Week6/original/GenotypeDetermination/Determining_Genotypes.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "f16b94cc",
   "metadata": {},
   "source": [
    "# Determining genotypes\n",
    "\n",
    "This excersize aims at applying Bayesian statistics to calculate the probability of a specific genotype. In particular we will:\n",
    "1. Combine two .\n",
    "2. Compare the computed results with simple simulations.\n",
    "\n",
    "The exercise is made to play around with a simulated sample of genes and DNA. The goal is to calculate the probability of an original state, based on data and prior probability.\n",
    "\n",
    "### References:\n",
    "- Lecture on Bayesian statistics\n",
    "- Lecture on Markov Chains\n",
    "\n",
    "### Authors: \n",
    "- Mathias L. Heltberg (Niels Bohr Institute)\n",
    "\n",
    "### Date:    \n",
    "- 29-12-2021 (latest update)\n",
    "\n",
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fe5744e1",
   "metadata": {},
   "source": [
    "As always we will include a collection of libraries (Standard)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 497,
   "id": "85972497",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np                                     # Matlab like syntax for linear algebra and functions\n",
    "from numpy.linalg import matrix_power                  # This is to raise matrices to powers\n",
    "import matplotlib.pyplot as plt                        # Plots and figures like you know them from Matlab\n",
    "import seaborn as sns                                  # Make the plots nicer to look at\n",
    "from iminuit import Minuit                             # The actual fitting tool, better than scipy's\n",
    "import sys                                             # Module to see files and folders in directories\n",
    "from scipy import stats"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8bbf0231",
   "metadata": {},
   "source": [
    "We will also (big surprise...) need a random generator:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 498,
   "id": "94c16014",
   "metadata": {},
   "outputs": [],
   "source": [
    "r = np.random # Random generator\n",
    "r.seed(42)    # Set a random seed (but a fixed one)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "24b9c77b",
   "metadata": {},
   "source": [
    "And now for the actual problem: You are given a sample of a particular gene (for simplicity say eyecolor). This gene is found in two versions: A and B. Given that we all have DNA from our fathers and mothers, there are 3 possibilities of combinations for genotypes: AA, AB and BB.\n",
    "\n",
    "So say you measure everything optimally, if you have 8 versions of the gene, coming from AB it might look like: \n",
    "- [A,B,A,B,A,A,A,B]\n",
    "\n",
    "However, you don't have the best equipment and there is a possibility that you measure a gene wron. This is given by a matrix, XX.\n",
    "\n",
    "\n",
    ".............................................................................................................................................................................................................\n",
    "\n",
    "Assume you get the sequence: [A,A,A,A,B]. We want to compute the probability for each of the three genotypes given sequences of data.\n",
    "\n",
    ".............................................................................................................................................................................................................\n",
    "\n",
    "Start by writing on paper, thinking about how you would calculate this probability."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "465f10c0",
   "metadata": {},
   "source": [
    "Information 1: The matrix of transformations (meaning the probability that your machine measures A if it was really a B), takes the form:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 522,
   "id": "ffb86a25",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "XX (i.e. the matrix of transformations error) = \n",
