{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import scipy.stats as stats"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "%load_ext dotmagic"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Markov Chains\n",
    "\n",
    "A Markov chain is a sequence of events in which the probability of the next event depends only on the state of the current event. For example, we have previously encountered Markov chains in the random walk and Google Page Rank algorithm. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example: Random walk and diffusion"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "n = 1000\n",
    "k = 100\n",
    "xs = np.c_[np.zeros(n), np.random.choice([-1,1], (n, k))]\n",
    "xs = np.cumsum(xs, axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Xr2SQ3L17N8ePHycyMpKRI0f+4VuJMU1P5bpMZC4ODy2lr+O52JpSxOPrz+Ci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470WbMxNG5M+KKFOIdq3w5ObvqSbZt1GPW59Aldgt/jy8G3EZz8htMr57I1axyunq70m9IR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\naQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x107b75860>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for x in xs:\n",
    "    plt.plot(np.arange(k+1), x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Snapshots of displacement after $k$ steps follow normal distribution with $\\sigma = \\sqrt{k}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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VeHcQySJcvtnpg2FMOnvrJecxQRUYAJ1V15M7HIEW+4wYC0tgpIu+DqekNlQ3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\nWwEFe39jOolwiOKaRxmJSeFUyQ2mo9jO2Mj8iZftWbfA6AD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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1093c72e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(1, 5, figsize=(15, 3), sharex=True)\n",
    "for i, k in enumerate(range(20, 101, 20)):\n",
    "    axes[i].hist(xs[:, k], alpha=0.3, normed=True)\n",
    "    axes[i].set_title('t = %d' % k)\n",
    "    xp = np.linspace(-25, 25, 100)\n",
    "    axes[i].plot(xp, stats.norm(loc=0, scale=np.sqrt(k)).pdf(xp))\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Properties of states and Markov chains"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "A Markov chain is irreducible if it is possible to get from any state to any state. Otherwise it is reducible. \n",
    "\n",
    "A state has period $k$ if it must return to that state in multiples of $k$ moves. If $k=1$, the state is aperiodic. If all states are aperiodic, then the Markov chain is aperiodic. \n",
    "\n",
    "If any state in an irreducible Markov chain is aperiodic, then all states are aperiodic. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Reducible and aperiodic\n",
    "\n",
    "A is a transient state. B and C are recurrent states. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
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   "source": [
    "%%dot\n",
    "\n",
    "digraph g {\n",
    "    node [shape=circle]\n",
    "    A -> B\n",
    "    B -> C\n",
    "    C -> B\n",
    "    C -> C\n",
    "}"
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Irreducible and periodic\n",
    "\n",
    "A, B, and C are recurrent states."
   ]
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  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
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   "source": [
    "%%dot\n",
    "\n",
    "digraph g {\n",
    "    layout=\"circo\";\n",
    "    node [shape=circle]\n",
    "    A -> B\n",
    "    B -> C\n",
    "    C -> A\n",
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Absorbing Markov chain\n",
    "\n",
    "D is an absorbing state. A, B and C are transient states. Since every state can reach an absorbing state, this is an absorbing Markov chain"
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  {
   "cell_type": "code",
   "execution_count": 8,
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   "source": [
    "%%dot\n",
    "\n",
    "digraph g {\n",
    "    node [shape=circle]\n",
    "    A -> B\n",
    "    B -> C\n",
    "    C -> B\n",
    "    C -> C\n",
    "    B -> D\n",
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   "cell_type": "markdown",
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   "source": [
    "#### Ergodic\n",
    "\n",
    "An ergodic state is aperiodic and positive recurrent. If all states are ergodic, then we have an ergodic Markov chain. A finite chain that is aperiodic and irreducible is ergodic."
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  {
   "cell_type": "code",
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    "%%dot\n",
    "\n",
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    "### Markov Chain\n",
    "\n",
    "Suppose we have the following transition table:\n",
    "\n",
    "|             | Raleigh | Chapel Hill | Durham |\n",
    "|:------------|:--------|:------------|:-------|\n",
    "| Raleigh     | 0.9     | 0.05        | 0.05   |\n",
    "| Chapel Hill | 0.1     | 0.8         | 0.1    |\n",
    "| Durham      | 0.04    | 0.01        | 0.95   |\n",
    "\n",
    "This says that a resident of Raleigh this year has a 90% chance of stying in Raleigh and a 5% chance of relocating to Chapel Hill or Durham the following year. Note that the probabilities only depend on the current year. The transitions between states (Raleigh, Chapel Hill and Durham) are then said to be modeled by a Markov chain. \n",
    "\n",
    "If Raleigh, Chapel Hill and Durham each started with 300,000 residents, what is the long run distribution assuming no immigration or emigration?"
