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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"%load_ext autoreload\n",
"%autoreload 2\n",
"\n",
"import sys\n",
"sys.path.append('/Users/saad/python-modules')\n",
"from mh import MH, plot_samples\n",
"import numpy as np\n",
"import pandas as pd\n",
"import seaborn as sns\n",
"import matplotlib.pyplot as plt\n",
"import sys, os, glob\n",
"sns.set()\n"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(554, 29)"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Read in design matrix\n",
"df = pd.read_csv('/Users/saad/Desktop/input_vars_design_mat.csv')\n",
"# Read entropy\n",
"#en = np.loadtxt('/Users/saad/Desktop/entropy.txt')\n",
"\n",
"# Remove entropy-outlier subjects\n",
"#outliers = en.mean(axis=0)<1.4\n",
"\n",
"#df = df.iloc[~outliers,:]\n",
"#en = en[:,~outliers]\n",
"\n",
"# Read in the tracts volumes\n",
"\n",
"tracts_dir = '/Users/saad/Desktop/tmp_matteo'\n",
"tracts_files = sorted(glob.glob(os.path.join(tracts_dir,'*_resorted.txt')))\n",
"\n",
"tracts_names = []\n",
"tracts_vols = []\n",
"for i in range(len(tracts_files)):\n",
" a = os.path.splitext(os.path.split(tracts_files[i])[-1])[-2].split(\"_\", 2)\n",
" tracts_names.append(a[0]+\"_\"+a[1])\n",
" tracts_vols.append(np.loadtxt(tracts_files[i])[:,1])\n",
"\n",
"tracts_vols = np.asarray(tracts_vols).T\n",
"tracts_vols.shape"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": 28,
"metadata": {},
"outputs": [],
"source": [
"# Prepare data\n",
"def prepare(df,name=None,Y=None):\n",
" # Data and regressors\n",
" if name is not None:\n",
" Y = np.array(df[name])\n",
" b = np.array(df['age_birth'])\n",
" s = np.array(df['age_scan'])\n",
" # Confounds\n",
" #df['brain_vol'] = np.array(df['gm_vol'])+np.array(df['wm_vol'])+np.array(df['ven_vol'])\n",
" conf = np.array(df[['qc_snr','qc_cnr400','qc_cnr1000','qc_cnr2600']])\n",
" # Regress out confounds from data\n",
" from sklearn.linear_model import LinearRegression\n",
" reg = LinearRegression(fit_intercept=True, normalize=False).fit(conf, Y)\n",
" Y_deconf = Y - reg.predict(conf) + reg.intercept_ \n",
" # Normalise to 95th percentile\n",
" Y_deconf = Y_deconf/np.quantile(Y_deconf,.95,axis=0)*100 \n",
"\n",
" return Y_deconf,b,s\n",
" \n",
" \n",
"# Various forward models\n",
"# Only one slope (beta1=beta2)\n",
"def forward_0(p,s,b):\n",
" return p[0]*s-p[0]*p[1]\n",
"\n",
"# Same post-birth slopes for term and prem\n",
"def forward_1(p,s,b):\n",
" pred = p[0]*b + p[1]*(s-b)- p[0]*p[2] \n",
" return pred\n",
"# Post-birth slope is different\n",
"def forward_2(p,s,b):\n",
" term = b>=37\n",
" prem = b<37\n",
" \n",
" pred = p[0]*b - p[0]*p[3]\n",
" pred[term] += p[1]*(s[term]-b[term])\n",
" pred[prem] += p[2]*(s[prem]-b[prem])\n",
" return pred\n",
"# All slopes different - same onset\n",
"def forward_3(p,s,b):\n",
" term = b>=37\n",
" prem = b<37\n",
" \n",
" pred = np.zeros(s.size)\n",
" pred[term] = p[0]*b[term] + p[1]*(s[term]-b[term])- p[0]*p[4]\n",
" pred[prem] = p[2]*b[prem] + p[3]*(s[prem]-b[prem])- p[2]*p[4]\n",
" \n",
" return pred\n",
"def forward_4(p,s,b):\n",
" term = b>=p[4]\n",
" prem = b<p[4]\n",
" \n",
" pred = p[0]*b - p[0]*p[3]\n",
" pred[term] += p[1]*(s[term]-b[term])\n",
" pred[prem] += p[2]*(s[prem]-b[prem])\n",
" \n",
" return pred\n",
"\n",
"\n",
"class ForwardModel:\n",
" def __init__(self,modelid):\n",
" self.modelid = modelid\n",
" if modelid == 0:\n",
" self.forward = forward_0\n",
" self.nparams = 2\n",
" self.labels = ['beta1','onset']\n",
" elif modelid == 1:\n",
" self.forward = forward_1\n",
" self.nparams = 3\n",
" self.labels = ['beta1','beta2','onset']\n",
" elif modelid == 2:\n",
" self.forward = forward_2\n",
" self.nparams = 4\n",
" self.labels = ['beta1','beta2-term','beta2-prem','onset']\n",
" elif modelid == 3:\n",
" self.forward = forward_3\n",
" self.nparams = 5\n",
" self.labels = ['beta1-term','beta2-term','beta1-prem','beta2-prem','onset']\n",
" elif modelid == 4:\n",