      "[[0.85 0.15]\n",
      " [0.05 0.95]]\n"
     ]
    }
   ],
   "source": [
    "XX = np.zeros((2,2)); XX[0,0] = 0.85; XX[0,1] = 0.15; XX[1,0] = 0.05; XX[1,1] = 0.95;\n",
    "print(\"XX (i.e. the matrix of transformations error) = \")\n",
    "print(XX)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "077eec97",
   "metadata": {},
   "source": [
    "Information 2: You know that in the population, there are the probabilities for each combination:\n",
    "- AA = 0.45\n",
    "- BB = 0.40\n",
    "- AB = 0.15"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 523,
   "id": "b38f26bf",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Prior = \n",
      "[0.45 0.15 0.4 ]\n"
     ]
    }
   ],
   "source": [
    "Pri = np.zeros(3); Pri[0] = 0.45; Pri[1] = 0.15; Pri[2] = 0.40;\n",
    "print(\"Prior = \")\n",
    "print(Pri)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 524,
   "id": "0783cb3f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "S = \n",
      "[[0.66666667 0.33333333 0.        ]\n",
      " [0.         0.33333333 0.66666667]]\n"
     ]
    }
   ],
   "source": [
    "S = np.zeros((2,3)); \n",
    "S[0,0] = 2./3; S[0,1] = 1./3; S[1,1] = 1./3; S[1,2] = 2./3 ## Matrix to end up in a genotype\n",
    "print(\"S = \")\n",
    "print(S)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "47272eb2",
   "metadata": {},
   "source": [
    "We can now construct a full matrix of the seven states:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 525,
   "id": "c7e44a0b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "M = \n",
      "[[0.         0.         0.85       0.05       0.         0.\n",
      "  0.        ]\n",
      " [0.         0.         0.15       0.95       0.         0.\n",
      "  0.        ]\n",
      " [0.         0.         0.         0.         0.66666667 0.33333333\n",
      "  0.        ]\n",
      " [0.         0.         0.         0.         0.         0.33333333\n",
      "  0.66666667]\n",
      " [0.         0.         0.         0.         0.         0.\n",
      "  0.        ]\n",
      " [0.         0.         0.         0.         0.         0.\n",
      "  0.        ]\n",
      " [0.         0.         0.         0.         0.         0.\n",
      "  0.        ]]\n"
     ]
    }
   ],
   "source": [
    "M = np.zeros((7,7)); M[0:2,2:4] = np.transpose(XX); M[2:4,4:] = S; \n",
    "print(\"M = \")\n",
    "print(M)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ddca7463",
   "metadata": {},
   "source": [
    "So what is the probability a measured base B comes from the genotype BB?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 526,
   "id": "00a161a8",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.1        0.36666667 0.63333333]\n"
     ]
    }
   ],
   "source": [
    "V1 = np.zeros(2); V1[1] = 1;\n",
    "XX2 = np.transpose(XX) \n",
    "P = np.matmul(V1,np.matmul(XX2,S)); \n",
    "print(P)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fe0adaf1",
   "metadata": {},
   "source": [
    "Think about why do we use the transposed matrix? \n",
    "\n",
    "So now the probability that the sequence [A,A,A,A,B] comes from the 3 genotypes must bu the product of these probabilities (think about why this has to be the case):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 527,
   "id": "7711e774",
   "metadata": {},
   "outputs": [],
   "source": [
    "Seq = [0,0,0,0,1]\n",
    "LLout = np.ones(3)\n",
    "LLoutFull = np.ones(3)\n",
    "for igeno in range(3):    \n",
    "    V2 = np.zeros(3); V2[igeno]= 1;\n",
    "    V2Full = np.zeros(7); V2Full[4+igeno]= 1;\n",
    "    for iseq in range(len(Seq)):\n",
    "        V1Full = np.zeros([1,7]); V1Full[0,Seq[iseq]] = 1;\n",
    "        LLoutFull[igeno] *= np.matmul(np.matmul(V1Full,np.linalg.matrix_power(M,2)),V2Full)\n",
    "        V1 = np.zeros([1,2]); V1[0,Seq[iseq]] = 1;        \n",
    "        LLout[igeno] *= np.matmul(np.matmul(V1,np.matmul(XX2,S)),V2)\n",
    "        "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a45ef7ad",
