From 005fe0618c29172cb574a30951243208ce7ca638 Mon Sep 17 00:00:00 2001 From: Roger Labbe Date: Sun, 17 Jan 2016 12:36:02 -0800 Subject: [PATCH] Edits for conciseness. --- 03-Gaussians.ipynb | 110 +++++++++++++++++++++------------------------ 1 file changed, 51 insertions(+), 59 deletions(-) diff --git a/03-Gaussians.ipynb b/03-Gaussians.ipynb index e4df7be..e7275f1 100644 --- a/03-Gaussians.ipynb +++ b/03-Gaussians.ipynb @@ -28,7 +28,7 @@ "@import url('http://fonts.googleapis.com/css?family=Source+Code+Pro');\n", "@import url('http://fonts.googleapis.com/css?family=Vollkorn');\n", "@import url('http://fonts.googleapis.com/css?family=Arimo');\n", - "@import url('http://fonts.googleapis.com/css?family=Fira_sans');\n", + "@import url('http://fonts.googleapis.com/css?family=Fira+sans');\n", "\n", ".CodeMirror pre {\n", " font-family: 'Source Code Pro', Consolas, monocco, monospace;\n", @@ -42,7 +42,7 @@ " background: transparent;\n", " color: #000000;\n", " font-weight: 600;\n", - " font-size: 11pt;\n", + " font-size: 12pt;\n", " font-style: bold;\n", " font-family: 'Source Code Pro', Consolas, monocco, monospace;\n", " }\n", @@ -123,11 +123,10 @@ " white-space: nowrap;\n", " }\n", " div.text_cell_render{\n", - " font-family: 'Fira sans', verdana,arial,sans-serif;\n", + " /*font-family: 'Vollkorn', verdana,arial,sans-serif;*/\n", " line-height: 150%;\n", - " font-size: 110%;\n", - " font-weight: 400;\n", - " text-align:justify;\n", + " font-size: 130%;\n", + " text-align: justify;\n", " text-justify:inter-word;\n", " }\n", " div.output_subarea.output_text.output_pyout {\n", @@ -288,7 +287,7 @@ "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 (12.34, -95.54, 2389.5) where that is latitude, longitude, and altitude. We do not want our filter to tell us \"it might be at (1.65, -78.01, 2100.45) or it might be at (34.36, -98.23, 2543.79).\" That doesn't match our physical intuition of how the world works, and as we discussed, it can be prohibitively expensive to compute the multimodal case. And, of course, multiple position estimates makes navigating impossible.\n", "\n", - "So we desire a unimodal, continuous way to represent probabilities that models how the real world works, and that is computationally efficient to calculate. As you might guess from the chapter name, Gaussian distributions provide all of these features." + "We desire a unimodal, continuous way to represent probabilities that models how the real world works, and that is computationally efficient to calculate. As you might guess from the chapter name, Gaussian distributions provide all of these features." ] }, { @@ -407,7 +406,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "The *mode* of a set of numbers is the number that occurs most often. If only one number occurs most often we say it is a *unimodal* set, and if two or more numbers occur the most with equal frequency than te set is *multimodal*. For example the set {1, 2, 2, 2, 3, 4, 4, 4} has modes 2 and 4, which is multimodal, and the set {5, 7, 7, 13} has the mode 7, and so is unimodal. We will not be computing the mode in this manner in this book, but we do use the concepts of unimodal and multimodal in a more general sense. For example, in the **Discrete Bayes** chapter we talked about our belief in the dog's position as a *multimodal distribution* because we assigned different probabilities to different positions.\n", + "The *mode* of a set of numbers is the number that occurs most often. If only one number occurs most often we say it is a *unimodal* set, and if two or more numbers occur the most with equal frequency than te set is *multimodal*. For example the set {1, 2, 2, 2, 3, 4, 4, 4} has modes 2 and 4, which is multimodal, and the set {5, 7, 7, 13} has the mode 7, and so it is unimodal. We will not be computing the mode in this manner in this book, but we do use the concepts of unimodal and multimodal in a more general sense. For example, in the **Discrete Bayes** chapter we talked about our belief in the dog's position as a *multimodal distribution* because we assigned different probabilities to different positions.\n", "\n", "Finally, the *median* of a set of numbers is the middle point of the set so that half the values are below the median and half are above the median. Here, above and below is in relation to the set being sorted. If the set contains an even number of values then the two middle numbers are averaged together.\n", "\n", @@ -441,9 +440,9 @@ "\n", "The *expected value* of a random variable is the average value it would have if we took an infinite number of samples of it and then averaged those samples together. Let's say we have $x=[1,3,5]$ and each value is equally probable. What would we *expect* $x$ to have, on average?\n", "\n", - "It would be the average of 1, 3, and 5, of course, which is 3. That should make sense; we would expect equal numbers of 1, 3, and 5 to occur, so $(1+3+5)/3=3$ is clearly the average of that infinite series of samples. In other words, here the expected value is just the *mean* of the sample space.\n", + "It would be the average of 1, 3, and 5, of course, which is 3. That should make sense; we would expect equal numbers of 1, 3, and 5 to occur, so $(1+3+5)/3=3$ is clearly the average of that infinite series of samples. In other words, here the expected value is the *mean* of the sample space.