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     "source": [
      "[Table of Contents](http://nbviewer.ipython.org/github/rlabbe/Kalman-and-Bayesian-Filters-in-Python/blob/master/table_of_contents.ipynb)"
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     "source": [
      "Gaussian Probabilities"
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      "#format the book\n",
      "%matplotlib inline\n",
      "from __future__ import division, print_function\n",
      "import matplotlib.pyplot as plt\n",
      "import book_format\n",
      "book_format.load_style()"
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     "source": [
      "Introduction"
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     "source": [
      "The last chapter ended by discussing some of the drawbacks of the Discrete Bayesian filter. For many tracking and filtering problems our desire is to have a filter that is *unimodal* and *continuous*. That is, we want to model our system using floating point math (continuous) and to have only one belief represented (unimodal). For example, we want to say an aircraft is at (12.34381, -95.54321,2389.5) where that is latitude, longitude, and altitude. We do not want our filter to tell us \"it might be at (1,65,78) or at (34,656,98)\" That doesn't match our physical intuition of how the world works, and as we discussed, it is prohibitively expensive to compute.\n",
      "\n",
      ">So we desire a unimodal, continuous way to represent probabilities that models how the real world works, and that is very computationally efficient to calculate. As you might guess from the chapter name, Gaussian distributions provide all of these features.\n",
      "\n",
      "Before we go into the math, lets just look at a graph of the Gaussian distribution to get a sense of what we are talking about."
     ]
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     "input": [
      "from stats import plot_gaussian\n",
      "\n",
      "plot_gaussian(mean=100, variance=15**2, xlabel='IQ')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
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JIX7Y8RU6NeiHpl4dJLajqmCM+yHVPOayHzZuXPFVECv9MsMvegOrLVu24LPPPsOmTZtQ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\nRGQwGFCIiIiIiMhgMKAQEREREZHB+H87nlqe8JwAzQAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f7c5d274cc0>"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Probably this is immediately recognizable to you as a 'bell curve'. This curve is ubiquitous because under real world conditions most observations are distributed in such a manner. In fact, this is the bell curve for IQ (Intelligence Quotient). You've probably seen this before, and understand it. It tells us that the average IQ is 100, and that the number of people that have IQs higher or lower than that drops off as they get further away from 100. It's hard to see the exact number, but we can see that very few people have an IQ over 150 or under 50, but a lot have an IQ of 90 or 110. \n",
      "\n",
      "This curve is not unique to IQ distributions - a vast amount of natural phenomena exhibits this sort of distribution, including the sensors that we use in filtering problems. As we will see, it also has all the attributes that we are looking for - it represents a unimodal belief or value as a probability, it is continuous, and it is computationally efficient. We will soon discover that it also other desirable qualities that we do not yet recognize we need.\n",
      "<p>\n",
      "<p>"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Nomenclature"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "A bit of nomenclature before we continue - this chart depicts the *probability density* of of a *random variable* having any value between ($-\\infty..\\infty)$. What does that mean? Imagine we take an infinite number of infinitely precise measurements of the speed of automobiles on a section of highway. We could then plot the results by showing the relative number of cars going at any given speed. If the average was 120 kph, it might look like this:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plot_gaussian(mean=120, variance=17**2, xlabel='speed(kph)')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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tpxG9JhiypJRTWrdnmUmNAHg6BhQAuI08R54WrpuhvDy7MwsOqqyHop8s5Cyg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\niIiIiKjJ+H/I+FW8U9TcngAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f7c5d06ee10>"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The y-axis depicts the *probability density* - the relative amount of cars that are going the speed at the corresponding x-axis.\n",
      "\n",
      "> *Random variable* will be precisely defined later. For now just think of it as a variable that can 'freely' and 'randomly' vary. A dog's position in a hallway, air temperature, and a drone's height above the ground are all random variables. The position of the North Pole is not, nor is a sin wave (a sin wave is anything but 'free').\n",
