CreateLongData.ipynb

{
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  {
   "cell_type": "markdown",
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   "source": [
    "The following notebook goes through the process of creating the dataset needed to construct the Bayesian model which analyzes the relationship between farm infection status and various other farm covariates.\n",
    "\n",
    "The following function simulates one outbreak and returns an array of: farmID, infection status as an indicator variable, distance of each farm to the index infected farm, number of cows at each farm, and number of sheep at each farm. Thus if we are interested in a simulation with 500 farms, this function will return an array that is 500x5."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
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   "outputs": [
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     "text": [
      "/Users/sandyalakkur/anaconda/envs/py3k/lib/python3.4/site-packages/IPython/kernel/__main__.py:61: DeprecationWarning: using a non-integer number instead of an integer will result in an error in the future\n",
      "/Users/sandyalakkur/anaconda/envs/py3k/lib/python3.4/site-packages/IPython/kernel/__main__.py:94: DeprecationWarning: using a non-integer number instead of an integer will result in an error in the future\n",
      "/Users/sandyalakkur/anaconda/envs/py3k/lib/python3.4/site-packages/IPython/kernel/__main__.py:103: DeprecationWarning: using a non-integer number instead of an integer will result in an error in the future\n"
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       "array([[  1.00000000e+00,   0.00000000e+00,   0.00000000e+00,\n",
       "          2.50000000e+02,   2.50000000e+02],\n",
       "       [  2.00000000e+00,   0.00000000e+00,   6.56989389e-01,\n",
       "          2.50000000e+02,   2.50000000e+02],\n",
       "       [  3.00000000e+00,   0.00000000e+00,   9.36146705e-01,\n",
       "          2.50000000e+02,   2.50000000e+02],\n",
       "       ..., \n",
       "       [  9.98000000e+02,   1.00000000e+00,   2.62560755e+01,\n",
       "          2.50000000e+02,   2.50000000e+02],\n",
       "       [  9.99000000e+02,   0.00000000e+00,   2.51401969e+01,\n",
       "          2.50000000e+02,   2.50000000e+02],\n",
       "       [  1.00000000e+03,   1.00000000e+00,   2.53760693e+01,\n",
       "          2.50000000e+02,   2.50000000e+02]])"
      ]
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     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
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   "source": [
    "def Outbreaks(Size,N,Y0,farms,start,end,x,y,Maxtime=1000):\n",
    "    #This is an attempt of converting the Matlab Program 7.6 Code into Python\n",
    "    import numpy as np\n",
    "    import pandas as pd\n",
    "    from math import pi\n",
    "    #Generate dataset (assume there are the same amount of animals at each farm)\n",
    "    #np.random.seed(10)\n",
    "    #x = Size*np.random.rand(N)\n",
    "    #np.random.seed(11)\n",
    "    #y = Size*np.random.rand(N)\n",
    "    Cows = np.array([250]*N)  #Number of cows at each farm\n",
    "    Sheep = np.array([250]*N)  #Number of cows at each farm\n",
    "    Status = np.array([0]*N)    #Initial Status of each farm\n",
    "    for i in range(Y0):\n",
    "        Status[i] = 1\n",
    "\n",
    "    #Cows are 10.5 times more susceptible to disease than sheep\n",
    "    Suscept = Sheep+10.5*Cows\n",
    "    Transmiss = 5.1e-7*Sheep + 7.7e-7*Cows \n",
    "\n",
    "    #Calculates which grid square a particular location is in (turn a 2-d coordinate into a scalar)\n",
    "    def WhichGrid(x,y,XRange,YRange,XNum,YNum):\n",
    "        #Essentially: floor(Unif[0,1)griddim)griddim+floor(Unif[0,1)griddim)+1\n",
    "        #Returns a number from 1 to griddim^2\n",
    "        return(np.floor(x*(XNum/XRange))*YNum+np.floor(y*(YNum/YRange))+1)\n",