" self.forward = forward_4\n",
" self.nparams = 5\n",
" self.labels = ['beta1','beta2-term','beta2-prem','onset','thresh']\n",
" else:\n",
" raise Exception('Unknown model id.')\n",
" def bounds(self): \n",
" if self.modelid == 0:\n",
" LB = np.array([-np.inf,0])\n",
" UB = np.array([ np.inf,40])\n",
" return LB,UB\n",
" elif self.modelid == 1:\n",
" LB = np.array([-np.inf,-np.inf,0])\n",
" UB = np.array([ np.inf, np.inf,40])\n",
" return LB,UB\n",
" elif self.modelid == 2:\n",
" LB = np.array([-np.inf,-np.inf,-np.inf,0])\n",
" UB = np.array([ np.inf, np.inf,np.inf,40])\n",
" return LB,UB\n",
" elif self.modelid == 3:\n",
" LB = np.array([-np.inf,-np.inf,-np.inf,-np.inf,0])\n",
" UB = np.array([ np.inf, np.inf, np.inf, np.inf,40])\n",
" return LB,UB\n",
" elif self.modelid == 4:\n",
" LB = np.array([-np.inf,-np.inf,-np.inf,0,0])\n",
" UB = np.array([ np.inf, np.inf, np.inf,40,40])\n",
" return LB,UB\n",
" else:\n",
" raise Exception('Unknown model id.')\n",
" def init(self): \n",
" if self.modelid == 0:\n",
" return np.array([0,0.00001])\n",
" elif self.modelid == 1:\n",
" return np.array([0,0,0.00001])\n",
" elif self.modelid == 2:\n",
" return np.array([0,0,0,0.00001])\n",
" elif self.modelid == 3:\n",
" return np.array([0,0,0,0,0.00001])\n",
" elif self.modelid == 4:\n",
" return np.array([0,0,0,0.0001,37])\n",
" else:\n",
" raise Exception('Unknown model id.')\n",
" \n",
" \n",
"# Fit model to data\n",
"def do_fit(Y,b,s,forward_model):\n",
" loglik = lambda p : np.log(np.linalg.norm(Y-forward_model.forward(p,s,b)))*Y.size/2\n",
" logpr = lambda p : 0 #uniform priors\n",
" # Bounds\n",
" LB,UB = forward_model.bounds()\n",
" # Initialise\n",
" p0 = forward_model.init()\n",
"\n",
" mh = MH(loglik,logpr,njumps=10000)\n",
" import time\n",
" start = time.time()\n",
" samples = mh.fit(p0,LB=LB,UB=UB)\n",
" ML = mh.marglik_Laplace(samples)\n",
" #print(\"Elapsed time : {}\".format(time.time() - start))\n",
" #print('Marginal Likelihood : {}'.format(ML))\n",
" \n",
" return samples, ML\n",
"\n",
"def do_pca_fit(Y,b,s,forward_model,keep=10):\n",
" # PCA the data prior to fitting\n",
" if Y.shape[0]>Y.shape[1]:\n",
" raise Exception(\"Data must be transposed\")\n",
" import scipy as sp\n",
" U,S,V = sp.sparse.linalg.svds(Y-Y.mean(axis=0),k=keep)\n",
" \n",
" \n",
" all_betas = np.zeros((fm.nparams,keep))\n",
" for i in range(keep):\n",
" samples, _ = do_fit(Y@V[i,:].T,b,s,forward_model)\n",
" betas = samples[:,:-1].mean(axis=0)\n",
" betas = np.append(betas,-samples[:,-1].mean(axis=0)*betas[0])\n",
" all_betas[:,i] = betas\n",
" all_betas = all_betas@V\n",
" grot1 = all_betas[:-1,:]\n",
" grot2 = -all_betas[-1,:]/all_betas[0,:]\n",
" all_betas = np.concatenate((grot1,grot2[None,:]))\n",
" return all_betas\n"
]
},
{
"cell_type": "code",
"execution_count": 31,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/Library/Frameworks/Python.framework/Versions/3.6/lib/python3.6/site-packages/ipykernel_launcher.py:55: RuntimeWarning: overflow encountered in multiply\n",
"/Users/saad/python-modules/mh.py:345: RuntimeWarning: overflow encountered in multiply\n",
" prop *= np.sqrt((1+acc)/(1+rej))\n",
"/Library/Frameworks/Python.framework/Versions/3.6/lib/python3.6/site-packages/numpy/core/_methods.py:75: RuntimeWarning: overflow encountered in reduce\n",
" ret = umr_sum(arr, axis, dtype, out, keepdims)\n",
"/Library/Frameworks/Python.framework/Versions/3.6/lib/python3.6/site-packages/numpy/linalg/linalg.py:2022: RuntimeWarning: invalid value encountered in det\n",
" r = _umath_linalg.det(a, signature=signature)\n",
"/Users/saad/python-modules/mh.py:184: RuntimeWarning: invalid value encountered in true_divide\n",
" std_pos = np.sqrt(np.sum(np.maximum(0,samples-mean)**2,axis=0) / np.sum((samples-mean)>0,axis=0))\n",
"/Library/Frameworks/Python.framework/Versions/3.6/lib/python3.6/site-packages/matplotlib/axes/_axes.py:2951: RuntimeWarning: invalid value encountered in double_scalars\n",
