More improvements to Bayes' theorem coverage.
Mostly rearranging descriptions from chapter 2 to 3, after I cover probability distributions. I think some more work needs to be done, mainly I think I go on for too long on pdfs, using first cars, then temperatures, to explain the same thing.
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@@ -1703,15 +1703,15 @@
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"\n",
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"We implemented the `update()` function with this probability calculation:\n",
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"\n",
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"$$ \\mathtt{posterior} = \\frac{\\mathtt{likelihood}\\times \\mathtt{prior}}{\\mathtt{normalization}}$$ \n",
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"$$ \\mathtt{posterior} = \\frac{\\mathtt{likelihood}\\times \\mathtt{prior}}{\\mathtt{normalization\\, factor}}$$ \n",
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"\n",
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"We haven't developed the mathematics to discuss Bayes yet, but this is Bayes' theorem. Every filter in this book is an expression of Bayes theorem. In the next chapter we will develop the mathematics, but in many ways that obscures the simple idea expressed in this equation:\n",
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"We haven't developed the mathematics to discuss Bayes yet, but this is Bayes' theorem. Every filter in this book is an expression of Bayes' theorem. In the next chapter we will develop the mathematics, but in many ways that obscures the simple idea expressed in this equation:\n",
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"\n",
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"$$ updated\\,knowledge = \\big\\|likelihood\\,of\\,new\\,knowledge\\times prior\\, knowledge \\big\\|$$\n",
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"\n",
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"where $\\| \\cdot\\|$ expresses normalizing the term.\n",
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"\n",
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"We came to this with simple reasoning about a dog walking down a hallway. Yet, as we will see, the same equation applies to a universe of filtering problems. We will use this equation in every subsequent chapter.\n",
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"We came to this with simple reasoning about a dog walking down a hallway. Yet, as we will see the same equation applies to a universe of filtering problems. We will use this equation in every subsequent chapter.\n",
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"\n",
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"Likewise, the `predict()` step computes the total probability of multiple possible events. This is known as the *Total Probability Theorem* in statistics, and we will also cover this in the next chapter after developing some supporting math.\n",
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"\n",
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@@ -1792,7 +1792,7 @@
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.6.5"
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"version": "3.6.4"
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},
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"widgets": {
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"application/vnd.jupyter.widget-state+json": {
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+190
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@@ -11,7 +11,7 @@
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Gaussian Probabilities"
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"# Probabilities, Gaussians, and Bayes' Theorem"
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]
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},
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{
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@@ -36,7 +36,7 @@
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" <style>\n",
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" .output_wrapper, .output {\n",
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" height:auto !important;\n",
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" max-height:10000px; \n",
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" max-height:100000px; \n",
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" }\n",
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" .output_scroll {\n",
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" box-shadow:none !important;\n",
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@@ -77,13 +77,13 @@
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"source": [
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"## Mean, Variance, and Standard Deviations\n",
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"\n",
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"Most of you will have had exposure to at least basic statistics, but allow me to cover this material anyway. I ask that you read the material even if you are sure you know it well. I ask for two reasons. First, I want to be sure that we are using terms in the same way. Second, I strive to form an intuitive understanding of statistics that will serve you well in later chapters. It's easy to go through a stats course and only remember the formulas and calculations, and perhaps be fuzzy on the implications of what you have learned.\n",
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"Most of you will have had exposure to statistics, but allow me to cover this material anyway. I ask that you read the material even if you are sure you know it well. I ask for two reasons. First, I want to be sure that we are using terms in the same way. Second, I strive to form an intuitive understanding of statistics that will serve you well in later chapters. It's easy to go through a stats course and only remember the formulas and calculations, and perhaps be fuzzy on the implications of what you have learned.\n",
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"\n",
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"### Random Variables\n",
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"\n",
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"Each time you roll a die the *outcome* will be between 1 and 6. If we rolled a fair die a million times we'd expect to get a one 1/6 of the time. Thus we say the *probability*, or *odds* of the outcome 1 is 1/6. Likewise, if I asked you the chance of 1 being the result of the next roll you'd reply 1/6. \n",
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"\n",
