Statistics with Python/An_Intro_to_Markov_chains_with_Python!.ipynb

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    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
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  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
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      "source": [
        "<a href=\"https://colab.research.google.com/github/ad17171717/YouTube-Tutorials/blob/main/Statistics%20with%20Python/An_Intro_to_Markov_chains_with_Python!.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "BaEUpxTP1avj"
      },
      "source": [
        "import numpy as np\n",
        "import pandas as pd\n",
        "import random\n",
        "import matplotlib.pyplot as plt"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "t7hPpfN7A5zI"
      },
      "source": [
        "#matplotlib parameters\n",
        "plt.rcParams[\"figure.figsize\"] = (12, 8)\n",
        "plt.rcParams.update({'font.size': 14})"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6x7vkfVR1j-M"
      },
      "source": [
        "# **What is a stochastic process?**\n",
        "**A stochastic process is a collection of random\n",
        "variables: $\\{X_t,t \\in I \\},$ Where: $X_t$ is the set of random variables at time $t$, and $I$ is the index set of the process.**\n",
        "\n",
        "**Discrete time stochastic processes which we will focus on in this tutorial are sequences of random variables.**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8n-gtIgXKNUN"
      },
      "source": [
        "## **Simulation of Gambler's Ruin**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3cqE6EBl7rGW"
      },
      "source": [
        "**We can use the famous example of gambler's ruin which is a stochastic process.**\n",
        "\n",
        "**In our case, a gambler starts off with \\$50. To keep things simple, they can only bet in increments of \\$1. They can only win or lose \\$1 per bet. They will keep gambling until they either lost all their money (leave with \\$0) or if they win \\$100. We can formalize this with the following notation:**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "4q1aH0x4HMVl"
      },
      "source": [
        "$\\begin{equation}\n",
        "  X_{g} =\n",
        "    \\begin{cases}\n",
        "      \\$+1, & \\text{with a probability of 50%}\\\\\n",
        "      \\$-1, & \\text{with a probability of 50%}\\\\\n",
        "    \\end{cases}       \n",
        "\\end{equation}$\n",
        "\n",
        "**Where: $X_g$ is the gambling outcome in dollars.**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "B1mv3Wg5G1Kd"
      },
      "source": [
        "<sup>Source: [Introduction to Stochastic Processes with R](https://www.amazon.com/Introduction-Stochastic-Processes-Robert-Dobrow/dp/1118740653) by Robert P. Dobrow</sup>"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "wraHpemkBbc8"
      },
      "source": [
        "def gamblers_ruin():\n",
        "  gambling_money = 50\n",
        "  gambling_goal = 100\n",
        "  gambling_simulation = []\n",
        "\n",
        "  while gambling_money in range(1,gambling_goal):\n",
        "    bet_size = 1\n",
        "    w_or_l = random.randrange(-1, 2, step = 2)\n",
        "    gambling_money += bet_size * w_or_l\n",
        "    gambling_simulation.append(gambling_money)\n",
        "  return gambling_simulation"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 525
        },
        "id": "pfO74v3by36e",
        "outputId": "db7955aa-a146-40c0-d512-e5d9197a883f"
      },
      "source": [
        "plt.plot(gamblers_ruin())\n",
        "plt.yticks(np.arange(-20,120,10))\n",
        "plt.axhline(y=0, color='r', linestyle='-')\n",
        "plt.axhline(y=100, color='black', linestyle='-')\n",
        "plt.xlabel('Number of bets')\n",
        "plt.ylabel('Winnings')\n",
        "plt.title('Gambling Simulation');"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
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\n",
            "text/plain": [
              "<Figure size 864x576 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "FxX1VzISmiUJ"
      },
      "source": [
        "def prob_of_ruin(gambling_goal, initial_gambling_money):\n",
        "  return (gambling_goal - initial_gambling_money)/gambling_goal"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "xPt6Wz-un3CW",