      "\n",
      "You may object that human IQs or automobile speeds cannot be less than zero, let alone $-\\infty$. This is true, but this is a common limitation of mathematical modeling. \"The map is not the territory\" is a common expression, and it is true for Bayesian filtering and statistics. The Gaussian distribution above very closely models the distribution of IQ test results, but being a model it is necessarily imperfect. The difference between model and reality will come up again and again in these filters. \n",
      "\n",
      "You will see these distributions called *Gaussian distributions*, *normal distributions*, and *bell curves*. Bell curve is ambiguous because there are other distributions which also look bell shaped but are not Gaussian distributions, so we will not use it further in this book. But *Gaussian* and *normal* both mean the same thing, and are used interchangeably. I will use both throughout this book as different sources will use either term, and so I want you to be used to seeing both. Finally, as in this paragraph, it is typical to shorten the name and just talk about a *Gaussian* or *normal* - these are both typical shortcut names for the *Gaussian distribution*. "
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Gaussian Distributions"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "So let us explore how Gaussians work. A Gaussian is a *continuous probability distribution* that is completely described with two parameters, the mean ($\\mu$) and the variance ($\\sigma^2$). It is defined as:\n",
      "$$ \n",
      "f(x, \\mu, \\sigma) = \\frac{1}{\\sigma\\sqrt{2\\pi}} e^{-\\frac{1}{2}{(x-\\mu)^2}/\\sigma^2 }\n",
      "$$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<p> Don't be dissuaded by the equation if you haven't seen it before; you will not need to memorize or manipulate it. The computation of this function is stored in `stats.py` with the function `gaussian(x, mean, var)`.\n",
      "\n",
      "> **Optional:** Let's remind ourselves how to look at a function stored in a file by using the *%load* magic. If you type *%load -s gaussian stats.py* into a code cell and then press CTRL-Enter, the notebook will create a new input cell and load the function into it.\n",
      "\n",
      "    %load -s gaussian stats.py\n",
      "    \n",
      "    def gaussian(x, mean, var):\n",
      "        \"\"\"returns normal distribution for x given a \n",
      "        gaussian with the specified mean and variance. \n",
      "        \"\"\"\n",
      "        return math.exp((-0.5*(x-mean)**2)/var) / \\\n",
      "                         math.sqrt(_two_pi*var)"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<p><p><p><p>We will plot a Gaussian with a mean of 22 $(\\mu=22)$, with a variance of 4 $(\\sigma^2=4)$, and then discuss what this means. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from stats import gaussian, norm_cdf\n",
      "plot_gaussian(22, 4, mean_line=True, xlabel='$^{\\circ}C$')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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RkelxatAIwwOnCNmxi/txPyNZUiMismQcPojIIj3Iulfu2PXQgMlwatBIUiMi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\nrkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f7c5cff8fd0>"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "So what does this curve *mean*? Assume for a moment that we have a thermometer, which reads 22$\\,^{\\circ}C$. No thermometer is perfectly accurate, and so we normally expect that thermometer will read $\\pm$ that temperature by some amount each time we read it. Furthermore, a theorem called  **Central Limit Theorem** states that if we make many measurements that the measurements will be normally distributed. So, when we look at this chart we can *sort of* think of it as representing the probability of the thermometer reading a particular value given the actual temperature of 22$^{\\circ}C$. However, that is not quite accurate mathematically. \n",
      "\n",
      "Recall that we said that the distribution is *continuous*. Think of an infinitly long straight line - what is the probability that a point you pick randomly is at, say, 2.0. Clearly 0%, as there is an infinite number of choices to choose from. The same is true for normal distributions; in the graph above the probability of being *exactly* 22$^{\\circ}C$ is 0% because there are an infinite number of values the reading can take.\n",
      "\n",
      "So what then is this curve? It is something we call the *probability density function.* Later we will delve into this in greater detail; for now just understand that the area under the curve at any region gives you the probability of those values. So, for example, if you compute the area under the curve between 20 and 22 the result will be the probability of the temperature reading being between those two temperatures."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "So how do you compute the probability, or area under the curve? Well, you integrate the equation for the Gaussian \n",