\n", "\n", - "Now suppose that each value has a different probability of happening. Say 1 has an 80% chance of occurring, 3 has an 15% chance, and 5 has only a 5% chance. In this case we compute the expected value by multiplying each value of $x$ by the percent chance of it occurring, and summing the result. So for this case we could compute\n", + "Now suppose that each value has a different probability of happening. Say 1 has an 80% chance of occurring, 3 has an 15% chance, and 5 has only a 5% chance. In this case we compute the expected value by multiplying each value of $x$ by the percent chance of it occurring, and summing the result. For this case we could compute\n", "\n", "$$\\mathbb E[X] = (1)(0.8) + (3)(0.15) + (5)(0.05) = 1.5$$\n", "\n", @@ -527,7 +526,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "So the mean tells us something about the data, but it does not tell the whole story. We want to be able to specify how much *variation* there is between the heights of the students. You can imagine a number of reasons for this. Perhaps a school district needs to order 5,000 desks, and they want to be sure they buy sizes that accommodate the range of heights of the students. \n", + "The mean tells us something about the data, but not the whole story. We want to be able to specify how much *variation* there is between the heights of the students. You can imagine a number of reasons for this. Perhaps a school district needs to order 5,000 desks, and they want to be sure they buy sizes that accommodate the range of heights of the students. \n", "\n", "Statistics has formalized this concept of measuring variation into the notion of *standard deviation* and *variance*. The equation for computing the *variance* is\n", "\n", @@ -640,7 +639,7 @@ "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAvUAAAC1CAYAAADfhQDIAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAACAAEdTDwAAAAQ4mnoAAAAgwP0/GEFkITvIRY4AAAAASUVORK5CYII=\n", "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -674,9 +673,9 @@ "outputs": [ { "data": { - "image/png": "iVBORw0KGgoAAAANSUhEUgAAAvcAAADxCAYAAABPuZiPAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAJOguAcAAABM4v8BeW5Sk76Yjs8AAAAASUVORK5CYII=\n", + "image/png": "iVBORw0KGgoAAAANSUhEUgAAAvcAAADxCAYAAABPuZiPAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAACLoLgHAAAALILiHgAAALCI/wNqZeiGhYTEfAAAAABJRU5ErkJggg==\n", "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -686,8 +685,8 @@ "name": "stdout", "output_type": "stream", "text": [ - "mean = 1.809\n", - "std = 0.137\n" + "mean = 1.810\n", + "std = 0.167\n" ] } ], @@ -802,7 +801,7 @@ "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAtgAAACxCAYAAAD+t8q+AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n", "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -896,7 +895,7 @@ "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAvAAAADxCAYAAACtZYP2AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n", "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -913,10 +912,12 @@ "cell_type": "markdown", "metadata": {}, "source": [ + "This curves is a *probability density function* or *pdf* for short. It shows the relative likelihood for the random variable to take on a value. In the chart above, a student is somewhat more likely to have a height near 1.8 m than 1.7 m, and far more likely to have a height of 1.9 m vs 1.1 m.\n", + "\n", "> I explain how to plot Gaussians, and much more, in the Notebook *Computing_and_Plotting_PDFs* in the \n", "Supporting_Notebooks folder. You can read it online [here](https://github.com/rlabbe/Kalman-and-Bayesian-Filters-in-Python/blob/master/Supporting_Notebooks/Computing_and_plotting_PDFs.ipynb) [1].\n", "\n", - "This may be recognizable to you as a 'bell curve'. This curve is ubiquitous because under real world conditions many observations are distributed in such a manner. In fact, this is the curve for the student heights given earlier. I will not use the term 'bell curve' to refer to a Gaussian because many probability distributions have a similar bell curve shape. Non-mathematical sources might not be so precise, so be judicious in what you conclude when you see the term used without definition.\n", + "This may be recognizable to you as a 'bell curve'. This curve is ubiquitous because under real world conditions many observations are distributed in such a manner. In fact, this is the curve for the student heights given earlier. I will not use the term 'bell curve' to refer to a Gaussian because many probability distributions have a similar bell curve shape. Non-mathematical sources might not be as precise, so be judicious in what you conclude when you see the term used without definition.\n", "\n", "This curve is not unique to heights — 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 has other desirable qualities which we may not realize we desire.