CS146 Session 2.2 Pre-Class Work

CS146 Session 2.2 Pre-Class Work.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Pre-Class Work\n",
    "\n",
    "## Plot histograms and pdfs\n",
    "\n",
    "For each of the gamma, normal, and beta distributions, use Python to do the following:\n",
    "1. On the same set of axes, plot the distribution for 2 different values of its parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import scipy.stats as stats \n",
    "from matplotlib import pyplot as plt\n",
    "import random"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "### Gamma Distribution ###\n",
    "\n",
    "plt.figure(figsize=(8, 4)) # Create a new figure with a particular size\n",
    "x = np.linspace(0, 100, 200) # Array with 200 linearly spaced points in [-5,5]\n",
    "# Plot 2 gamma distributions with different loc and scale parameters\n",
    "plt.plot(x, stats.gamma.pdf(x, a=100, scale=1/3), label=r'$\\alpha=100, \\beta=3$')\n",
    "plt.plot(x, stats.gamma.pdf(x, a=20, scale=0.5), label=r'$\\alpha=20, \\beta=2$')\n",
    "plt.legend() # Show the legend in the top right corner\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "### Normal Distribution ###\n",
    "\n",
    "plt.figure(figsize=(8, 4)) # Create a new figure with a particular size\n",
    "x = np.linspace(-5, 5, 200) # Array with 200 linearly spaced points in [-5,5]\n",
    "# Plot 2 normal distributions with different loc and scale parameters\n",
    "plt.plot(x, stats.norm.pdf(x, scale=2), label='scale = 2')\n",
    "plt.plot(x, stats.norm.pdf(x, scale=1/2), label='scale = 1/2')\n",
    "plt.legend() # Show the legend in the top right corner\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "### Beta Distribution ###\n",
    "\n",
    "plt.figure(figsize=(8, 4)) # Create a new figure with a particular size\n",
    "x = np.linspace(-5, 5, 200) # Array with 200 linearly spaced points in [-5,5]\n",
    "# Plot 2 beta distributions with different loc and scale parameters\n",
    "plt.plot(x, stats.beta.pdf(x, a=0.5, b=0.2), label=r'$\\alpha=0.5, \\beta=0.2$')\n",
    "plt.plot(x, stats.beta.pdf(x, a=(x**2)+2, b=(x**2)), label=r'$\\alpha=x^2+2, \\beta=x^2$')\n",
    "plt.legend() # Show the legend in the top right corner\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "2. Generate 100 samples from the distribution for one setting of its parameters and plot a histogram of the sample values. On the same plot, compare the histogram to the probability density function. The histogram will be noisy, but should align fairly well with the pdf."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 193,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "### Gamma Distribution ###\n",
    "\n",
    "plt.figure(figsize=(8, 4)) # Create a new figure with a particular size\n",
    "x = np.linspace(25, 40, 200) # Array with 200 linearly spaced points in [-5,5]\n",
    "gamma_distribution = stats.gamma(a=100, scale=1/3) #set parameters for gamma distribution\n",
    "# Plot 1 gamma distribution with different loc and scale parameters\n",
    "plt.plot(x, gamma_distribution.pdf(x))\n",
    "# Plot its corresponding histogram\n",
    "samples = gamma_distribution.rvs(size=100)\n",
    "weights = (np.ones_like(x)/float(len(x)))*100\n",
    "plt.hist(samples, range=[25, 40], bins = 100)\n",
    "plt.title('histogram of random samples')\n",
    "plt.show()\n",
    "\n",
    "# I'm not sure how to increase the height of the gamma distribution curve or decrease the height of the histogram."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "### Normal Distribution ###\n",
    "\n",
    "plt.figure(figsize=(8, 4)) # Create a new figure with a particular size\n",
    "x = np.linspace(-5, 5, 200) # Array with 200 linearly spaced points in [-5,5]\n",
    "norm_distribution = stats.norm(x, scale=2) #set parameters for normal distribution\n",
    "# Plot the normal distributions\n",
    "plt.plot(x, norm_distribution.pdf(x))\n",
    "# Plot its corresponding histogram\n",
    "samples2 = norm_distribution.rvs()\n",
    "plt.hist(samples2, range=[0, 7], bins = 100, density = True)\n",
    "plt.title('histogram of random samples')\n",
    "plt.show()\n",
    "\n",
    "# Not exactly the best plot - I tried normalizing the histogram, and I managed to do that, but now the normal \n",