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"This combination of values and associated probabilities is called a [*random variable*](https://en.wikipedia.org/wiki/Random_variable). Here *random* does not mean the process is nondeterministic, only that we lack information. The result of a die toss is deterministic, but we lack enough information to compute the result. We don't know what will happen, except probabilistically.\n",
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"This combination of values and associated probabilities is called a [*random variable*](https://en.wikipedia.org/wiki/Random_variable). Here *random* does not mean the process is nondeterministic, only that we lack information about the outcome. The result of a die toss is deterministic, but we lack enough information to compute the result. We don't know what will happen, except probabilistically.\n",
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"\n",
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"While we are defining terms, the range of values is called the [*sample space*](https://en.wikipedia.org/wiki/Sample_space). For a die the sample space is {1, 2, 3, 4, 5, 6}. For a coin the sample space is {H, T}. *Space* is a mathematical term which means a set with structure. The sample space for the die is a subset of the natural numbers in the range of 1 to 6.\n",
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"\n",
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@@ -93,7 +93,7 @@
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"\n",
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"Do not confuse the *measurement* of the random variable with the actual value. If we can only measure the height of a person to 0.1 meters we would only record values from 0.1, 0.2, 0.3...2.7, yielding 27 discrete choices. Nonetheless a person's height can vary between any arbitrary real value between those ranges, and so height is a continuous random variable. \n",
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"\n",
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"In statistics capital letters are used for random variables, usually from the latter half of the alphabet. So, we might say that $X$ is the random variable representing the die toss, or $Y$ are the heights of the students in the freshmen poetry class. Later chapters use linear algebra to solve these problems, and so there we will follow the convention of using lower case for vectors, and upper case for matrices. Unfortunately these conventions clash, and you will have to determine which an author is using from context. "
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"In statistics capital letters are used for random variables, usually from the latter half of the alphabet. So, we might say that $X$ is the random variable representing the die toss, or $Y$ are the heights of the students in the freshmen poetry class. Later chapters use linear algebra to solve these problems, and so there we will follow the convention of using lower case for vectors, and upper case for matrices. Unfortunately these conventions clash, and you will have to determine which an author is using from context. I always use bold symbols for vectors and matrices, which helps distinguish between the two."
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]
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},
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{
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@@ -118,11 +118,11 @@
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"\n",
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"$$P(X{=}4) = p(4) = \\frac{1}{6}$$\n",
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"\n",
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"This states that the probability of the die landing on 4 is $\\frac{1}{6}$. $P(X{=}x_k)$ is notation for \"the probability of $X$ being $x_k$\".\n",
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"This states that the probability of the die landing on 4 is $\\frac{1}{6}$. $P(X{=}x_k)$ is notation for \"the probability of $X$ being $x_k$\". Note the subtle notational difference. The capital $P$ denotes the probability of a single event, and the lower case $p$ is the probability distribution function. This can lead you astray if you are not observent. Some texts use $Pr$ instead of $P$ to ameliorate this. \n",
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"\n",
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"Another example is a fair coin. It has the sample space {H, T}. The coin is fair, so the probability for heads (H) is 50%, and the probability for tails (T) is 50%. We write this as\n",
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"\n",
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"$$\\begin{gathered}p(X{=}H) = 0.5\\\\p(X{=}T)=0.5\\end{gathered}$$\n",
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"$$\\begin{gathered}P(X{=}H) = 0.5\\\\P(X{=}T)=0.5\\end{gathered}$$\n",
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"\n",
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"Sample spaces are not unique. One sample space for a die is {1, 2, 3, 4, 5, 6}. Another valid sample space would be {even, odd}. Another might be {dots in all corners, not dots in all corners}. A sample space is valid so long as it covers all possibilities, and any single event is described by only one element. {even, 1, 3, 4, 5} is not a valid sample space for a die since a value of 4 is matched both by 'even' and '4'.\n",
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"\n",
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@@ -146,11 +146,18 @@
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"execution_count": 3,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"sum = 1.0\n"
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]
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},
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{
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"data": {
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truncated
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"image/png": "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 truncated
|
||||
"text/plain": [
|
||||
"<Figure size 800x200 with 1 Axes>"
|
||||
"<matplotlib.figure.Figure at 0x1d9166773c8>"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
@@ -162,8 +169,10 @@
|
||||
"import kf_book.book_plots as book_plots\n",
|
||||
"\n",
|
||||
"belief = np.array([1, 4, 2, 0, 8, 2, 2, 35, 4, 3, 2])\n",
|
||||
"belief = belief / np.sum(belief)\n",
|
||||
"with book_plots.figsize(y=2):\n",
|
||||
" book_plots.bar_plot(belief/sum(belief))"
|
||||
" book_plots.bar_plot(belief)\n",
|
||||
"print('sum = ', np.sum(belief))"
|
||||
]
|
||||
},
|
||||
{
|
||||
@@ -255,7 +264,7 @@
|
||||
"\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",
|
||||
"Numpy provides `numpy.median()` to compute the median. As you can see the median of {1.8, 2.0, 1.7, 1.9, 1.6} is 1.8, because 1.8 is the third element of this set after being sorted."