\n", "\n", @@ -934,7 +935,7 @@ "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAtkAAACBCAYAAAAVD6YtAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n", "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -973,7 +974,7 @@ "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAusAAADxCAYAAAByK/npAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nERER0SDFYp2IiIiIaJD6f7vJHnCj2kdDAAAAAElFTkSuQmCC\n", "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -1007,13 +1008,13 @@ "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", + "Let's 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", "$$ \n", "f(x, \\mu, \\sigma) = \\frac{1}{\\sigma\\sqrt{2\\pi}} \\exp\\big [{-\\frac{(x-\\mu)^2}{2\\sigma^2} }\\big ]\n", "$$\n", "\n", - "$\\exp[x]$ is notation for $e^x$; I avoid using superscripts in print so that the fonts are larger and more readable." + "$\\exp[x]$ is notation for $e^x$." ] }, { @@ -1056,7 +1057,7 @@ "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAuIAAADxCAYAAACOPtIjAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAAAASUVORK5CYII=\n", "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -1072,24 +1073,24 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "So what does this curve *mean*? Assume we have a thermometer which reads 22°C. No thermometer is perfectly accurate, and so we normally expect that thermometer will read slightly plus or minus that temperature each time we read it. However, 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°C. \n", + "What does this curve *mean*? Assume we have a thermometer which reads 22°C. No thermometer is perfectly accurate, and so we expect that each reading will be slightly off the actual value. However, a theorem called *Central Limit Theorem* states that if we make many measurements that the measurements will be normally distributed. 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°C. \n", "\n", "Recall that a Gaussian distribution is *continuous*. Think of an infinitely long straight line - what is the probability that a point you pick randomly is at 2. 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* 2°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.* 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 resulting area will be the probability of the temperature reading being between those two temperatures. \n", + "What is this curve? It is something we call the *probability density function.* 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 resulting area will be the probability of the temperature reading being between those two temperatures. \n", "\n", - "We can think of this in Bayesian terms or frequentist terms. As a Bayesian, if the thermometer reads exactly 22°C, then our belief is described by the curve - our belief that the actual (system) temperature is near 22 is very high, and our belief that the actual temperature is near 18 is very low. As a frequentist we would say that if we took 1 billion temperature measurements of a system at exactly 22°C, then a histogram of the measurements would look like this curve. \n" + "We can think of this in Bayesian terms or frequentist terms. As a Bayesian, if the thermometer reads exactly 22°C, then our belief is described by the curve - our belief that the actual (system) temperature is near 22 is very high, and our belief that the actual temperature is near 18 is very low. As a frequentist we would say that if we took 1 billion temperature measurements of a system at exactly 22°C, then a histogram of the measurements would look like this curve. " ] }, { "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", + "How do you compute the probability, or area under the curve? 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 `filterpy.stats.norm_cdf` which computes the integral for you. So, for example, we can compute" + "I wrote `filterpy.stats.norm_cdf` which computes the integral for you. For example, we can compute" ] }, { @@ -1119,7 +1120,7 @@ "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°C, so that is what we used for the mean. \n", + "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°C, so that is what we used for the mean. \n", "\n", "The notation for a normal distribution for a random variable $X$ is $X \\sim\\ \\mathcal{N}(\\mu,\\sigma^2)$ where $\\sim$ means *distributed according to*. This means I can express the temperature reading of our thermometer as\n", "\n", @@ -1182,7 +1183,7 @@ "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAuIAAADaCAYAAADjVSfWAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n", "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -1204,7 +1205,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "So what is this telling us? The Gaussian with $\\sigma^2=0.05$ is very narrow. It is saying that we believe $x=23$, and that we are very sure about that. In contrast, the Gaussian with $\\sigma^2=5$ 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. $\\sigma^2=0.05$ has almost completely eliminated $22$ or $24$ as possible values, whereas $\\sigma^2=5$ considers them nearly as likely as $23$.\n", + "What is this telling us? The Gaussian with $\\sigma^2=0.05$ is very narrow. It is saying that we believe $x=23$, and that we are very sure about that. In contrast, the Gaussian with $\\sigma^2=5$ 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. $\\sigma^2=0.05$ has almost completely eliminated $22$ or $24$ as possible values, whereas $\\sigma^2=5$ 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 curve for $\\sigma^2=0.05$ represents a very accurate thermometer, and curve for $\\sigma^2=5$ represents a fairly inaccurate one. 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", @@ -1214,9 +1215,9 @@ "\n", "## The 68-95-99.7 Rule\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 ($\\pm1\\sigma$) of the mean, 95% falls within two standard deviations ($\\pm2\\sigma$), and 99.7% within three ($\\pm3\\sigma$). 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 $71 \\pm (2 * 9.4)$). \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 ($\\pm1\\sigma$) of the mean, 95% falls within two standard deviations ($\\pm2\\sigma$), and 99.7% within three ($\\pm3\\sigma$). This is often called the 68-95-99.7 rule. 