ABC_Method.ipynb

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    "#Distance function - Absolute difference \n",
    "def distance_function(X,Y):\n",
    "    distance = (1/len(X))*abs(sum(X)-sum(Y))\n",
    "    return distance\n",
    "\n",
    "#The ABC method with uniform prior, returns samples from the posterior\n",
    "def ABC_Method_Uniform_Prior(Observed_data,Number_of_Samples,threshold):\n",
    "    #The observed data \n",
    "    #initialise Posterior array\n",
    "    Posterior_distribution = []\n",
    "    #trials\n",
    "    n = len(Observed_data) \n",
    "    #loop through to get the samples. \n",
    "    for i in range(0,Number_of_Samples):\n",
    "        distance = threshold+1\n",
    "        #While the distance is greater than the threshold continue to sample theta from the beta distribution\n",
    "        while distance > threshold:\n",
    "            #sample theta from the prior\n",
    "            theta = np.random.beta(1, 1, size=1)[0]\n",
    "            # generate the sim data \n",
    "            X = np.random.binomial(1, theta, n)\n",
    "            # calcalute the distance from Y \n",
    "            distance = distance_function(X,Observed_data)\n",
    "        Posterior_distribution.append(theta)\n",
    "    return Posterior_distribution"
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