    "# distribution is flattened. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 202,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "### Beta Distribution ###\n",
    "\n",
    "plt.figure(figsize=(8, 4)) # Create a new figure with a particular size\n",
    "x = np.linspace(-1, 2, 200) # Array with 200 linearly spaced points in [-1,2]\n",
    "beta_distribution = stats.beta(a=(x**2)+2, b=(x**2))\n",
    "# Plot the beta distribution with different loc and scale parameters\n",
    "plt.plot(x, beta_distribution.pdf(x))\n",
    "samples3 = beta_distribution.rvs()\n",
    "weights3 = (np.ones_like(x)/float(len(x)))*9\n",
    "plt.hist(samples3, range=[-1, 2], bins = 100, weights = weights3)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Call center data modeling"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This task is divided into 3 parts — pre-class work, problem solving in class, and your current assignment. You should focus on doing the pre-class work as thoroughly as possible, to be ready for extending your work in class, and then extending it further in the assignment. \n",
    "\n",
    "You should see this task as a guided tour through the data modeling process."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Scenario\n",
    "\n",
    "You are advising a client on the number of call center agents they need to handle their customer support load. We start by modeling the number of phone calls we expect to come into the call center during each hour of the day.\n",
    "\n",
    "You are provided with a data set of the intervals between phone calls arriving during one day. Each value is a time in minutes indicating the amount of time that passed between receiving two consecutive phone calls.\n",
    "\n",
    "### Loading the data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import scipy as sp\n",
    "import scipy.stats as sts\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Size of data set: 5856\n",
      "First 3 values in data set: [30.   3.4  3.2]\n",
      "Sum of data set: 1441.6838153800093\n"
     ]
    }
   ],
   "source": [
    "# Load the data set containing durations between calls arriving at the call\n",
    "# center during 1 day. All values are in minutes.\n",
    "waiting_times_day = np.loadtxt('call_center.csv')\n",
    "\n",
    "# Display some basic information about the data set.\n",
    "print('Size of data set:', len(waiting_times_day))\n",
    "print('First 3 values in data set:', waiting_times_day[:3])\n",
    "print('Sum of data set:', sum(waiting_times_day))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since the values are intervals between calls measured in minutes, this means\n",
    "\n",
    "* we assume the first call happened at 00:00 (midnight),\n",
    "* the second call happened at about 00:30 (30 minutes after midnight),\n",
    "* the third call happened at about 00:33 (30 + 3.4 minutes),\n",
    "* the fourth call happened at about 00:37, etc.\n",
    "\n",
    "When we sum the values, we get about 1440 minutes (1 day)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You are told that the number of calls arriving varies quite a lot, depending on which hour of the day it is. The smallest number of calls usually occur around 3am or 4am. Most calls usually come in between 11am and 1pm.\n",
    "\n",
    "## Data pre-processing\n",
    "Since we expect different call rates during different hours, we split the data set into 24 separate series — one for each hour of the day."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "00:00-01:00 - 5 calls\n",
      "01:00-02:00 - 4 calls\n",
      "02:00-03:00 - 6 calls\n",
      "03:00-04:00 - 8 calls\n",
      "04:00-05:00 - 26 calls\n",
      "05:00-06:00 - 53 calls\n",
      "06:00-07:00 - 93 calls\n",
      "07:00-08:00 - 173 calls\n",
      "08:00-09:00 - 254 calls\n",
      "09:00-10:00 - 345 calls\n",
      "10:00-11:00 - 496 calls\n",
      "11:00-12:00 - 924 calls\n",
      "12:00-13:00 - 858 calls\n",
      "13:00-14:00 - 382 calls\n",
      "14:00-15:00 - 185 calls\n",
      "15:00-16:00 - 207 calls\n",
      "16:00-17:00 - 263 calls\n",
      "17:00-18:00 - 419 calls\n",
      "18:00-19:00 - 531 calls\n",
      "19:00-20:00 - 400 calls\n",
      "20:00-21:00 - 137 calls\n",