|
||||
"Numpy provides `numpy.median()` to compute the median. As you can see the median of {1.8, 2.0, 1.7, 1.9, 1.6} is 1.8, because 1.8 is the third element of this set after being sorted. In this case the median equals the mean, but that is not generally true."
|
||||
]
|
||||
},
|
||||
{
|
||||
@@ -304,7 +313,7 @@
|
||||
"\n",
|
||||
"If $x$ is continuous we substitute the sum for an integral, like so\n",
|
||||
"\n",
|
||||
"$$\\mathbb E[X] = \\int_{-\\infty}^\\infty x\\, f(x) \\,dx$$\n",
|
||||
"$$\\mathbb E[X] = \\int_{a}^b\\, f(x) \\,dx$$\n",
|
||||
"\n",
|
||||
"where $f(x)$ is the probability distribution function of $x$. We won't be using this equation yet, but we will be using it in the next chapter.\n",
|
||||
"\n",
|
||||
@@ -319,7 +328,7 @@
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"1.500732"
|
||||
"1.500406"
|
||||
]
|
||||
},
|
||||
"execution_count": 7,
|
||||
@@ -345,6 +354,38 @@
|
||||
"You can see that the computed value is close to the analytically derived value. It is not exact because getting an exact values requires an infinite sample size."
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"### Exercise\n",
|
||||
"\n",
|
||||
"What is the expected value of a die role?\n",
|
||||
"\n",
|
||||
"### Solution\n",
|
||||
"\n",
|
||||
"Each side is equally likely, so each has a probability of 1/6. Hence\n",
|
||||
"$$\\begin{aligned}\n",
|
||||
"\\mathbb E[X] &= 1/6\\times1 + 1/6\\times 2 + 1/6\\times 3 + 1/6\\times 4 + 1/6\\times 5 + 1/6\\times6 \\\\\n",
|
||||
"&= 1/6(1+2+3+4+5+6)\\\\&= 3\\end{aligned}$$\n",
|
||||
"\n",
|
||||
"### Exercise\n",
|
||||
"\n",
|
||||
"Given the uniform continuous distribution\n",
|
||||
"\n",
|
||||
"$$f(x) = \\frac{1}{b - a}$$\n",
|
||||
"\n",
|
||||
"compute the expected value for $a=0$ and $B=20$.\n",
|
||||
"\n",
|
||||
"### Solution\n",
|
||||
"$$\\begin{aligned}\n",
|
||||
"\\mathbb E[X] &= \\int_0^{20}\\, x\\frac{1}{20} \\,dx \\\\\n",
|
||||
"&= \\bigg[\\frac{x^2}{40}\\bigg]_0^{20} \\\\\n",
|
||||
"&= 10 - 0 \\\\\n",
|
||||
"&= 10\n",
|
||||
"\\end{aligned}$$"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
@@ -499,9 +540,9 @@
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"image/png": 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truncated
|
||||
"image/png": 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truncated
|
||||
"text/plain": [
|
||||
"<Figure size 900x400 with 1 Axes>"
|
||||
"<matplotlib.figure.Figure at 0x1d9169a12b0>"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
@@ -531,9 +572,9 @@
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"image/png": 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truncated
|
||||
"image/png": "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 truncated
|
||||
"text/plain": [
|
||||
"<Figure size 900x400 with 1 Axes>"
|
||||
"<matplotlib.figure.Figure at 0x1d9173e5f28>"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
@@ -543,8 +584,8 @@
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"mean = 1.804\n",
|
||||
"std = 0.156\n"
|
||||
"mean = 1.789\n",
|
||||
"std = 0.137\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
@@ -573,7 +614,7 @@
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"67.0"
|
||||
"71.0"
|
||||
]
|
||||
},
|
||||
"execution_count": 14,
|
||||
@@ -681,9 +722,9 @@
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"image/png": 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truncated
|
||||
"image/png": 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truncated
|
||||
"text/plain": [
|
||||
"<Figure size 900x400 with 1 Axes>"
|
||||
"<matplotlib.figure.Figure at 0x1d91761b4a8>"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
@@ -766,9 +807,9 @@
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"image/png": 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truncated
|
||||
"image/png": 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truncated
|
||||
"text/plain": [
|
||||
"<Figure size 900x400 with 1 Axes>"
|
||||
"<matplotlib.figure.Figure at 0x1d917603f98>"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
@@ -804,9 +845,9 @@
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"image/png": 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truncated
|
||||
"image/png": 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truncated
|
||||
"text/plain": [
|
||||
"<Figure size 900x400 with 1 Axes>"