   "metadata": {},
   "source": [
    "Note that we could use the full matrix and square it, and we could use the combination of our XX matrix and S. These give the same:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 528,
   "id": "9ca6c150",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The likelihood using the squared matrix is:\n",
      "[1.03112346e-02 2.97000000e-03 7.81893004e-07]\n",
      "The likelihood using the two submatrices is:\n",
      "[1.03112346e-02 2.97000000e-03 7.81893004e-07]\n"
     ]
    }
   ],
   "source": [
    "print(\"The likelihood using the squared matrix is:\")\n",
    "print(LLoutFull)\n",
    "print(\"The likelihood using the two submatrices is:\")\n",
    "print(LLout)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e51f8e23",
   "metadata": {},
   "source": [
    "Now we should produce a probability based on this likelihood. We can get a probability by including the prior or not - but these results differ of course!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 529,
   "id": "d024db6f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Probabilities with the included prior \n",
      "0.9123428429943053\n",
      "0.08759566166558512\n",
      "6.149534010968829e-05\n",
      " \n",
      "Probabilities without the included prior \n",
      "0.776330506610318\n",
      "0.2236106248431463\n",
      "5.886854653558605e-05\n"
     ]
    }
   ],
   "source": [
    "print(\"Probabilities with the included prior \")\n",
    "for i in range(3):\n",
    "    print(LLout[i]/np.dot(LLout,Pri)*Pri[i])\n",
    "print(\" \")\n",
    "print(\"Probabilities without the included prior \")\n",
    "for i in range(3):\n",
    "    print(LLout[i]/np.sum(LLout))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4b05c38a",
   "metadata": {},
   "source": [
    "So now we have obtained the predicted probabilites based on our calculations."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c45d23f5",
   "metadata": {},
   "source": [
    "Lets make a simulation to test if this is true!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 530,
   "id": "03b63353",
   "metadata": {},
   "outputs": [
    {
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\n",
      "text/plain": [
       "<Figure size 1332x756 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "c = 0 ## counter \n",
    "nsave = 100 ## 100 datapoints to save - only for plotting!\n",
    "lseq = 5 ## length of the sequence\n",
    "Ntest = 10000 ## Number of points to generate\n",
    "PlAr = np.zeros((nsave,3))\n",
    "ntrue = np.zeros(Ntest) ## array where we save the actual genotype that gave rise to a sequence\n",
    "ns = np.zeros(5) ## Here we put the test-sequence for all runs\n",
    "click = 1\n",
    "\n",
    "while(c<Ntest):\n",
    "    A = np.random.random() ## This is a random number to determine genotype    \n",
    "    if (A<Pri[0]): ## For genotype AA\n",
    "        ntrue[c] = 0\n",
    "        for i in range(lseq):\n",
    "            B = np.random.random()\n",
    "            if (B<XX[0,0]):\n",
    "                ns[i] = 0\n",
    "            else:\n",
    "                ns[i] = 1\n",
    "    elif (A<Pri[0]+Pri[1]): ## For genotype AB\n",
    "        ntrue[c] = 1\n",
    "        for i in range(lseq):\n",
    "            if (np.random.random()<0.5):\n",
    "                B = np.random.random()\n",
    "                if (B<XX[0,0]):\n",
    "                    ns[i] = 0\n",
    "                else:\n",
    "                    ns[i] = 1\n",
    "            else: \n",
    "                B = np.random.random()\n",
    "                if (B<XX[1,0]):\n",
    "                    ns[i] = 0\n",
    "                else:\n",
    "                    ns[i] = 1\n",
    "    else: ## For genotype BB\n",
    "        ntrue[c] = 2\n",
    "        for i in range(lseq):\n",
    "            B = np.random.random()\n",
    "            if (B<XX[1,0]):\n",
    "                ns[i] = 0\n",
    "            else:\n",