    "\n",
    "    #Set up the grid\n",
    "    grid = WhichGrid(x,y,Size,Size,10.0,10.0)\n",
    "    tmp = sorted(grid) #Sort grid values\n",
    "    i = np.argsort(grid) #get indexed values after sort\n",
    "    x = x[i]\n",
    "    y = y[i]\n",
    "    Status = Status[i]\n",
    "    grid = grid[i]\n",
    "    Xgrid = []\n",
    "    Ygrid = []\n",
    "    Num = []\n",
    "    first_in_grid = []\n",
    "    last_in_grid = []\n",
    "    Max_Sus_grid = []\n",
    "    for i in range(1,int(max(grid))+1):\n",
    "        #turn the grid square number into an x-coordinate and y-coordinate (should not exceed XNum)\n",
    "        Xgrid.append(np.floor((i-1)/10))\n",
    "        Ygrid.append((i-1)%10)\n",
    "        m = np.array(np.where(grid==i))\n",
    "        Num.append(m.shape[1])\n",
    "    \n",
    "        if Num[i-1] > 0:\n",
    "            first_in_grid.append(m.min()+1) #Add the \"+1\" here so the indicies match those in the Keeling code\n",
    "            last_in_grid.append(m.max()+1)\n",
    "            Max_Sus_grid.append(Suscept[m].max())\n",
    "        else:\n",
    "            first_in_grid.append(0)\n",
    "            last_in_grid.append(-1)\n",
    "            Max_Sus_grid.append(0)\n",
    "\n",
    "    #Work out grid to maximum grid transmission probabilities\n",
    "    from numpy import ndarray\n",
    "    MaxRate = ndarray((max(grid),max(grid)))\n",
    "    def Kernel(dist_squared):\n",
    "        dist_squared = np.asarray(dist_squared)\n",
    "        is_scalar = False if dist_squared.ndim > 0 else True\n",
    "        dist_squared.shape = (1,)*(1-dist_squared.ndim) + dist_squared.shape\n",
    "        K = 1 / (pi * (1 + dist_squared**2))\n",
    "        K[(dist_squared < 0.0138)] = 0.3093\n",
    "        K[(dist_squared > 60*60)] = 0\n",
    "        return(K if not is_scalar else K[0])\n",
    "\n",
    "    #Determine maximum number of animals to be infected in each grid square\n",
    "\n",
    "    for i in range (1,int(max(grid))+1):\n",
    "       for j in range(1,int(max(grid))+1):\n",
    "           if ((i-1)==(j-1)) | (Num[i-1]==0) | (Num[j-1] == 0):\n",
    "               MaxRate[i-1,j-1] = np.inf\n",
    "           else:\n",
    "               Dist2 = (Size*max([0,(abs(Xgrid[i-1]-Xgrid[j-1])-1)])/10)**2+(Size*max([0,(abs(Ygrid[i-1]-Ygrid[j-1])-1)])/10)**2\n",
    "               MaxRate[i-1,j-1] = Max_Sus_grid[j-1]*Kernel(Dist2)\n",
    "\n",
    "    #Susceptible, Exposed, Infectious, Reported.==> latent period is 4 days\n",
    "    i=1; S=len(np.where(Status==0)); E=len(np.where(np.logical_and(Status>0, Status<=5)));I=len(np.where(np.logical_and(Status>5, Status<=9))); R=len(np.where(Status==10)); R2=len(np.where(Status>9)); CullSheep=0; CullCattle=0;\n",
    "    i=i+1;  IterateFlag=1;\n",
    "\n",
    "    def Iterate(Status, x, y, Suscept, Transmiss, grid, first_in_grid, last_in_grid, Num, MaxRate):\n",
    "        Event = 0*Status\n",
    "        INF = np.where(np.logical_and(Status>5, Status<=12))[0]\n",
    "        NI = INF.size # Note reported farms still infectious\n",
    "        IGrids = grid[INF]-1\n",
    "        \n",
    "        for ii in range(NI):\n",
    "            INFi = INF[ii]\n",
    "            trans = np.multiply(-Transmiss[INFi],Num) #transmissibility of infected farm to all other grid squares \n",
    "            maxr = MaxRate[IGrids[ii],:] #max number of animals to be infected in infected grid square\n",
    "            # Elementwise multiplication\n",
    "            rate = np.multiply(trans, maxr) #max number of animals to be infected in each grid square based on infected grid square\n",
    "            MaxProb = 1 - np.exp(rate) #Max probability that infected farm infected noninfected farm\n",
    "            rng = np.random.rand(len(MaxProb))\n",
    "            m = np.where((MaxProb - rng)>0)[0]  #these grid squares need further consideration\n",