      "21:00-22:00 - 51 calls\n",
      "22:00-23:00 - 20 calls\n",
      "23:00-24:00 - 16 calls\n"
     ]
    }
   ],
   "source": [
    "# Make 24 empty lists, one per hour.\n",
    "waiting_times_per_hour = [[] for _ in range(24)]\n",
    "\n",
    "# Split the data into 24 separate series, one for each hour of the day.\n",
    "current_time = 0\n",
    "for t in waiting_times_day:\n",
    "    current_hour = int(current_time // 60)\n",
    "    current_time += t\n",
    "    waiting_times_per_hour[current_hour].append(t)\n",
    "\n",
    "for hour, calls_in_hour in enumerate(waiting_times_per_hour):\n",
    "    print(f'{hour:02}:00-{hour + 1:02}:00 - {len(calls_in_hour)} calls')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Task 1: Plot the number of calls per hour\n",
    "Use Matplotlib to visualize the number of calls that arrive during each hour of the day, stored in the variable `waiting_times_per_hour`. The call numbers are shown in the output above. You should find an appropriate way to visualize it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "calls = [] # creating an empty list to store the data for the number of calls in each hour\n",
    "for hour, calls_in_hour in enumerate(waiting_times_per_hour):\n",
    "    calls.append(len(calls_in_hour))\n",
    "  \n",
    "# x-coordinates of left sides of bars  \n",
    "x = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23] \n",
    "  \n",
    "# heights of bars \n",
    "y = calls\n",
    "  \n",
    "# labels for bars \n",
    "tick_label = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24] \n",
    "  \n",
    "# set size of figure\n",
    "plt.figure(figsize=(12, 8))\n",
    "    \n",
    "# plotting a bar chart \n",
    "plt.bar(x, y, tick_label = tick_label, width = 0.8) \n",
    "\n",
    "# naming the x-axis \n",
    "plt.xlabel('Hour #') \n",
    "# naming the y-axis \n",
    "plt.ylabel('Number of calls') \n",
    "# plot title \n",
    "plt.title('Number of calls per hour in a day') \n",
    "  \n",
    "# function to show the plot \n",
    "plt.show() "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Task 2: Plot a histogram of the durations for one hour\n",
    "Take the data for the 9th hour (so between 9am and 10am) and plot a histogram showing the distribution over waiting times between calls during that hour."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10, 7))\n",
    "plt.hist(waiting_times_per_hour[9], bins = 20)\n",
    "plt.xlabel('Waiting time between calls (mins)') \n",
    "plt.ylabel('Count') \n",
    "plt.title('The distribution over waiting times between calls in the 9th hour')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Task 3: Guess the distribution\n",
    "What type of distribution best represents the data in your histogram?\n",
    "\n",
    "* Identify a type of distribution. **In class you will use this distribution as your likelihood function in a Bayesian inference problem.**\n",
    "* Guess what the parameters of the distribution are. (This is just a guess for now. In class we will infer the values of the parameters.)\n",
    "* Plot the pdf of your best guess on top of your histogram, to see if they match.\n",
    "* **Important:** You have to normalize your histogram so that it will have the same vertical scale as the plot of the pdf. You can normalize a histogram by using the argument `density=True` in the `hist` function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# For this case, I believe an exponential distribution is the most appropriate for this histogram.\n",
    "lambda_exp = 1/(sum(waiting_times_per_hour[9])/len(waiting_times_per_hour[9]))\n",
    "x = np.linspace(0, 1.5, 1000)\n",
    "\n",
    "plt.figure(figsize=(10, 7))\n",
    "plt.hist(waiting_times_per_hour[9], density=True, bins = 20, label = 'Waiting times between calls in the 9th hour')\n",
    "plt.plot(x, sts.expon(scale=1/lambda_exp).pdf(x), label=f'Expnonential distribution, $\\lambda$ = {format(lambda_exp)}')\n",
    "plt.xlabel('Waiting time between calls (mins)') \n",
    "plt.ylabel('Count (normalized)') \n",
    "plt.title('Distribution of waiting times in 9th hour')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  }
 ],
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