|
||||
"<matplotlib.figure.Figure at 0x1d91745b160>"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
@@ -842,9 +883,9 @@
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"image/png": 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truncated
|
||||
"image/png": "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 truncated
|
||||
"text/plain": [
|
||||
"<Figure size 900x400 with 1 Axes>"
|
||||
"<matplotlib.figure.Figure at 0x1d917486630>"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
@@ -880,17 +921,50 @@
|
||||
"\n",
|
||||
"$\\exp[x]$ is notation for $e^x$.\n",
|
||||
"\n",
|
||||
"<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, normed=True)`.\n",
|
||||
"<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, normed=True)`. \n",
|
||||
" \n",
|
||||
"Shorn of the constants, you can see it is a simple exponential:\n",
|
||||
" \n",
|
||||
"$$f(x)\\propto e^{-x^2}$$\n",
|
||||
"\n",
|
||||
"Let's remind ourselves how to look at the code for a function. In a cell, type the function name followed by two question marks and press return. This will open a popup window displaying the source. Uncomment the next cell and try it now."
|
||||
"which has the familiar bell curve shape"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 22,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"image/png": "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 truncated
|
||||
"text/plain": [
|
||||
"<matplotlib.figure.Figure at 0x1d917414908>"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
"output_type": "display_data"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"x = np.arange(-3, 3, .01)\n",
|
||||
"plt.plot(x, np.exp(-x**2));"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"Let's remind ourselves how to look at the code for a function. In a cell, type the function name followed by two question marks and press CTRL+ENTER. This will open a popup window displaying the source. Uncomment the next cell and try it now."
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 23,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"from filterpy.stats import gaussian\n",
|
||||
"#gaussian??"
|
||||
]
|
||||
},
|
||||
@@ -898,21 +972,21 @@
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"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. "
|
||||
"Let's plot a Gaussian with a mean of 22 $(\\mu=22)$, with a variance of 4 $(\\sigma^2=4)$. "
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 23,
|
||||
"execution_count": 24,
|
||||
"metadata": {
|
||||
"scrolled": true
|
||||
},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"image/png": 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truncated
|
||||
"image/png": 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truncated
|
||||
"text/plain": [
|
||||
"<Figure size 900x400 with 1 Axes>"
|
||||
"<matplotlib.figure.Figure at 0x1d91756c5f8>"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
@@ -927,7 +1001,7 @@
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"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*](https://en.wikipedia.org/wiki/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",
|
||||
"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*](https://en.wikipedia.org/wiki/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 see it is proportional to 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",
|
||||
@@ -939,7 +1013,9 @@
|
||||
"\n",
|
||||
"We do the same with *probability density*. If you want to know the temperature being between 20°C and 21°C kph you would integrate the curve above from 20 to 21. As you know the integral of a curve gives you the area under the curve. Since this is a curve of the probability density, the integral of the density is the probability. \n",
|
||||
"\n",
|
||||
"What is the probability of a the temperature being exactly 22°C? Intuitively, 0. These are real numbers, and the odds of 22°C vs, say, 22.00000000000017°C is infitesimal. Mathematically, what would we get if we integrate from 22 to 22? Zero. \n",
|
||||
"What is the probability of a the temperature being exactly 22°C? Intuitively, 0. These are real numbers, and the odds of 22°C vs, say, 22.00000000000017°C is infinitesimal. Mathematically, what would we get if we integrate from 22 to 22? Zero. \n",
|
||||
"\n",
|
||||