    "            for n in range(len(m)):\n",
    "                s = 1\n",
    "                M = m[n]\n",
    "                PAB = 1 - np.exp(-Transmiss[INFi]*MaxRate[IGrids[ii],M]) #Max probability that infected farm infects noninfected farms under consideration\n",
    "                if (PAB == 1):\n",
    "                    # Calculate the infection probability for each farm in the susceptible grid\n",
    "                    leng = last_in_grid[M]-first_in_grid[M]+1\n",
    "                    R = np.random.rand(leng)\n",
    "                    for j in range(leng):\n",
    "                        ind1 = first_in_grid[M]+j-1\n",
    "                        Q = 1 - np.exp(-Transmiss[INFi]*Suscept[ind1]*Kernel((x[INFi]-x[ind1]**2+(y[INFi]-y[ind1])**2)))\n",
    "                        if ((R[j] < Q) & (Status[ind1] == 0)):\n",
    "                            Event[ind1] = 1\n",
    "                else:\n",
    "                    R = np.random.rand(Num[M])\n",
    "                    # Loop through all susceptible farms in the grids where an infection event occurred.  \n",
    "                    for j in range(Num[M]):\n",
    "                        P = 1 - s*(1 - PAB)**(Num[M] - j)\n",
    "                        if (R[j] < (PAB / P)):\n",
    "                            s = 0\n",
    "                            ind1=first_in_grid[M]+j-1\n",
    "                            Q=1-np.exp(-Transmiss[INFi]*Suscept[ind1]*Kernel((x[INFi]-x[ind1]**2+(y[INFi]-y[ind1])**2)))\n",
    "                            if ((R[j]< Q/P) & (Status[ind1] == 0)):\n",
    "                                Event[ind1] = 1\n",
    "        # Evolve the infection process of those farms which have been exposed and already infectious ones.  \n",
    "        Status[Status > 0] += 1\n",
    "        Status = Status + Event\n",
    "        m=np.where(Status==13); # Initiate Ring Culling Around Reported Farm\n",
    "        for i in range(len(m)):\n",
    "            Status[m[i]]=-1;\n",
    "        return {'Status':Status,'NI':NI}\n",
    "    \n",
    "    S=[]\n",
    "    E=[]\n",
    "    I=[]\n",
    "    R=[]\n",
    "    R2=[]\n",
    "    CullSheep=[]\n",
    "    CullCattle=[]\n",
    "    t=[]\n",
    "    t.append(0)\n",
    "    results = np.c_[np.array([1]*N),np.arange(1,N+1),np.array([0]*N)]\n",
    "    \n",
    "    while(np.logical_and(t[-1]<Maxtime, IterateFlag)):\n",
    "        Status=Iterate(Status, x, y, Suscept, Transmiss, grid, first_in_grid, last_in_grid, Num, MaxRate)['Status']\n",
    "        Sus=np.where(Status==0)[0]; Exp=np.where(np.logical_and(Status>0, Status<=5))[0]; Inf=np.where(np.logical_and(Status>5, Status<=9))[0]; \n",
    "        Rep=np.where(Status>9)[0]; Culled=np.where(Status<0)[0];\n",
    "        S.append(len(Sus)); E.append(len(Exp)); I.append(len(Inf)); R.append(len(np.where(Status==10))); R2.append(len(Rep));CullSheep.append(np.sum(Sheep[Culled])); CullCattle.append(np.sum(Cows[Culled]))\n",
    "        t.append(t[i-2]+1);i+=1;\n",
    "    \n",
    "        #This is how I stop the simulation (all farms are infected)\n",
    "        if t[-1]>5:\n",
    "            if (E[-4]+I[-4]+R2[-4]==0):\n",
    "                IterateFlag=0\n",
    "        from scipy.stats import itemfreq\n",
    "        sim_num = np.array([i-1]*N)\n",
    "        seq = np.arange(1,N+1)\n",
    "        results_full = np.r_[results,np.c_[sim_num,seq,Status]]\n",
    "        results = results_full\n",
    "\n",
    "    #Return information regarding only farm of interest\n",
    "    this = results_full[np.logical_or.reduce([results_full[:,1] == x for x in farms])]\n",
    "    #Extract rows relating to timepoint of interest\n",
    "    no_this = this[this[:,0]==end]\n",
    "    #turn status to an indicator\n",
    "    Status_ind = (np.logical_and(no_this[:,2]>5,no_this[:,2]<13)).astype(int)\n",
    "    #Calculate distance to index farm - first infected is first in list of coords\n",
