Score-Driven Modeling of Spatio-Temporal Data

Figures & data

Fig. 1 Left panel: representation of fiber count matrix (F) for subject 6. Middle panel: Euclidean distance among ROIs matrix (D), equal for all subjects. Right panel: spatial matrix (W) for subject 6 given as a weighted combination of F and D.

Fig. 2 Estimates of vector $\text{exp}\hspace{0.17em}\left\{\mathit{\lambda }\right\}$ for subject 6 (left panel) and subject 13 (right panel).

Fig. 3 Estimates of vector $\mathit{\kappa }$ for subject 6 (left panel) and subject 13 (right panel).

Table 1 Estimates of the scalar static parameters of the model for all subjects. Asymptotic standard errors are reported in brackets.

	subjects
	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16
$\widehat{\varphi }$	0.815	0.701	0.699	0.738	0.810	0.828	0.789	0.799	0.787	0.743	0.852	0.709	0.803	0.849	0.650	0.786
	(0.006)	(0.006)	(0.008)	(0.005)	(0.004)	(0.004)	(0.005)	(0.004)	(0.004)	(0.006)	(0.003)	(0.005)	(0.004)	(0.006)	(0.006)	(0.004)
${\widehat{\rho }}_1$	0.710	0.753	0.658	0.784	0.765	0.731	0.797	0.772	0.779	0.783	0.826	0.772	0.661	0.672	0.785	0.784
	(0.009)	(0.004)	(0.006)	(0.007)	(0.003)	(0.003)	(0.004)	(0.004)	(0.005)	(0.005)	(0.005)	(0.003)	(0.004)	(0.008)	(0.003)	(0.004)
${\widehat{\beta }}_0$	0.006	0.006	0.004	0.023	0.017	−0.013	0.011	0.013	−0.002	0.013	−0.054	0.012	−0.002	0.009	−0.001	0.009
	(0.110)	(0.067)	(0.075)	(0.089)	(0.114)	(0.116)	(0.101)	(0.110)	(0.104)	(0.101)	(0.170)	(0.117)	(0.154)	(0.094)	(0.108)	(0.111)
$\widehat{\nu }$	82.216	142.204	292.837	41.782	69.645	36.485	149.722	60.648	56.911	62.087	15.874	93.069	108.711	176.853	195.265	46.044
	(17.650)	(14.940)	(69.336)	(6.888)	(6.668)	(3.081)	(16.234)	(4.533)	(5.647)	(7.394)	(2.196)	(6.760)	(8.565)	(49.160)	(18.418)	(4.994)

Fig. 4 Left panel: R-fMRI times series and spontaneous activations (dots) detected in ROI lh-parahippocampal (left hemisphere, parahippocampal). Right panel: corresponding residuals and outliers (dots). Top panels: subject 6. Bottom panels: subject 13.

Fig. 5 Spontaneous activations detected for subject 6 (top) and 13 (bottom) over time (x-axis) for all ROIs (y-axis); above the black line we record the ROI in the right hemisphere, while below the black line we record the ROIs in the left hemisphere.

Fig. 6 Dice similarity index computed across activations recorded over time for subject 6 (left panel) and subject 13 (right panel).