        "outputId": "54d5ab4e-4dd1-4940-c71a-3e425a27c23d"
      },
      "source": [
        "prob_of_ruin(100,50)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.5"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 6
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "x-uwe_ac1CZu",
        "outputId": "c1352b1e-0679-495f-a50b-23a99a1acb9a"
      },
      "source": [
        "sim_list = []\n",
        "\n",
        "while len(sim_list) < 500:\n",
        "  sim_list.append(gamblers_ruin()[-1])\n",
        "\n",
        "np.mean(sim_list)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "54.2"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 7
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Hhrnn7wcLy9i"
      },
      "source": [
        "<sup>Source: [Introduction to Stochastic Processes with R](https://www.amazon.com/Introduction-Stochastic-Processes-Robert-Dobrow/dp/1118740653) by Robert P. Dobrow</sup>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "jhm3TmM3jduN"
      },
      "source": [
        "# **Markov Chains**\n",
        "\n",
        "**A Markov chain is a type of stochastic process.**\n",
        "\n",
        "**A Markov chain is a collection of random variables ($X_t$) where the future states ($j$) only depend on the current state ($i$). Markov chains can be either discrete or continuous.**\n",
        "\n",
        "**For a Markov chain transition matrix (denoted as $P$):**\n",
        "\n",
        " - **Each row must add to one, where: $\\sum\\limits_{j}P_{ij} = 1$.**\n",
        " - **The probabilities must be non-negative where: $P_{ij} \\geq 0 \\ \\ \\forall \\ \\ i,j$**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "z9vimR0PNyFy"
      },
      "source": [
        "<sup>Source: [Introduction to Stochastic Processes with R](https://www.amazon.com/Introduction-Stochastic-Processes-Robert-Dobrow/dp/1118740653) by Robert P. Dobrow</sup>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "coRJhidvSScz"
      },
      "source": [
        "<sup>Source: [Markov Chain](https://mathworld.wolfram.com/MarkovChain.html?utm_source=twitterfeed&utm_medium=twitter) from Wolfram MathWorld</sup>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "jAhv0DcGgDgj"
      },
      "source": [
        "## **Markov Chain Simulation**\n",
        "\n",
        "**A Markov chain can be simulated from an initial distribution and transition matrix. In our case, the initial state is New York City. From the initial state we can travel to: Paris, Cairo, Seoul or even within New York City.**\n",
        "\n",
        "**The transition matrix contains the one step transition probabilities of\n",
        "moving from state to state.**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "dQ1SU8YDLvrR"
      },
      "source": [
        "<sup>Source: [Introduction to Stochastic Processes with R](https://www.amazon.com/Introduction-Stochastic-Processes-Robert-Dobrow/dp/1118740653) by Robert P. Dobrow</sup>"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "HjcYJSrCwKfu"
      },
      "source": [
        "mc_example = {'NYC': [.25,0,.75,1],\n",
        "              'Paris': [.25,.25,0,0],\n",
        "              'Cairo': [.25,.25,.25,0],\n",
        "              'Seoul': [.25,.5,0,0]}\n",
        "\n",
        "mc = pd.DataFrame(data = mc_example, index = ['NYC', 'Paris', 'Cairo', 'Seoul'])"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "l4dvLC1vUQR8"
      },
      "source": [
        "### **Markov Transition Graph**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9yEfWcCKtPMP"
      },
      "source": [
        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)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "wY51JpjtBaGe"
      },
      "source": [
        "**We can formalize the movement for the Markov chain at the initial starting point (New York City) with the following notation:**\n",
        "\n",
        "$P(X_1 = \\text{New York}|X_0 = \\text{New York})=P(X_1 = \\text{Paris}|X_0 = \\text{New York})=P(X_1 = \\text{Cairo}|X_0 = \\text{New York}) = P(X_1 = \\text{Seoul}|X_0 = \\text{New York}) = 25\\%$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ZgRHstTUH5TE"
      },
      "source": [
        "travel_sim = []\n",
        "travel_sim.append(mc.iloc[0].index[0])\n",