    "    coords = list(zip(x,y))\n",
    "    index = np.array((coords[0][0],coords[0][1]))\n",
    "    dist = []\n",
    "    dist.append(0)\n",
    "    for i in range(1,N):\n",
    "        b = np.array((coords[i][0],coords[i][1]))\n",
    "        dist.append(np.linalg.norm(index-b))\n",
    "    to_return = np.c_[no_this[:,1],Status_ind,dist,Cows,Sheep]\n",
    "    #Returns array: farmID, Status_ind, dist_to_index, num_Cows,num_Sheep\n",
    "    return(to_return)\n",
    "    \n",
    "    \n",
    "#import numpy as np\n",
    "#Size = 20\n",
    "#N = 1000    \n",
    "#x = Size*np.random.rand(N)\n",
    "#y = Size*np.random.rand(N)     \n",
    "#Outbreaks(Size=Size,N=N,Y0=1,farms = np.arange(1,N+1),start=20,end=30,x=x,y=y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now that we have working code to generate a dataset for one outbreak, we need to be able to simulate the outbreak multiple times. The following code performs this action and adds a column indicating which outbreak simulation the data corresponds to. Thus, if there are 500 farms in the simulation and we repeat the simulation 10 times, the followinf code will generate an array that is 5000x5."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/sandyalakkur/anaconda/envs/py3k/lib/python3.4/site-packages/IPython/kernel/__main__.py:61: DeprecationWarning: using a non-integer number instead of an integer will result in an error in the future\n",
      "/Users/sandyalakkur/anaconda/envs/py3k/lib/python3.4/site-packages/IPython/kernel/__main__.py:94: DeprecationWarning: using a non-integer number instead of an integer will result in an error in the future\n",
      "/Users/sandyalakkur/anaconda/envs/py3k/lib/python3.4/site-packages/IPython/kernel/__main__.py:103: DeprecationWarning: using a non-integer number instead of an integer will result in an error in the future\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "Size = 20\n",
    "N = 1000    \n",
    "x = Size*np.random.rand(N)\n",
    "y = Size*np.random.rand(N)\n",
    "Outbreak = Outbreaks(Size=Size,N=N,Y0=1,farms = np.arange(1,N+1),start=20,end=30,x=x,y=y)\n",
    "Num_outbreaks = 100\n",
    "for i in range(Num_outbreaks):\n",
    "    new_Outbreak = np.r_[Outbreak,Outbreaks(Size=Size,N=N,Y0=1,farms = np.arange(1,N+1),start=20,end=30,x=x,y=y)]\n",
    "    Outbreak = new_Outbreak \n",
    "run = np.ravel(list([i]*N for i in range(1,Num_outbreaks+2)))\n",
    "data = np.c_[run,Outbreak]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(101000, 6)"
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#For ease turn data array into data frame\n",
    "import pandas as pd\n",
    "df = pd.DataFrame(data)\n",
    "df.columns = ['run','farmID','Status','DistToIndex','NumCows','NumSheep']\n",
    "df.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now that you have a dataset containing information from multiple outbreak we can attempt to fit a random intercept model, where the group in this case is the simulation run. We are assuming here that there is some correlation of becoming infected within a simulation but not between, thus \"run\" will act as a random effect. NOTE: when you ran this the first time you had the same number of cows and sheep at each farm causing the model to not converge. If you think of this in the least-squares sense you have a non-invertible coefficient matrix. For this reason you need to have some randomness in the number of sheep and cows per farm."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#THIS MODEL DIDN'T CONVERGE, NEED MORE ITERATIONS OR CHANGE PRIORS\n",
    "run = df['run']\n",
    "dist = df['DistToIndex']\n",
    "cows = df['NumCows']\n",
    "sheep = df['NumSheep']\n",
    "status = df['Status']\n",
    "from pymc import Normal, Binomial, Gamma, Lambda, invlogit, MCMC, Matplot\n",
    "N = df.shape[0]\n",
    "\n",
    "def varying_intercept():\n",
    "    \n",
    "    # Priors\n",