"Thinking back to the rock, what is the weight of an single point on the rock? An infinitesimal point must have no weight. It makes no sense to ask the weight of a single point, and it makes no sense to ask about the probability of a continuous distribution having a single value. The answer for both is obviously zero.\n",
|
||||
"\n",
|
||||
"In practice our sensors do not have infinite precision, so a reading of 22°C implies a range, such as 22 $\\pm$ 0.1°C, and we can compute the probability of that range by integrating from 21.9 to 22.1.\n",
|
||||
"\n",
|
||||
@@ -956,7 +1032,7 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 24,
|
||||
"execution_count": 25,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
@@ -1002,7 +1078,7 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 25,
|
||||
"execution_count": 26,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
@@ -1028,7 +1104,7 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 26,
|
||||
"execution_count": 27,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
@@ -1056,7 +1132,7 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 27,
|
||||
"execution_count": 28,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
@@ -1080,16 +1156,16 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 28,
|
||||
"execution_count": 29,
|
||||
"metadata": {
|
||||
"scrolled": true
|
||||
},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"image/png": 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truncated
|
||||
"image/png": "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 truncated
|
||||
"text/plain": [
|
||||
"<Figure size 900x400 with 1 Axes>"
|
||||
"<matplotlib.figure.Figure at 0x1d917a45160>"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
@@ -1132,14 +1208,14 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 29,
|
||||
"execution_count": 30,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"image/png": 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truncated
|
||||
"text/plain": [
|
||||
"<Figure size 900x400 with 1 Axes>"
|
||||
"<matplotlib.figure.Figure at 0x1d9179be128>"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
@@ -1162,18 +1238,33 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 30,
|
||||
"execution_count": 31,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"application/vnd.jupyter.widget-view+json": {
|
||||
"model_id": "a17934eb0c544f588d48c5118ebf748e",
|
||||
"model_id": "592797026a1346119330de5fe1ef9016",
|
||||
"version_major": 2,
|
||||
"version_minor": 0
|
||||
},
|
||||
"text/html": [
|
||||
"<p>Failed to display Jupyter Widget of type <code>interactive</code>.</p>\n",
|
||||
"<p>\n",
|
||||
" If you're reading this message in the Jupyter Notebook or JupyterLab Notebook, it may mean\n",
|
||||
" that the widgets JavaScript is still loading. If this message persists, it\n",
|
||||
" likely means that the widgets JavaScript library is either not installed or\n",
|
||||
" not enabled. See the <a href=\"https://ipywidgets.readthedocs.io/en/stable/user_install.html\">Jupyter\n",
|
||||
" Widgets Documentation</a> for setup instructions.\n",
|
||||
"</p>\n",
|
||||
"<p>\n",
|
||||
" If you're reading this message in another frontend (for example, a static\n",
|
||||
" rendering on GitHub or <a href=\"https://nbviewer.jupyter.org/\">NBViewer</a>),\n",
|
||||
" it may mean that your frontend doesn't currently support widgets.\n",
|
||||
"</p>\n"
|
||||
],
|
||||
"text/plain": [
|
||||
"interactive(children=(FloatSlider(value=5.0, description='mu', max=7.0, min=3.0), FloatSlider(value=0.03, desc…"
|
||||
"interactive(children=(FloatSlider(value=5.0, description='mu', max=7.0, min=3.0), FloatSlider(value=0.03, description='variance', max=1.0, min=0.01), Output()), _dom_classes=('widget-interact',))"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
@@ -1219,14 +1310,14 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 31,
|
||||
"execution_count": 32,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"image/png": "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 truncated
|
||||
"image/png": "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 truncated
|
||||
"text/plain": [
|
||||
"<Figure size 900x400 with 1 Axes>"
|
||||
"<matplotlib.figure.Figure at 0x1d91792c080>"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
@@ -1255,14 +1346,14 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 32,
|
||||