        "city = np.random.choice(mc.iloc[0].index, p = mc.iloc[0])\n",
        "travel_sim.append(city)\n",
        "\n",
        "while len(travel_sim) < 25:\n",
        "  city = np.random.choice(mc.iloc[mc.index.get_loc(city)].index, p = mc.iloc[mc.index.get_loc(city)])\n",
        "  travel_sim.append(city)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Z_-PtgIeOGah",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "2352d8e6-ce3e-4c35-8e19-90812bb8f330"
      },
      "source": [
        "travel_sim"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "['NYC',\n",
              " 'Paris',\n",
              " 'Paris',\n",
              " 'Seoul',\n",
              " 'NYC',\n",
              " 'Seoul',\n",
              " 'NYC',\n",
              " 'Seoul',\n",
              " 'NYC',\n",
              " 'Cairo',\n",
              " 'NYC',\n",
              " 'Seoul',\n",
              " 'NYC',\n",
              " 'Seoul',\n",
              " 'NYC',\n",
              " 'Seoul',\n",
              " 'NYC',\n",
              " 'Paris',\n",
              " 'Seoul',\n",
              " 'NYC',\n",
              " 'NYC',\n",
              " 'Cairo',\n",
              " 'NYC',\n",
              " 'Seoul',\n",
              " 'NYC']"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 10
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 174
        },
        "id": "XDtMqLBUo7WO",
        "outputId": "c6b7212b-9bed-4963-d552-87e2428e6cb1"
      },
      "source": [
        "mc"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>NYC</th>\n",
              "      <th>Paris</th>\n",
              "      <th>Cairo</th>\n",
              "      <th>Seoul</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>NYC</th>\n",
              "      <td>0.25</td>\n",
              "      <td>0.25</td>\n",
              "      <td>0.25</td>\n",
              "      <td>0.25</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Paris</th>\n",
              "      <td>0.00</td>\n",
              "      <td>0.25</td>\n",
              "      <td>0.25</td>\n",
              "      <td>0.50</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Cairo</th>\n",
              "      <td>0.75</td>\n",
              "      <td>0.00</td>\n",
              "      <td>0.25</td>\n",
              "      <td>0.00</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Seoul</th>\n",
              "      <td>1.00</td>\n",
              "      <td>0.00</td>\n",
              "      <td>0.00</td>\n",
              "      <td>0.00</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "        NYC  Paris  Cairo  Seoul\n",
              "NYC    0.25   0.25   0.25   0.25\n",
              "Paris  0.00   0.25   0.25   0.50\n",
              "Cairo  0.75   0.00   0.25   0.00\n",
              "Seoul  1.00   0.00   0.00   0.00"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 11
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-LzP2fXpFFWt"
      },
      "source": [
        "### **Memorylessness: The future is independent of the past given the present**\n",
        "\n",
        "**An important feature of Markov chains is that they are memorylessness. If we look at our example, the only state that matters is the current state. If our salesperson started in New York City ($X_0 = NYC$) and traveled to Paris ($X_1 = Paris$), then the movement to the next city ($X_2$) only depends on the probabilities of travel from Paris. The fact that the salesperson originally started in New York does not effect the movement to $X_2.$** "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "n8ISFYx-mdlV"
      },
      "source": [
        "## **$n$ Step Transition Matrix**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "VRA5knsYDllT",
        "outputId": "da6ab6eb-20e9-4f07-e985-7d16a4d0e0f8"
      },
      "source": [
        "mc.to_numpy()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[0.25, 0.25, 0.25, 0.25],\n",
              "       [0.  , 0.25, 0.25, 0.5 ],\n",
              "       [0.75, 0.  , 0.25, 0.  ],\n",
              "       [1.  , 0.  , 0.  , 0.  ]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 12
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "5v8jEuHqcQQl"
      },
      "source": [
        "def matrix_power(matrix, power):\n",
        "  if power == 0:\n",