" low = [thisx - thiserr for (thisx, thiserr)\n"
]
},
{
"ename": "ValueError",
"evalue": "color kwarg must have one color per dataset",
"output_type": "error",
"traceback": [
"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
"\u001b[0;31mValueError\u001b[0m Traceback (most recent call last)",
"\u001b[0;32m<ipython-input-31-3eb95b14daae>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m 8\u001b[0m \u001b[0mplot_samples\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msamples\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mlabels\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mfm\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlabels\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mplot_type\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'vector'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 9\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 10\u001b[0;31m \u001b[0mplot_samples\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msamples\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mlabels\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mfm\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlabels\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mplot_type\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'matrix'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
"\u001b[0;32m~/python-modules/mh.py\u001b[0m in \u001b[0;36mplot_samples\u001b[0;34m(samples, labels, plot_type)\u001b[0m\n\u001b[1;32m 176\u001b[0m \u001b[0mdf\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mpd\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mDataFrame\u001b[0m\u001b[0;34m(\u001b[0m \u001b[0mdata\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0msamples\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcolumns\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mlabels\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 177\u001b[0m \u001b[0mg\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0msns\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mPairGrid\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdf\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 178\u001b[0;31m \u001b[0mg\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmap_diag\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mhist\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 179\u001b[0m \u001b[0mg\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmap_offdiag\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msns\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mkdeplot\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 180\u001b[0m \u001b[0;32melif\u001b[0m \u001b[0mplot_type\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;34m'vector'\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
"\u001b[0;32m/Library/Frameworks/Python.framework/Versions/3.6/lib/python3.6/site-packages/seaborn/axisgrid.py\u001b[0m in \u001b[0;36mmap_diag\u001b[0;34m(self, func, **kwargs)\u001b[0m\n\u001b[1;32m 1397\u001b[0m \u001b[0mcolor\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mfixed_color\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 1398\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1399\u001b[0;31m \u001b[0mfunc\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdata_k\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlabel\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mlabel_k\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcolor\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mcolor\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 1400\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 1401\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_clean_axis\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0max\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