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 $71 \\pm (2 * 9.4)$). \n", "\n", - "Finally, these are not arbitrary numbers. If the Gaussian for our position is $\\mu=22$ meters, then the standard deviation also has units meters. Thus $\\sigma=0.2$ implies that 68% of the measurements range from 21.8 to 22.2 meters. Variance is the standard deviation squared, so $\\sigma^2 = .04$ meters$^2$." + "Finally, these are not arbitrary numbers. If the Gaussian for our position is $\\mu=22$ meters, then the standard deviation also has units meters. Thus $\\sigma=0.2$ implies that 68% of the measurements range from 21.8 to 22.2 meters. Variance is the standard deviation squared, thus $\\sigma^2 = .04$ meters$^2$." ] }, { @@ -1237,7 +1238,7 @@ "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAr8AAADTCAYAAACIsHvmAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nrkJggg==\n", "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -1275,7 +1276,7 @@ "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAt4AAADaCAYAAACRmkVgAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nA0gXYwAAAABJRU5ErkJggg==\n", "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -1320,7 +1321,7 @@ "\n", "A typical textbook would directly launch into a multi-page 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 computationally feasible. Said another way, Kalman filters use Gaussians *because* they are so computationally nice. " + "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 computationally feasible. Said another way, Kalman filters use Gaussians *because* they are computationally nice. " ] }, { @@ -1334,9 +1335,9 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "In this chapter I have used custom code from FilterPy 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 statistics and probabilities.\n", + "In this chapter I used code from FilterPy to compute and plot Gaussians. I did 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`. So let's walk through how to use scipy.stats to compute statistics and probabilities.\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 from FilterPy." + "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. 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 from FilterPy." ] }, { @@ -1398,9 +1399,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "If we look at the documentation for `scipy.stats.norm` [here](http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.norm.html#scipy.stats.normfor) [2] 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." + "The documentation for [scipy.stats.norm](http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.norm.html#scipy.stats.normfor) [2] lists many other functions. For example, we can generate $n$ samples from the distribution with the `rvs()` function." ] }, { @@ -1414,9 +1413,9 @@ "name": "stdout", "output_type": "stream", "text": [ - "[ 0.409 2.668 6.657 2.062 4.686 4.65 -2.214\n", - " -2.35 6.065 1.219 -0.904 5.647 8.615 -4.476\n", - " 0.463]\n" + "[ 3.527 2.952 3.709 1.501 -0.532 -0.173 2.264\n", + " 4.293 5.036 6.365 2.79 4.76 -0.052 0.789\n", + " 2.733]\n" ] } ], @@ -1482,13 +1481,6 @@ "print('mean is', n23.mean())" ] }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "There are many other functions available, and if you are interested I urge you to peruse the documentation. Sometimes the documentation is terse, but with a bit of searching 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 SciPy tutorial [3] is quite approachable, and I suggest starting there. " - ] - }, { "cell_type": "markdown", "metadata": {}, @@ -1500,7 +1492,7 @@ "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 variable 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", + "Earlier I mentioned the *central limit theorem*, which states that under certain conditions the arithmetic sum of any independent random variable will be normally distributed, regardless of how the random variables are distributed. This is important to us because 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. \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*. Tails is a colloquial term for the far left and right side parts of the curve where the probability density is close to zero.\n", "\n", @@ -1520,7 +1512,7 @@ "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAu8AAADaCAYAAAAWq6xmAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nshP/H/VN5Q2UfDpMAAAAAElFTkSuQmCC\n", "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -1543,7 +1535,7 @@ "\n", "Kalman filters use sensors to measure the world. The errors in a sensor's measurements are rarely truly Gaussian. 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 an 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 white 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" + "Let's say I want to model a sensor that has some white 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. I can simulate this with:" ] }, { @@ -1575,9 +1567,9 @@ "outputs": [ { "data": { - "image/png": "iVBORw0KGgoAAAANSUhEUgAAAuYAAADaCAYAAADqvoesAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nYII=\n", + "image/png": "iVBORw0KGgoAAAANSUhEUgAAAuYAAADaCAYAAADqvoesAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n", "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -1628,9 +1620,9 @@ "outputs": [ { "data": { - "image/png": "iVBORw0KGgoAAAANSUhEUgAAAukAAADaCAYAAAAbtdwhAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n", + "image/png": "iVBORw0KGgoAAAANSUhEUgAAAukAAADaCAYAAAAbtdwhAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nacBGAAAAAElFTkSuQmCC\n", "text/plain": [ - "" + "" ] }, "metadata": {},