      "\n",
      "$$ \\int^{x_1}_{x_0}  \\frac{1}{\\sigma\\sqrt{2\\pi}} e^{-\\frac{1}{2}{(x-\\mu)^2}/\\sigma^2 } dx$$\n",
      "\n",
      "I wrote `stats.norm_cdf` which computes the integral for you. So, for example, we can compute"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print('Probability of value in range 21.5 to 22.5 is {:.2f}%'.format(\n",
      "      norm_cdf((21.5, 22.5), 22,4)*100))\n",
      "print('Probability of value in range 23.5 to 24.5 is {:.2f}%'.format(\n",
      "      norm_cdf((23.5, 24.5), 22,4)*100))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Probability of value in range 21.5 to 22.5 is 19.74%\n",
        "Probability of value in range 23.5 to 24.5 is 12.10%\n"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "So the mean ($\\mu$) is what it sounds like - the average of all possible probabilities. Because of the symmetric shape of the curve it is also the tallest part of the curve. The thermometer reads $22^{\\circ}C$, so that is what we used for the mean.  \n",
      "\n",
      "> *Important*: I will repeat what I wrote at the top of this section: \"A Gaussian...is completely described with two parameters\"\n",
      "\n",
      "The standard notation for a normal distribution for a random variable $X$ is $X \\sim\\ \\mathcal{N}(\\mu,\\sigma^2)$. This means I can express the temperature reading of our thermometer as\n",
      "\n",
      "$$temp = \\mathcal{N}(22,4)$$\n",
      "\n",
      "This is an **extremely important** result. Gaussians allow me to capture an infinite number of possible values with only two numbers! With the values $\\mu=22$ and $\\sigma^2=4$ I can compute the distribution of measurements for over any range."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "The Variance"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Since this is a probability density distribution it is required that the area under the curve always equals one. This should be intuitively clear - the area under the curve represents all possible occurences, which must sum to one. We can prove this ourselves with a bit of code. (If you are mathematically inclined, integrate the Gaussian equation from $-\\infty$ to $\\infty$)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print(norm_cdf((-1e8, 1e8), mu=0, var=4))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "1.0\n"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This leads to an important insight. If the variance is small the curve will be narrow. this is because the variance is a measure of *how much* the samples vary from the mean. To keep the area equal to 1, the curve must also be tall. On the other hand if the variance is large the curve will be wide, and thus it will also have to be short to make the area equal to 1.\n",
      "\n",
      "Let's look at that graphically:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np\n",
      "import matplotlib.pyplot as plt\n",
      "    \n",
      "xs = np.arange(15, 30, 0.05)\n",
      "plt.plot(xs, [gaussian(x, 23, .2) for x in xs], label='var=0.2')\n",
      "plt.plot(xs, [gaussian(x, 23, 1) for x in xs], label='var=1')\n",
      "plt.plot(xs, [gaussian(x, 23, 5) for x in xs], label='var=5')\n",
      "plt.legend()\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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nx+/R3j0excXFbnujv/nmGy1btkwXXXSRevfu7fEYAkmrgUdqaqpsNpuKiooM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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f7c595a2f28>"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "So what is this telling us? The blue gaussian is very narrow. It is saying that we believe $x=23$, and that we are very sure about that. In contrast, the red gaussian also believes that $x=23$, but we are much less sure about that. Our believe that $x=23$ is lower, and so our belief about the likely possible values for $x$ is spread out - we think it is quite likely that $x=20$ or $x=26$, for example. The blue gaussian has almost completely eliminated $22$ or $24$ as possible value - their probability is almost $0\\%$, whereas the red curve considers them nearly as likely as $23$.\n",
      "\n",
      "If we think back to the thermometer, we can consider these three curves as representing the readings from three different thermometers. The blue curve represents a very accurate thermometer, and the red one represents a fairly inaccurate one. Green of course represents one in between the two others. Note the very powerful property the Gaussian distribution affords us - we can entirely represent both the reading and the error of a thermometer with only two numbers - the mean and the variance.\n",
      "\n",