"\u001b[0;32m/Library/Frameworks/Python.framework/Versions/3.6/lib/python3.6/site-packages/matplotlib/pyplot.py\u001b[0m in \u001b[0;36mhist\u001b[0;34m(x, bins, range, normed, weights, cumulative, bottom, histtype, align, orientation, rwidth, log, color, label, stacked, hold, data, **kwargs)\u001b[0m\n\u001b[1;32m 3079\u001b[0m \u001b[0mhisttype\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mhisttype\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0malign\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0malign\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0morientation\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0morientation\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 3080\u001b[0m \u001b[0mrwidth\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mrwidth\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlog\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mlog\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcolor\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mcolor\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlabel\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mlabel\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 3081\u001b[0;31m stacked=stacked, data=data, **kwargs)\n\u001b[0m\u001b[1;32m 3082\u001b[0m \u001b[0;32mfinally\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 3083\u001b[0m \u001b[0max\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_hold\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mwashold\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
"\u001b[0;32m/Library/Frameworks/Python.framework/Versions/3.6/lib/python3.6/site-packages/matplotlib/__init__.py\u001b[0m in \u001b[0;36minner\u001b[0;34m(ax, *args, **kwargs)\u001b[0m\n\u001b[1;32m 1896\u001b[0m warnings.warn(msg % (label_namer, func.__name__),\n\u001b[1;32m 1897\u001b[0m RuntimeWarning, stacklevel=2)\n\u001b[0;32m-> 1898\u001b[0;31m \u001b[0;32mreturn\u001b[0m \u001b[0mfunc\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0max\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 1899\u001b[0m \u001b[0mpre_doc\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0minner\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m__doc__\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 1900\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mpre_doc\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
"\u001b[0;32m/Library/Frameworks/Python.framework/Versions/3.6/lib/python3.6/site-packages/matplotlib/axes/_axes.py\u001b[0m in \u001b[0;36mhist\u001b[0;34m(***failed resolving arguments***)\u001b[0m\n\u001b[1;32m 6166\u001b[0m \u001b[0mcolor\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mmcolors\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mto_rgba_array\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcolor\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 6167\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcolor\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m!=\u001b[0m \u001b[0mnx\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 6168\u001b[0;31m \u001b[0;32mraise\u001b[0m \u001b[0mValueError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"color kwarg must have one color per dataset\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 6169\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 6170\u001b[0m \u001b[0;31m# Save the datalimits for the same reason:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
"\u001b[0;31mValueError\u001b[0m: color kwarg must have one color per dataset"
]
},
{
"data": {
"text/plain": [
"<matplotlib.figure.Figure at 0x126916c18>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x126545518>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/plain": [
"<matplotlib.figure.Figure at 0x1269161d0>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x126860390>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Quick fit a model and look at the resuts\n",
"model = 4\n",
"fm = ForwardModel(model)\n",