    "    mu_a = Normal('mu_a', mu=0., tau=0.0001)\n",
    "    tau_a = Gamma('tau_a', 1, 0.1, value=1)\n",
    "    \n",
    "    # Random intercepts\n",
    "    a = Normal('a', mu=mu_a, tau=tau_a, size=len(set(run)))\n",
    "    # Common slope\n",
    "    b = Normal('b', mu=0., tau=0.0001, value = [0]*3)\n",
    "    \n",
    "    prob = Lambda('prob', lambda a=a, b=b: invlogit(a[run-1] + b[0]*dist + b[1]*cows + b[2]*sheep))\n",
    "    \n",
    "    y = Binomial('y', n=N, p=prob, value=status, observed=True)\n",
    "    \n",
    "    return locals()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " [-----------------100%-----------------] 10000 of 10000 complete in 522.8 sec"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/sandyalakkur/anaconda/envs/py3k/lib/python3.4/site-packages/IPython/kernel/__main__.py:20: DeprecationWarning: non integer (and non boolean) array-likes will not be accepted as indices in the future\n"
     ]
    }
   ],
   "source": [
    "chains = 2\n",
    "iterations = 10000\n",
    "burn = 5000\n",
    "M_pooled = MCMC(varying_intercept())\n",
    "#M_pooled.use_step_method(AdaptiveMetropolis, M_pooled.beta)\n",
    "for i in range(chains):\n",
    "    M_pooled.sample(iterations, burn)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "metadata": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x108fcf278>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "Matplot.summary_plot(M_pooled.b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Plotting b_0\n",
      "Plotting b_1\n",
      "Plotting b_2\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/sandyalakkur/anaconda/envs/py3k/lib/python3.4/site-packages/matplotlib/collections.py:590: FutureWarning: elementwise comparison failed; returning scalar instead, but in the future will perform elementwise comparison\n",
      "  if self._edgecolors == str('face'):\n"
     ]
    },
    {
     "data": {
      "image/png": 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APth6VRHnE3OYhFl0VgIeFJH7gCSf0VIuh9rhbi7LTrIdjvJO6MuW1+5EIm6V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\nrCT+D9m0U/IPswsGAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10907d630>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Matplot.plot(M_pooled.b, common_scale=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "b:\n",
      " \n",
      "\tMean             SD               MC Error        95% HPD interval\n",
      "\t------------------------------------------------------------------\n",
      "\t0.069            0.001            0.0              [ 0.066  0.071]\n",
      "\t3.298            0.004            0.0              [ 3.295  3.307]\n",
      "\t-3.127           0.004            0.0              [-3.135 -3.124]\n",
      "\t\n",
      "\t\n",
      "\tPosterior quantiles:\n",
      "\t\n",
      "\t2.5             25              50              75             97.5\n",
      "\t |---------------|===============|===============|---------------|\n",
      "\t0.066            0.068           0.069          0.07          0.071\n",
      "\t3.294            3.296           3.297          3.299         3.307\n",
      "\t-3.135           -3.128          -3.125         -3.125        -3.123\n",
      "\t\n"
     ]
    }
   ],
   "source": [
    "M_pooled.b.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "Another NOTE: there were a few issues with the above model:\n",
    "\n",
    "1) the distribution is bernoulli not binomial since each row is considered an observation\n",
    "\n",
    "2) you need to specify more informative initials for the model to converge\n",
    "\n",
    "3) since your data is created by many simulations of the outbreak there is no need to let \"run\" be a random effect\n",
    "\n",
    "Refer to BayesianModelRandLocAndSize for appropriate model and analysis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.4.3"
  }
 },
 "nbformat": 4,
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}