      "The standard notation for a normal distribution for a random variable $X$ is just $X \\sim\\ \\mathcal{N}(\\mu,\\sigma^2)$ where $\\mu$ is the mean and $\\sigma^2$ is the variance. It may seem odd to use $\\sigma$ squared - why not just $\\sigma$? We will not go into great detail about the math at this point, but in statistics $\\sigma$ is the *standard deviation* of a normal distribution. *Variance* is defined as the square of the standard deviation, hence $\\sigma^2$.\n",
      "\n",
      "It is worth spending a few words on standard deviation now. The standard deviation is a measure of how much variation from the mean exists. For Gaussian distributions, 68% of all the data falls within one standard deviation($1\\sigma$) of the mean, 95% falls within two standard deviations ($2\\sigma$), and 99.7% within three ($3\\sigma$). This is often called the 68-95-99.7 rule. So if you were told that the average test score in a class was 71 with a standard deviation of 9.4, you could conclude that 95% of the students received a score between 52.2 and 89.8 if the distribution is normal (that is calculated with $71 \\pm (2 * 9.4)$). "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The following graph depicts the relationship between the standard deviation and the normal distribution. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from gaussian_internal import display_stddev_plot\n",
      "display_stddev_plot()\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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yXQMISDsPbbjuG+oB4GYY/gBu2+z4ccrJvfKwrsiI4gbbAP6vWtm6tuNpPNQL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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f7c595a2b38>"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "> An equivalent formation for a Gaussian is $\\mathcal{N}(\\mu,1/\\tau)$ where $\\mu$ is the *mean* and $tau$ the *precision*. Here $1/\\tau = \\sigma^2$; it is the reciprocal of the variance. While we do not use this formulation in this book, it underscores that the variance is a measure of how precise our data is. A small variance yields large precision - our measurement is very precise. Conversely, a large variance yields low precision - our belief is spread out across a large area. You should become comfortable with thinking about Gaussians in these equivalent forms. Gaussians reflect our *belief* about a measurement, they express the *precision* of the measurement, and they express how much *variance* there is in the measurements. These are all different ways of stating the same fact.</div>"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Interactive Gaussians"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "For those that are reading this in IPython Notebook, here is an interactive version of the Gaussian plots. Use the sliders to modify $\\mu$ and $\\sigma^2$. Adjusting $\\mu$ will move the graph to the left and right because you are adjusting the mean, and adjusting $\\sigma^2$ will make the bell curve thicker and thinner."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "from IPython.html.widgets import interact, interactive, fixed\n",
      "import IPython.html.widgets as widgets\n",
      "\n",
      "def plt_g(mu,variance):\n",
      "    xs = np.arange(2, 8, 0.1)\n",
      "    ys = [gaussian (x, mu, variance) for x in xs]\n",
      "    plt.plot(xs, ys)\n",
      "    plt.ylim((0, 1))\n",
      "    plt.show()\n",
      "\n",
      "interact (plt_g, mu=(0, 10), \n",
      "          variance=widgets.FloatSliderWidget(value=0.6, min=0.2, max=4.5))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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KBQDmoGgAwK8kHNyiL9b+1zCr5heoqDHPKrAaawHBfN5ePrpn1F8VVLOBYb46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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f7c5d00ee10>"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 9,
       "text": [
        "<function __main__.plt_g>"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Finally, if you are reading this in an IPython Notebook, here is an animation of a Gaussian. First, the mean is being shifted to the right. Then the mean is centered at $\\mu=5$ and the variance is modified.\n",
      "\n",
      "<img src='animations/04_gaussian_animate.gif'>"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Computational Properties of the Gaussian"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Recall how our discrete Bayesian filter worked. We had a vector implemented as a numpy array representing our belief at a certain moment in time. When we performed another measurement using the `update()` function we had to multiply probabilities together, and when we performed the motion step using the `predict()` function we had to shift and add probabilities. I've promised you that the Kalman filter uses essentially the same process, and that  it uses Gaussians instead of histograms, so you might reasonable expect that we will be multiplying, adding, and shifting Gaussians in the Kalman filter.\n",
      "\n",