"name = 'ven_vol'\n",
"data,birth,scan = prepare(df,name=name)\n",
"samples, ML = do_fit(data,birth,scan,fm)\n",
"\n",
"plot_samples(samples,labels=fm.labels,plot_type='vector')\n",
"\n",
"plot_samples(samples,labels=fm.labels,plot_type='matrix')\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/Library/Frameworks/Python.framework/Versions/3.6/lib/python3.6/site-packages/scipy/linalg/basic.py:1226: RuntimeWarning: internal gelsd driver lwork query error, required iwork dimension not returned. This is likely the result of LAPACK bug 0038, fixed in LAPACK 3.2.2 (released July 21, 2010). Falling back to 'gelss' driver.\n",
" warnings.warn(mesg, RuntimeWarning)\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x108904780>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x12151a438>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1215b5908>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"\n",
"# COMPARE CSF,GM,WM \n",
"\n",
"fm = ForwardModel(2)\n",
"param_list = [0,1,2]\n",
"\n",
"for name in ['csf_vol','gm_vol','wm_vol']:\n",
" Y,b,s = prepare(df,name)\n",
" samples,_ = do_fit(Y,b,s,fm) \n",
" plt.figure()\n",
" [plt.hist(samples[:,i],histtype='step') for i in param_list]\n",
" plt.legend([ fm.labels[i] for i in param_list ])\n",
" plt.title(name)\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[[1. 1. 1.]\n",
" [1. 1. 1.]\n",
" [1. 1. 1.]]\n"
]
}
],
"source": [
"# BAYESIAN MODEL COMPARISON\n",
"# WITH APPROX MARGINAL LIKELIHOOD\n",
"\n",
"name = 'csf_vol'\n",
"nmodels = 3\n",
"\n",
"MLs = np.zeros(nmodels)\n",
"for modelid in [1,2,3]: \n",
" fm = ForwardModel(modelid)\n",
" Y,b,s = prepare(df,name)\n",
" samples, ML = do_fit(Y,b,s,fm)\n",
" MLs[modelid-1] = ML\n",
" \n",
"# Bayes factor\n",
"BF = np.zeros([nmodels,nmodels])\n",
"for i in range(nmodels):\n",
" for j in range(nmodels):\n",
" BF[i,j] = np.exp(MLs[i]-MLs[j])\n",
" \n",
"\n",
"print(\"{}\".format(np.round(BF)))\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"scrolled": true
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0\n",
"1\n",
"2\n",
"3\n",
"4\n",
"5\n",
"6\n",
"7\n",
"8\n",
"9\n",
"10\n",
"11\n",
"12\n",
"13\n",
"14\n",
"15\n",
"16\n",
"17\n",
"18\n",
"19\n",
"20\n",
"21\n",
"22\n",
"23\n",
"24\n",
"25\n",
"26\n",
"27\n",
"28\n"
]
}
],
"source": [
"# Loop through the tracts \n",
"model = 2\n",
"fm = ForwardModel(model)\n",
"results = []\n",
"for i in range(len(tracts_files)):\n",
" print(i)\n",
" data,birth,scan = prepare(df,Y=tracts_vols[:,i])\n",
" samples, ML = do_fit(data,birth,scan,fm)\n",
" results.append(samples)\n",
"\n",
"#plot_samples(samples[:,:-1],labels=fm.labels[:-1],plot_type='vector')\n",
"#plot_samples(samples,labels=fm.labels,plot_type='matrix')\n"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [],
"source": [
"beta1 = []\n",
"beta2_term = []\n",
"beta2_prem = []\n",
"onset = []\n",
"T1 = []\n",
"T2 = []\n",
"for i in range(len(results)):\n",
" beta1.append(results[i][:,0].mean())\n",
" beta2_term.append(results[i][:,1].mean())\n",
" beta2_prem.append(results[i][:,2].mean())\n",
" onset.append(results[i][:,3].mean())\n",
" \n",
" m1 = results[i][:,0].mean()\n",
" m2 = results[i][:,1].mean()\n",
" s1 = results[i][:,0].std()\n",
" s2 = results[i][:,1].std()\n",
" s = np.sqrt((s1**2+s2**2)/2)\n",
" T1.append( (m1-m2)/(s) )\n",
" \n",
" m1 = results[i][:,1].mean()\n",
" m2 = results[i][:,2].mean()\n",
" s1 = results[i][:,1].std()\n",
" s2 = results[i][:,2].std()\n",
" s = np.sqrt((s1**2+s2**2)/2)\n",
" T2.append( (m1-m2)/(s) )\n",
" \n",
"beta1 = np.asarray(beta1)\n",
"beta2_term = np.asarray(beta2_term)\n",
"beta2_prem = np.asarray(beta2_prem)\n",
"onset = np.asarray(onset)\n",
"T1 = np.asarray(T1)\n",
"T2 = np.asarray(T2)"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.text.Text at 0x12141fbe0>"
]
},
"execution_count": 17,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x124746128>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x124746940>"
]