    "                ns[i] = 1\n",
    "                \n",
    "    if (np.sum(ns) == 1): ## If our simulated sequence matches the desired sequence\n",
    "        c+= 1\n",
    "        \n",
    "        if (c > click*Ntest/nsave): \n",
    "            l1 = np.ones(c)\n",
    "            PlAr[click,0] = np.sum(l1[ntrue[0:c]==0])/len(ntrue[0:c])\n",
    "            PlAr[click,1] = np.sum(l1[ntrue[0:c]==1])/len(ntrue[0:c])\n",
    "            PlAr[click,2] = np.sum(l1[ntrue[0:c]==2])/len(ntrue[0:c])            \n",
    "            click+=1\n",
    "\n",
    "fig, ax = plt.subplots(3)\n",
    "ax[0].plot(np.linspace(1*Ntest/nsave,Ntest,nsave-1),PlAr[1:,0],'-g')\n",
    "ax[0].set_xlabel('# of tested sequence')\n",
    "ax[0].set_ylabel('Probability')\n",
    "ax[0].set_title('Probability of state AA')\n",
    "\n",
    "ax[1].plot(np.linspace(1*Ntest/nsave,Ntest,nsave-1),PlAr[1:,1],'-b')\n",
    "ax[1].set_xlabel('# of tested sequence')\n",
    "ax[1].set_ylabel('Probability')\n",
    "ax[1].set_title('Probability of state AB')\n",
    "\n",
    "ax[2].plot(np.linspace(1*Ntest/nsave,Ntest,nsave-1),PlAr[1:,2],'-r')\n",
    "ax[2].set_xlabel('# of tested sequence')\n",
    "ax[2].set_ylabel('Probability')\n",
    "ax[2].set_title('Probability of state BB')\n",
    "fig.tight_layout()\n",
    "fig.set_size_inches(18.5, 10.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 531,
   "id": "cfc5e36a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "When we measure a sequence [A,A,A,A,B] the fractions of genotypes are:\n",
      "0.9094\n",
      "0.0906\n",
      "0.0\n"
     ]
    }
   ],
   "source": [
    "l1 = np.ones(len(ntrue))\n",
    "print(\"When we measure a sequence [A,A,A,A,B] the fractions of genotypes are:\")\n",
    "print(np.sum(l1[ntrue==0])/len(ntrue))\n",
    "print(np.sum(l1[ntrue==1])/len(ntrue))\n",
    "print(np.sum(l1[ntrue==2])/len(ntrue))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "15212743",
   "metadata": {},
   "source": [
    "Clearly this agrees well with the calculated result when we use the prior!"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "13697161",
   "metadata": {},
   "source": [
    "Below here, this code can be used to calculate the probabilities by updating the prior:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 532,
   "id": "a581a44b",
   "metadata": {},
   "outputs": [],
   "source": [
    "######### Try to make an updated prior ##########\n",
    "Seq = [0,0,0,0,1]\n",
    "LLout = np.ones(3)\n",
    "XX2 = np.transpose(XX) \n",
    "Pri0 = np.zeros(3); Pri0[0] = 0.45; Pri0[1] = 0.15; Pri0[2] = 0.40;\n",
    "for iseq in range(len(Seq)): \n",
    "    V1 = np.zeros([1,2]); V1[0,Seq[iseq]] = 1;        \n",
    "    LLout = np.matmul(V1,np.matmul(XX2,S))\n",
    "    Pout = 0 ####### You write here but use Pri0\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5e311a8d",
   "metadata": {},
   "source": [
    "This piece of code can be used to generate sequences of length Nseq in order to calculate the probabilities for the questions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 540,
   "id": "64970294",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 2052x1476 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "######### Generate probabilities of arbitrary length ##########\n",
    "Nseq = 8\n",
    "ProbAA = np.zeros((Nseq,Nseq+1))\n",
    "ProbAB = np.zeros((Nseq,Nseq+1))\n",
    "ProbBB = np.zeros((Nseq,Nseq+1))\n",
    "MaxProb = np.zeros((Nseq,Nseq+1))\n",
    "for tseq in range(Nseq): \n",
    "    Seq = np.zeros(tseq, dtype=int)\n",
    "    for vseq in range(tseq+1):\n",
    "        if (vseq > 0):\n",
    "            Seq[vseq-1] = 1\n",
    "        LLout = np.ones(3)    \n",
    "        for iseq in range(tseq): \n",
    "            V1 = np.zeros([1,2]); V1[0,Seq[iseq]] = 1;   \n",
    "            L1 = np.matmul(V1,np.matmul(XX2,S))\n",
    "            LLout *= L1.flatten()\n",
    "        ProbAA[tseq,vseq] = LLout[0]/np.dot(LLout,Pri)*Pri[0]\n",