        "    return np.identity(len(matrix))\n",
        "  elif power == 1:\n",
        "    return matrix\n",
        "  else:\n",
        "    return np.dot(matrix, matrix_power(matrix, power-1))"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "rsakHnM1kB2f"
      },
      "source": [
        "<sup>Source: [Introduction to Stochastic Processes with R](https://www.amazon.com/Introduction-Stochastic-Processes-Robert-Dobrow/dp/1118740653) by Robert P. Dobrow</sup>"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "nKCZzPTA4Srp",
        "outputId": "326853d6-f1e3-4678-b950-f3a68a8f6e28"
      },
      "source": [
        "matrix_power(mc.to_numpy(), 2)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[0.5   , 0.125 , 0.1875, 0.1875],\n",
              "       [0.6875, 0.0625, 0.125 , 0.125 ],\n",
              "       [0.375 , 0.1875, 0.25  , 0.1875],\n",
              "       [0.25  , 0.25  , 0.25  , 0.25  ]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 14
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "rInv_lSI3JNa",
        "outputId": "a4a84231-be4f-4eb8-bca7-aaa41fa8bf13"
      },
      "source": [
        "np.dot(np.dot(mc.to_numpy(), mc.to_numpy()), mc.to_numpy())"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[0.453125, 0.15625 , 0.203125, 0.1875  ],\n",
              "       [0.390625, 0.1875  , 0.21875 , 0.203125],\n",
              "       [0.46875 , 0.140625, 0.203125, 0.1875  ],\n",
              "       [0.5     , 0.125   , 0.1875  , 0.1875  ]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 15
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "9eh7VV0V5eVr",
        "outputId": "57205620-dd32-4007-b594-ecc79fa856a8"
      },
      "source": [
        "np.dot(mc.to_numpy(), mc.to_numpy())"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[0.5   , 0.125 , 0.1875, 0.1875],\n",
              "       [0.6875, 0.0625, 0.125 , 0.125 ],\n",
              "       [0.375 , 0.1875, 0.25  , 0.1875],\n",
              "       [0.25  , 0.25  , 0.25  , 0.25  ]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 16
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "wPAZn5ENjiNY",
        "outputId": "87a7b2aa-3d7c-480c-8452-92760402c103"
      },
      "source": [
        "matrix_power(mc.to_numpy(), 3).sum(axis=1)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([1., 1., 1., 1.])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 17
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "xvhkn71plhzq"
      },
      "source": [
        "**What the above 2-step transition matrix is telling us is if we look at state $i$ for New York, in two steps there is a 50% probability that the salesperson ends up back in New York City, a 12.5% probability that they go onto Paris and an 18.75% chance that they end up in Cairo or Seoul.**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "MeJ3fgdsj4Mt",
        "outputId": "ac65dfd7-6eeb-4ab6-955e-87c2bece8ec5"
      },
      "source": [
        "for i in range(1,10,1):\n",
        "  print(f'n Step Transition Matrix at the nth power {i}\\n', matrix_power(mc.to_numpy(), i),'\\n')"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "n Step Transition Matrix at the nth power 1\n",
            " [[0.25 0.25 0.25 0.25]\n",
            " [0.   0.25 0.25 0.5 ]\n",
            " [0.75 0.   0.25 0.  ]\n",
            " [1.   0.   0.   0.  ]] \n",
            "\n",
            "n Step Transition Matrix at the nth power 2\n",
            " [[0.5    0.125  0.1875 0.1875]\n",
            " [0.6875 0.0625 0.125  0.125 ]\n",
            " [0.375  0.1875 0.25   0.1875]\n",
            " [0.25   0.25   0.25   0.25  ]] \n",
            "\n",
            "n Step Transition Matrix at the nth power 3\n",
            " [[0.453125 0.15625  0.203125 0.1875  ]\n",
            " [0.390625 0.1875   0.21875  0.203125]\n",
            " [0.46875  0.140625 0.203125 0.1875  ]\n",
            " [0.5      0.125    0.1875   0.1875  ]] \n",
            "\n",
            "n Step Transition Matrix at the nth power 4\n",
            " [[0.453125   0.15234375 0.203125   0.19140625]\n",
            " [0.46484375 0.14453125 0.19921875 0.19140625]\n",
            " [0.45703125 0.15234375 0.203125   0.1875    ]\n",
            " [0.453125   0.15625    0.203125   0.1875    ]] \n",
            "\n",
            "n Step Transition Matrix at the nth power 5\n",
