Projects:TractLongitudinalDTI - Revision history

Anuja: /* Parametric linear regression for distribution-valued data */

2014-10-15T23:11:21Z

Parametric linear regression for distribution-valued data

Anuja: /* Parametric linear regression for distribution-valued data */

2014-10-15T23:09:18Z

Parametric linear regression for distribution-valued data

Anuja: /* Parametric linear regression for distribution-valued data */

2014-10-15T23:07:39Z

Parametric linear regression for distribution-valued data

Anuja: /* Parametric linear regression for distribution-valued data */

2014-10-15T23:07:23Z

Parametric linear regression for distribution-valued data

Anuja: /* Parametric linear regression for distribution-valued data */

2014-10-15T23:06:05Z

Parametric linear regression for distribution-valued data

Anuja: /* Parametric linear regression for distribution-valued data */

2014-10-15T23:03:25Z

Parametric linear regression for distribution-valued data

Anuja: /* Parametric linear regression for distribution-valued data */

2014-10-15T23:00:41Z

Parametric linear regression for distribution-valued data

Anuja: /* Parametric linear regression for distribution-valued data */

2014-10-15T22:58:23Z

Parametric linear regression for distribution-valued data

Anuja: /* Parametric linear regression for distribution-valued data */

2014-10-15T22:46:34Z

Parametric linear regression for distribution-valued data

Anuja: /* Non-parametric regression for distribution-valued data */

2014-10-15T22:45:10Z

Non-parametric regression for distribution-valued data

@@ Line 170: / Line 170: @@
 {| border="0" style="background:transparent;"
-|[[Image:Baryhist3d1.png|thumb|400px|center|The independent variable is the barycentric FA distribution estimated at each arc length location along the tract, using the original FA distributions available from all subjects within the corresponding age group. The regression estimates the continuous spatiotemporal trends in terms of the model parameters using the respective pairs of age and FA distributions as the 'observed' data.]]
+|[[Image:Baryhist3d1.png|thumb|400px|center|The dependent variable is the barycentric FA distribution estimated at each arc length location along the tract, using the original FA distributions available from all subjects within the corresponding age group. The regression estimates the continuous spatiotemporal trends in terms of the model parameters using the respective pairs of age and FA distributions as the 'observed' data.]]
 |-
 |}

@@ Line 170: / Line 170: @@
 {| border="0" style="background:transparent;"
 |[[Image:Baryhist3d1.png|thumb|400px|center|The independent variable is the barycentric FA distribution estimated at each arc length location along the tract, using the original FA distributions available from all subjects within the corresponding age group. The regression estimates the continuous spatiotemporal trends in terms of the model parameters using the respective pairs of age and FA distributions as the 'observed' data.]]
 |-
@@ Line 177: / Line 176: @@
 {| border="0" style="background:transparent;"
-|[[Image:PopuCN_dist_3d1.png|thumb|400px|center|Continuous spatiotemporal normative growth trajectory: Estimated mean FA (gray), Age range where control
+|[[Image:PopuCN_dist_3d1.png|thumb|300px|center|Continuous spatiotemporal normative growth trajectory: Estimated mean FA (gray), Age range where control
 data is originally available (green, orange, purple).]]
-|[[Image:PopuvsKrabbe_dist_3d_2_edit1.png|thumb|400px|center|Krabbe's subject's scans (solid lines): (14 days, 6 mo., 1 yr.) with respect to the estimated healthy trajectory.]]
+|[[Image:PopuvsKrabbe_dist_3d_2_edit1.png|thumb|300px|center|Krabbe's subject's scans (solid lines): (14 days, 6 mo., 1 yr.) with respect to the estimated healthy trajectory.]]
-|[[Image:PopuvsKrabbe_dist_3d31.png|thumb|400px|center|Krabbe's subject's scans:mean FA (solid lines).Control population:estimated mean FA (dashed lines) +/- 3*std.dev. bounds (calculated for Gaussian age distributions centered at matched timepoints with std.dev.=5 days).]]
+|[[Image:PopuvsKrabbe_dist_3d31.png|thumb|300px|center|Krabbe's subject's scans:mean FA (solid lines).Control population:estimated mean FA (dashed lines) +/- 3*std.dev. bounds (calculated for Gaussian age distributions centered at matched timepoints with std.dev.=5 days).]]
 |-
 |}

@@ Line 170: / Line 170: @@
 {| border="0" style="background:transparent;"
-|[[Image:Baryhist3d1.png|thumb|400px|center|The independent variable is the age distribution of the healthy infants clustered around 2 months, 1 year and 2 year.]]
+|[[Image:Agedist.png|thumb|400px|center|The independent variable is the age distribution of the healthy infants clustered around 2 months, 1 year and 2 year.]]
 |[[Image:Baryhist3d1.png|thumb|400px|center|The independent variable is the barycentric FA distribution estimated at each arc length location along the tract, using the original FA distributions available from all subjects within the corresponding age group. The regression estimates the continuous spatiotemporal trends in terms of the model parameters using the respective pairs of age and FA distributions as the 'observed' data.]]
 |-

@@ Line 170: / Line 170: @@
 {| border="0" style="background:transparent;"
-|[[Image:Timedist_rev1.png|thumb|400px|center|The independent variable is the age distribution of the healthy infants clustered around 2 months, 1 year and 2 year.]]
+|[[Image:Baryhist3d1.png|thumb|400px|center|The independent variable is the age distribution of the healthy infants clustered around 2 months, 1 year and 2 year.]]
 |[[Image:Baryhist3d1.png|thumb|400px|center|The independent variable is the barycentric FA distribution estimated at each arc length location along the tract, using the original FA distributions available from all subjects within the corresponding age group. The regression estimates the continuous spatiotemporal trends in terms of the model parameters using the respective pairs of age and FA distributions as the 'observed' data.]]
 |-

@@ Line 170: / Line 170: @@
 {| border="0" style="background:transparent;"
-|[[Image:Timehistrev1.png|thumb|400px|center|The independent variable is the age distribution of the healthy infants clustered around 2 months, 1 year and 2 year.]]
+|[[Image:Timedist_rev1.png|thumb|400px|center|The independent variable is the age distribution of the healthy infants clustered around 2 months, 1 year and 2 year.]]
 |[[Image:Baryhist3d1.png|thumb|400px|center|The independent variable is the barycentric FA distribution estimated at each arc length location along the tract, using the original FA distributions available from all subjects within the corresponding age group. The regression estimates the continuous spatiotemporal trends in terms of the model parameters using the respective pairs of age and FA distributions as the 'observed' data.]]
 |-

@@ Line 167: / Line 167: @@
 experiment is conducted to show the improved reliability and robustness of this method when
 compared with methods working with statistical summaries of the underlying data.
 = References =

@@ Line 158: / Line 158: @@
 === Parametric linear regression for distribution-valued data ===
-Classic linear regression is adapted to employ distribution-valued variables for model estimation.
+We build on the motivation as highlighted in the previous distribution-based regression. However,
 = References =

@@ Line 145: / Line 145: @@
 {| border="0" style="background:transparent;"
 |[[Image:dist2_3d_bary_300_revrev.png|thumb|400px|center|Temporal evolution of the synthetic distributions between two timepoints as estimated by the proposed method.]]
 |[[Image:bary_stat_300.png|thumb|400px|center|Since the regression estimates the complete probability distribution continuously along time, we now have access to the complete variability information at the interpolated time points. This can enable statistical inference using statistical summary measures as well as distribution differences at time points where the original image data is not available.]]