      "A typical textbook would directly launch into a multipage proof of the behavior of Gaussians under these operations, but I don't see the value in that right now. I think the math will be much more intuitive and clear if we just start developing a Kalman filter using Gaussians. I will provide the equations for multiplying and shifting Gaussians at the appropriate time. You will then be able to develop a physical intuition for what these operations do, rather than be forced to digest a lot of fairly abstract math.\n",
      "\n",
      "The key point, which I will only assert for now, is that all the operations are very simple, and that they preserve the properties of the Gaussian. This is somewhat remarkable, in that the Gaussian is a nonlinear function, and typically if you multiply a nonlinear equation with itself you end up with a different equation. For example, the shape of `sin(x)sin(x)` is very different from `sin(x)`. But the result of multiplying two Gaussians is yet another Gaussian. This is a fundamental property, and a key reason why Kalman filters are possible."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Computing Probabilities with scipy.stats"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In this chapter I have used by custom written code for computing Gaussians, plotting, and so on. I chose to do that to give you a chance to look at the code and see how these functions are implemented.  However, Python comes with \"batteries included\" as the saying goes, and it comes with a wide range of statistics functions in the module scipy.stats. I find the performance of some of the functions rather slow (the scipy.stats documentation contains a warning to this effect), but this is offset by the fact that this is standard code available to everyone, and it is well tested. So let's walk through how to use scipy.stats to compute various things.\n",
      "\n",
      "The scipy.stats module contains a number of objects which you can use to compute attributes of various probability distributions. The full documentation for this module is here: http://http://docs.scipy.org/doc/scipy/reference/stats.html. However, we will focus on the  norm variable, which implements the normal distribution. Let's look at some code that uses `scipy.stats.norm` to compute a Gaussian, and compare its value to the value returned by the `gaussian()` function."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from scipy.stats import norm\n",
      "print(norm(2, 3).pdf(1.5))\n",
      "print(gaussian(x=1.5, mean=2, var=3*3))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "0.131146572034\n",
        "0.13114657203397997\n"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The call `norm(2,3)` creates what scipy calls a 'frozen' distribution - it creates and returns an object with a mean of 2 and a standard deviation of 3. You can then use this object multiple times to get the probability density of various values, like so:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "n23 = norm(2,3)\n",
      "print('probability density of 1.5 is %.4f' % n23.pdf(1.5))\n",
      "print('probability density of 2.5 is also %.4f' % n23.pdf(2.5))\n",
      "print('whereas probability density of 2 is %.4f' % n23.pdf(2))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "probability density of 1.5 is 0.1311\n",
        "probability density of 2.5 is also 0.1311\n",
        "whereas probability density of 2 is 0.1330\n"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "If we look at the documentation for `scipy.stats.norm` <a href=\"http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.norm.html#scipy.stats.normfor\">here</a>[1] we see that there are many other functions that norm provides.\n",
      "\n",
      "For example, we can generate $n$ samples from the distribution with the `rvs()` function."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print(n23.rvs(size=15))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[ 5.21312379  4.07998256 -1.88727855  1.8810597   5.83528749  3.17323975\n",
        "  3.61095259  6.35085461  0.85512558  7.86604454  1.68210737  4.50882311\n",
        "  6.25585727  7.3637816   2.37546818]\n"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We can get the *cumulative distribution function (CDF)*, which is the probability that a randomly drawn value from the distribution is less than or equal to $x$."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# probability that a random value is less than the mean 2\n",
      "print(n23.cdf(2))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "0.5\n"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We can get various properties of the distribution:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print('variance is', n23.var())\n",
      "print('standard deviation is', n23.std())\n",
      "print('mean is', n23.mean())"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "variance is 9.0\n",
        "standard deviation is 3.0\n",
