Violations with Lagrange Multiplier Tests.

Fig. (a) shows the LM-anomaly map testing for violation of the Double Gamma HRF. Activation maps are shown for the same data slice calculated using (b) the nonparametric Laguerre HRF basis set and (c) the Double Gamma HRF specification. Colours represent significance levels above a detection threshold of α = 0.01. Fig. (d) shows a map of voxels detected separately by the Double Gamma LM-anomaly test statistic (blue), the conventional Least-Squares activation test using nonparametric Laguerre HRF specification (red) and both (white).

Ben Cassidy, et al. IEEE Trans Med Imaging. 2012 July;31(7):1481-1492.

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