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   "execution_count": 10,
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   ],
   "source": [
    "%%dot\n",
    "\n",
    "digraph g {\n",
    "    node [shape=box]\n",
    "    R [label=\"Raleigh\"]\n",
    "    C [label=\"Chapel Hill\"]\n",
    "    D [label=\"Duham\"]\n",
    "    R -> R [label=0.9]\n",
    "    R -> C [label=0.05]\n",
    "    R -> D [label=0.05]\n",
    "    C -> R [label=0.1]\n",
    "    C -> C [label=0.8]\n",
    "    C -> D [label=0.1]\n",
    "    D -> R [label=0.04]\n",
    "    D -> C [label=0.01]\n",
    "    D -> D [label=0.95]\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "A = np.array([\n",
    "    [0.9, 0.05, 0.05],\n",
    "    [0.1, 0.8, 0.1],\n",
    "    [0.04, 0.01, 0.95]\n",
    "])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "x = np.array([300000, 300000, 300000]).reshape(-1,1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### After one year"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[312000., 258000., 330000.]])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.T @ A"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### After 2 years"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[319800., 225300., 354900.]])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.T @ A @ A"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Brute force solution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[300000.50469469, 100000.21203929, 499999.28326602]])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n = 100\n",
    "x.T @ np.linalg.matrix_power(A, n)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Eigenvector solution\n",
    "\n",
    "At steady state, we have\n",
    "\n",
    "$$\n",
    "p.T A = p.T\n",
    "$$\n",
    "\n",
    "Taking the transpose on both sides, we see that\n",
    "\n",
    "$$\n",
    "A^Tp = p\n",
    "$$\n",
    "\n",
    "suggesting that the steady state probability vector is the normalized eigenvector of $A^T$ with $\\lambda = 1$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "E, V = np.linalg.eig(A.T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.76479203, 0.88520797, 1.        ])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "E"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.33333333],\n",
       "       [0.11111111],\n",
       "       [0.55555556]])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p = V[:, 2:] / V[:, 2:].sum()\n",
    "p"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[300000.],\n",
       "       [100000.],\n",
       "       [500000.]])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p * x.sum()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Linear system solution\n",
    "\n",
    "We cannot solve $A^Tp - p= \\mathbb{0}$ directly because $A^T - I$ does not have full rank (since the last column of $A$ is fixed given the other columns).\n",
    "\n",
    "We need to add the constraint $\\sum{p} = 1$ and then we can solve the linear system to find $p$. \n",
    "\n",
    "$$\n",
    "\\begin{bmatrix}\n",
    "(A^T - I) \\\\\n",
    "\\mathbb{1}^T \n",
    "\\end{bmatrix} p = \\begin{bmatrix}\n",
    "\\mathbb{0} \\\\\n",
    "1 \\end{bmatrix}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linalg.matrix_rank(A.T - np.eye(3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "M = np.r_[A.T - np.eye(3), [np.ones(3)]]\n",
    "b = np.r_[np.zeros(3), 1].reshape(-1,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.1 ,  0.1 ,  0.04],\n",
       "       [ 0.05, -0.2 ,  0.01],\n",
       "       [ 0.05,  0.1 , -0.05],\n",
       "       [ 1.  ,  1.  ,  1.  ]])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "M"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.],\n",
       "       [0.],\n",
       "       [0.],\n",
       "       [1.]])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "x, res, rank, s = np.linalg.lstsq(M, b, rcond=None)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.33333333],\n",
       "       [0.11111111],\n",
       "       [0.55555556]])"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Markov chain averages\n",
    "\n",
    "We can also consider the perspective of a single individual in terms of the frequencies of places visited.\n",
    "\n",
    "The individual starts from one of the 3 places (Raleigh, Chapel Hill or Durham) and moves from place to place according to the probabilities in $A$ over a long time. In the long run, the average frequency of visits to a place is the steady state probability of visiting that place.\n",
    "\n",
    "This suggests that we can estimate the equilibrium or steady state distribution by using the long-run averages, which we'll revisit when we look at Markov chain Monte Carlo (MCMC). Note that the initial averages depend on the starting conditions, so it is common practice to discard some number of the initial iterations (burn-in)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.9 , 0.95, 1.  ],\n",
       "       [0.1 , 0.9 , 1.  ],\n",
       "       [0.04, 0.05, 1.  ]])"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "P = np.cumsum(A).reshape(A.shape) - np.array([0,1,2]).reshape(-1,1)\n",
    "P"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "n = int(1e6)\n",
    "xs = np.zeros(n+1).astype('int')\n",
    "xs[0] = np.random.choice([0,1,2])\n",
    "\n",
    "for t in range(n):\n",
    "    r = np.random.rand()\n",
    "    xs[t+1] = np.argmax(r < P[xs[t]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.33321566678433323, 0.11102688897311103, 0.5557574442425558)"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(xs==0), np.mean(xs==1), np.mean(xs==2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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