            " [[0.45703125 0.15136719 0.20214844 0.18945312]\n",
            " [0.45703125 0.15234375 0.20214844 0.18847656]\n",
            " [0.45410156 0.15234375 0.203125   0.19042969]\n",
            " [0.453125   0.15234375 0.203125   0.19140625]] \n",
            "\n",
            "n Step Transition Matrix at the nth power 6\n",
            " [[0.45532227 0.15209961 0.20263672 0.18994141]\n",
            " [0.4543457  0.15234375 0.20288086 0.19042969]\n",
            " [0.45629883 0.15161133 0.20239258 0.18969727]\n",
            " [0.45703125 0.15136719 0.20214844 0.18945312]] \n",
            "\n",
            "n Step Transition Matrix at the nth power 7\n",
            " [[0.45574951 0.15185547 0.20251465 0.18988037]\n",
            " [0.45617676 0.15167236 0.20239258 0.1897583 ]\n",
            " [0.45556641 0.15197754 0.20257568 0.18988037]\n",
            " [0.45532227 0.15209961 0.20263672 0.18994141]] \n",
            "\n",
            "n Step Transition Matrix at the nth power 8\n",
            " [[0.45570374 0.15190125 0.20252991 0.18986511]\n",
            " [0.45559692 0.15196228 0.20256042 0.18988037]\n",
            " [0.45570374 0.15188599 0.20252991 0.18988037]\n",
            " [0.45574951 0.15185547 0.20251465 0.18988037]] \n",
            "\n",
            "n Step Transition Matrix at the nth power 9\n",
            " [[0.45568848 0.15190125 0.20253372 0.18987656]\n",
            " [0.45569992 0.1518898  0.20252991 0.18988037]\n",
            " [0.45570374 0.15189743 0.20252991 0.18986893]\n",
            " [0.45570374 0.15190125 0.20252991 0.18986511]] \n",
            "\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Ac349T3izJAb"
      },
      "source": [
        "**We can see above that as the number of steps increase, the probabilities converge to what is called a stationary distribution (also known as a steady state vector).**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "FFEeJu0vy43j"
      },
      "source": [
        "**Let's say that this time our salesperson is starting their trip from Seoul. In this case, we can denote the initial distribution as: $\\alpha = [0,0,0,1]$. Now let's find what the probability of ending up back in Seoul is two trips from now.**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "f6LcSJvBzK4n",
        "outputId": "a7c343df-9e09-4dad-ab83-9731408f397c"
      },
      "source": [
        "initial_dist = np.asarray([0,0,0,1])\n",
        "\n",
        "mc_p2 = matrix_power(mc.to_numpy(),2)\n",
        "\n",
        "np.dot(initial_dist,mc_p2)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0.25, 0.25, 0.25, 0.25])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 19
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "hjYpgN5CLPYc"
      },
      "source": [
        "# **References and Additional Learning**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "k2mJACl_1htk"
      },
      "source": [
        "## **Online Course**\n",
        "\n",
        "- **[Introduction to Probability](https://ocw.mit.edu/resources/res-6-012-introduction-to-probability-spring-2018/) from MIT OpenCourseWare**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "LqdIXoRuLKi-"
      },
      "source": [
        "## **Textbook**\n",
        "- **[Introduction to Stochastic Processes with R](https://www.amazon.com/Introduction-Stochastic-Processes-Robert-Dobrow/dp/1118740653) by Robert P. Dobrow**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "L06qGkUbO0FP"
      },
      "source": [
        "## **Videos**\n",
        "- **[Markov Chains](https://www.youtube.com/watch?v=uvYTGEZQTEs) by patrickJMT**\n",
        "\n",
        "- **[Markov Steady-State Vectors](https://www.youtube.com/watch?v=D2wvhwOTWIo) by  Brandon Foltz**\n",
        "\n",
        "- **[Origin of Markov chains](https://www.youtube.com/watch?v=Ws63I3F7Moc) from Khan Academy Labs**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "kjyzJx1cLJcP"
      },
      "source": [
        "# **Connect**\n",
        "\n",
        "- **Feel free to connect with Adrian on [YouTube](https://www.youtube.com/channel/UCPuDxI3xb_ryUUMfkm0jsRA), [LinkedIn](https://www.linkedin.com/in/adrian-dolinay-frm-96a289106/), [Twitter](https://twitter.com/DolinayG) and [GitHub](https://github.com/ad17171717). Happy coding!**"
      ]
    }
  ]
}