Multivariate Modeling and Inference for Brain Networks: ERGMs and Mixed Models

Talk given during the "How To Be a Skeptical Neuroimager: Functional Connectivity & Causal Modelling" Half-Day Educational Course at the 2017 Organisation for Human Brain Mapping meeting, Monday 25 June

The nonzero entries of <i>β</i> showing a circular structure.

<p>The nonzero entries of <i>β</i> showing a circular structure.</p

(a) The BICs of models with increasing <i>n</i>.

<p>(b) The convergence of fix-effect estimates.</p

Estimates of the Mixed-Effects Model.

<p>Estimates of the Mixed-Effects Model.</p

Observed and fitted values of two randomly selected samples (as rows) from each noise level <i>σ</i> = 0.01,0.05,0.1 respectively from the leftmost column to the rightmost column.

<p>The observed data are represented in triangles (PER) and circles (dCLOCK), and the lines represent fitted values.</p

Sample of 100 simulated curves with added Gaussian noise of <i>σ</i> = 0.1.

<p>Sample of 100 simulated curves with added Gaussian noise of <i>σ</i> = 0.1.</p

A simplified model (a) of <i>Drosophilia</i> circadian oscillator and (b) the output of the system as a function of time.

<p>Fig 1(b) is a rendition of Fig 1A in [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0131371#pone.0131371.ref005" target="_blank">5</a>].</p

The mean and confidence interval of estimated <i>ρ</i>, shown as a single vector.

<p>The vertical lines represent the positions of true nonzero values. The three panels (top to bottom) respectively show results for three levels of noise: <i>σ</i> = 0.01,0.05,0.1.</p

Statistics on the Estimated Parameters.

<p>* k = predictor variable, j = estimated variable, <i>τ</i> = lag</p><p>Statistics on the Estimated Parameters.</p

The 24-h BP data of a subsample of 50 subjects before and after intervention.

<p>The 24-h BP data of a subsample of 50 subjects before and after intervention.</p