    "        ProbAB[tseq,vseq] = LLout[1]/np.dot(LLout,Pri)*Pri[1]\n",
    "        ProbBB[tseq,vseq] = LLout[2]/np.dot(LLout,Pri)*Pri[2]\n",
    "        MaxProb[tseq,vseq] = np.max(LLout/np.dot(LLout,Pri)*Pri)\n",
    "        \n",
    "fig, ax = plt.subplots(3)\n",
    "ax[0].set_title('Probability for AA')\n",
    "ax[0].imshow(ProbAA)\n",
    "ax[0].set_aspect('equal')\n",
    "ax[0].set_xlabel('Number of B in sequence')\n",
    "ax[0].set_ylabel('Sequence length')\n",
    "\n",
    "ax[1].set_title('Probability for AB')\n",
    "ax[1].imshow(ProbAB)\n",
    "ax[1].set_aspect('equal')\n",
    "ax[1].set_xlabel('Number of B in sequence')\n",
    "ax[1].set_ylabel('Sequence length')\n",
    "\n",
    "ax[2].set_title('Probability for BB')\n",
    "ax[2].imshow(ProbBB)\n",
    "ax[2].set_aspect('equal')\n",
    "ax[2].set_xlabel('Number of B in sequence')\n",
    "ax[2].set_ylabel('Sequence length')\n",
    "\n",
    "#fig.tight_layout()\n",
    "fig.set_size_inches(28.5, 20.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "60300e35",
   "metadata": {},
   "source": [
    "For the original values - why is the P(BB) band more narrow than the P(AA)?\n",
    "\n",
    "Here we can calculate some relevant probabilities, for instance the maximal probability of AB and the minimal value of the most probable sequence of bases for each length of sequences (make sure you understand this)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 545,
   "id": "4f9ea2fe",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Sequence length')"
      ]
     },
     "execution_count": 545,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "MinProb = np.zeros(Nseq)\n",
    "MaxProbAB = np.zeros(Nseq)\n",
    "for i in range(Nseq):\n",
    "    MinProb[i] = np.min(MaxProb[i,0:i+1])\n",
    "    MaxProbAB[i] = np.max(ProbAB[i,0:i+1])\n",
    "plt.plot(MinProb,'--xr')\n",
    "plt.plot(MaxProbAB,'--+g')\n",
    "plt.title('Probabilities for specific values at different sequence lengths')\n",
    "plt.xlabel('Probability')\n",
    "plt.ylabel('Sequence length')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e4af32a2",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "c2985c1b",
   "metadata": {},
   "source": [
    "# Questions:\n",
    "\n",
    "This excersize should make you think of how to combine two different types of uncertainty with the concept of a bayesian prior.\n",
    "\n",
    "1) Try to change the sequence of length 5 so no genotype probability is larger than 0.66? Can you make a sequence of length 10 that does not have any probability larger than 0.66?\n",
    "\n",
    "2) For the sequence of length 5: What happens if you update the prior for each base you are reading? Does it give the same result?\n",
    "\n",
    "3) Assume for this question that the priors P(AA) = P(BB) = 0.49. How long a sequence do you need to make the call (p>0.95) of a the genotype AB if you have equal number of A's and B's?\n",
    "\n",
    "4) Assume again that the priors P(AA) = P(BB) = 0.49 but that the matrix XX now has the values \n",
    "- XX[0,0] = 0.99. \n",
    "- XX[1,0] = 0.01. \n",
    "- XX[0,1] = 0.01. \n",
    "- XX[1,1] = 0.99. \n",
    "\n",
    "For the sequence: [A,A,A,A,B] - does the prior change the result in an important way? \n",
    "\n",
    "5) Lets say you are in charge of deciding the strategy of the lab department that should determine genotypes. Use the original prior. \n",
    "- How much do you need to improve the measurement accuracy, if you want p>0.95 for all sequences of length 10?\n",
    "\n",
    "### Advanced question:\n",
    "\n",
    "6) Assume that you had a 10% error in one of the measurement estimates (i.e. the entries in the matrix XX). Which one would afffect the probabilites the most?\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "5cd22494",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "541a8973",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "4e0439e9",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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