        "mean is 2.0\n"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "There are many other functions available, and if you are interested I urge you to peruse the documentation. I find the documentation to be excessively terse, but with a bit of googling you can find out what a function does and some examples of how to use it. Most of this functionality is not of immediate interest to the book, so I will leave the topic in your hands to explore. The <a href=\"http://docs.scipy.org/doc/scipy/reference/tutorial/stats.html\">SciPy tutorial</a> [2] is quite approachable, and I suggest starting there. "
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Fat Tails"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Earlier I spoke very briefly about the *central limit theorem*, which states that under certain conditions the arithmetic sum of **any** independent random variables will be normally distributed, regardless of how the random variables are distributed. This is extremely important for (at least) two reasons. First, nature is full of distributions which are not normal, but when we apply the central limit theorem over large populations we end up with normal distributions. Second, Gaussians are mathematically *tractable*. We will see this more as we develop the Kalman filter theory, but there are very nice closed form solutions for operations on Gaussians that allow us to use them analytically.\n",
      "\n",
      "However, a key part of the proof is \"under certain conditions\". These conditions often do not hold for the physical world. The resulting distributions are called *fat tailed*. Let's consider a trivial example. We think of things like test scores as being normally distributed. If you have ever had a professor 'grade on a curve' you have been subject to this assumption. But of course test scores cannot follow a normal distribution. This is because the distribution assigns a nonzero probability distribution for *any* value, no matter how far from the mean. So, for example, say your mean is 90 and the standard deviation is 13. The normal distribution assumes that there is a large chance of somebody getting a 90, and a small chance of somebody getting a 40. However, it also assumes that there is a tiny chance of somebody getting a -10, or of 150. It assumes that there is a infitesimal chance of getting a score of -1e300, or 4e50. In other words, the *tails* of the distribution are infinite. \n",
      "\n",
      "But for a test we know this is not true. You cannot get less than 0, or more than 100. Let's plot this using a normal distribution."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "xs = np.arange(10,100, 0.05)\n",
      "plt.plot(xs, [gaussian(x, 90, 13) for x in xs], label='var=0.2')\n",
      "plt.xlim((60,120))\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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PVwBgeBBWAMCHlVZzGORwGGdaB1RadeQyVwIAPImwAgA+rLSKwyCHg3kdkHmd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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f7c5d0c49b0>"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "So the problem with this chart is that the area under the drawn curve cannot equal 1, so it is not a probability distribution. What actually happens is that a few more students get scores nearer the upper end of the range (for example), and that tail becomes 'fat'. Also, the test is probably not able to perfectly distinguish incredibly minute differences in skill in the students, so the distribution to the left of the mean is also probably a bit bunched up in places. The resulting distribution is called a *fat tail distribution*.\n",
      "\n",
      "We are not going to be applying Kalman filters to grades of student papers, but we are using physical sensors to measure the world. The errors in sensor's measurements are rarely truly Gaussian. And, of course, the signal itself will have time dependent correlations. For example, consider a sensor mounted on a helicopter. The rotating blades cause vibrations in the air frame, which will cause small deviations in the flight path. This deviation will be related to the frequency of the vibration, hence the values at t and t+1 are not *independent*. The vibration will also effect sensors such as the INS. No physical object can react instantly to changes, so the INS will somewhat lag the vibrations in a perhaps quite complex way, and so the noise introduced by the vibration will be anything but independent. \n",
      "\n",
      "It is far too early to be talking about the difficulties that this presents to the Kalman filter designer. It is worth keeping in the back of your mind the fact that the Kalman filter math is based on a somewhat idealized model of the world.  For now I will present a bit of code that I will be using later in the book to form fat tail distributions to simulate various processes and sensors. This distribution is called the student's t distribution. \n",
      "\n",
      "Let's say I want to model a sensor that has some noise in the output. For simplicity, let's say the signal is a constant 10, and the standard deviation of the noise is 2. We can use the function `numpy.random.randn()` to get a random number with a mean of 0 and a standard deviation of 1. So I could simulate this sensor with"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from numpy.random import randn\n",
      "\n",
      "def sense():\n",
      "    return 10 + randn()*2"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 16
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Let's plot that signal and see what it looks like."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "zs = [sense() for i in range(5000)]\n",
      "plt.plot(zs, lw=1)\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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z5s2Dk2e7VPeL2vdDfdKAQJcON9xwA9x49bd1YV177bVwvDr5/MjoMKw5Hrsf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\nES5cuBB27twJPT09IElS9PqRI0dEJoMgC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       "text": [
        "<matplotlib.figure.Figure at 0x7f7c5d07d9b0>"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "That looks like I would expect. The signal is centered around 10. A standard deviation of 2 means that 68% of the measurements will be within $\\pm$ 2 of 10, and 99% will be within $\\pm$ 6 of 10, and that looks like what is happenning. \n",
      "\n",
      "Now let's look at a fat tailed distribution. There are many choices, I will use the Student's T distribution. I will not go into the math, but just give you the source code for it and then plot a distribution using it."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import random\n",
      "import math\n",
      "\n",
      "def rand_student_t(df, mu=0, std=1):\n",
      "    \"\"\"return random number distributed by student's t distribution with\n",
      "    `df` degrees of freedom with the specified mean and standard deviation.\n",
      "    \"\"\"\n",
      "    x = random.gauss(0, std)\n",
      "    y = 2.0*random.gammavariate(0.5*df, 2.0)\n",
      "    return x / (math.sqrt(y/df)) + mu  "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 18
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def sense_t():\n",
      "    return 10 + rand_student_t(7)*2\n",
      "\n",
      "zs = [sense_t() for i in range(5000)]\n",
      "plt.plot(zs, lw=1)\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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GsoomLZrjhl3L6DcJ1k1SHa6sKRWKIClKTf1hX322o7wE3/OqbfPg8TF3cK/b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\nesFVarJky+jHl94MAG6zIHn+eN1DWcnYdYavAPDfnZ+VR1l/Iz8TCV0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iKbZYOH3xdorC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       "text": [
        "<matplotlib.figure.Figure at 0x7f7c5cfb6978>"
       ]
      }
     ],
     "prompt_number": 19
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We can see from the plot that while the output is similar to the normal distribution there are outliers that go far more than 3 standard deviations from the mean. This is what causes the 'fat tail'.\n",
      "\n",
      "It is unlikely that the Student's T distribution is an accurate model of how your sensor (say, a GPS or doppler) performs, and this is not a book on how to model physical systems. However, it does produce reasonable data to test your filter's performance when presented with real world noise. We will be using distributions like these throughout the rest of the book in our simulations and tests. \n",
      "\n",
      "This is not an idle concern. The Kalman filter equations assume the noise is normally distributed, and perform sub-optimally if this is not true. Designers for mission critical filters, such as the filters on spacecraft, need to master a lot of theory and emperical knowledge about the performance of the sensors on their spacecraft. \n",
      "\n",
      "The code for rand_student_t is included in `filterpy.common`. You may use it with\n",
      "\n",
      "    from filterpy.common import rand_student_t"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Summary and Key Points"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The following points **must** be understood by you before we continue:\n",
      "\n",
      "* Normal distributions occur throughout nature\n",
      "* They express a continuous probability distribution\n",
      "* They are completely described by two parameters: the mean ($\\mu$) and variance ($\\sigma^2$)\n",
      "* $\\mu$ is the average of all possible values\n",
      "* The variance $\\sigma^2$ represents how much our measurements vary from the mean\n",
      "* The standard deviation ($\\sigma$) is the square root of the variance ($\\sigma^2$)"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "References"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "[1] http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.norm.html#scipy.stats.normfor\n",
      "\n",
      "[2] http://docs.scipy.org/doc/scipy/reference/tutorial/stats.html"
     ]
    }
   ],
   "metadata": {}
  }
 ]
}