"execution_count": 33,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"image/png": 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truncated
|
||||
"image/png": "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 truncated
|
||||
"text/plain": [
|
||||
"<Figure size 900x400 with 1 Axes>"
|
||||
"<matplotlib.figure.Figure at 0x1d9175e2eb8>"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
@@ -1309,14 +1400,14 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 33,
|
||||
"execution_count": 34,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"image/png": 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truncated
|
||||
"image/png": "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 truncated
|
||||
"text/plain": [
|
||||
"<Figure size 900x400 with 1 Axes>"
|
||||
"<matplotlib.figure.Figure at 0x1d9166a3da0>"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
@@ -1347,7 +1438,7 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 34,
|
||||
"execution_count": 35,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
@@ -1359,9 +1450,9 @@
|
||||
},
|
||||
{
|
||||
"data": {
|
||||
"image/png": 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truncated
|
||||
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truncated
|
||||
"text/plain": [
|
||||
"<Figure size 900x400 with 1 Axes>"
|
||||
"<matplotlib.figure.Figure at 0x1d9166a3e10>"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
@@ -1410,7 +1501,7 @@
|
||||
"source": [
|
||||
"### Bayes Theorem\n",
|
||||
"\n",
|
||||
"We developed the math in this chapter merely by reasoning about the information we have at each moment. In the process we discovered [*Bayes' Theorem*](https://en.wikipedia.org/wiki/Bayes%27_theorem). Bayes theorem tells us how to compute the probability of an event given previous information. \n",
|
||||
"In the last chapter we developed an algorithm by reasoning about the information we have at each moment, which we expressed as discrete probability distributions. In the process we discovered [*Bayes' Theorem*](https://en.wikipedia.org/wiki/Bayes%27_theorem). Bayes theorem tells us how to compute the probability of an event given prior information. \n",
|
||||
"\n",
|
||||
"We implemented the `update()` function with this probability calculation:\n",
|
||||
"\n",
|
||||
@@ -1431,8 +1522,6 @@
|
||||
"\n",
|
||||
"$$P(A \\mid B) = \\frac{P(B \\mid A)\\, P(A)}{P(B)}$$\n",
|
||||
"\n",
|
||||
"If you are not familiar with this notation, let's review. $P(A)$ means the probability of event $A$. If $A$ is the event of a fair coin landing heads, then $P(A) = 0.5$.\n",
|
||||
"\n",
|
||||
"$P(A \\mid B)$ is called a [*conditional probability*](https://en.wikipedia.org/wiki/Conditional_probability). That is, it represents the probability of $A$ happening *if* $B$ happened. For example, it is more likely to rain today compared to a typical day if it also rained yesterday because rain systems usually last more than one day. We'd write the probability of it raining today given that it rained yesterday as $P$(rain today $\\mid$ rain yesterday).\n",
|
||||
"\n",
|
||||
"\n",
|
||||
@@ -1440,21 +1529,21 @@
|
||||
"\n",
|
||||
"$$p(A \\mid B) = \\frac{p(B \\mid A)\\, p(A)}{p(B)}$$\n",
|
||||
"\n",
|
||||
"In the equation above $B$ is the *evidence*, $p(A)$ is the *prior*, $p(B \\mid A)$ is the *likelihood*, and $p(A \\mid B)$ is the *posterior*. By substituting the mathematical terms with the corresponding words you can see that Bayes theorem matches out update equation. Let's rewrite the equation in terms of our problem. We will use $x_i$ for the position at *i*, and $Z$ for the measurement. Hence, we want to know $P(x_i \\mid Z)$, that is, the probability of the dog being at $x_i$ given the measurement $Z$. \n",
|
||||
"In the equation above $B$ is the *evidence*, $p(A)$ is the *prior*, $p(B \\mid A)$ is the *likelihood*, and $p(A \\mid B)$ is the *posterior*. By substituting the mathematical terms with the corresponding words you can see that Bayes theorem matches out update equation. Let's rewrite the equation in terms of our problem. We will use $x_i$ for the position at *i*, and $z$ for the measurement. Hence, we want to know $P(x_i \\mid z)$, that is, the probability of the dog being at $x_i$ given the measurement $z$. \n",
|
||||
"\n",
|
||||
"So, let's plug that into the equation and solve it.\n",
|
||||
"\n",
|
||||
"$$p(x_i \\mid Z) = \\frac{p(Z \\mid x_i) p(x_i)}{p(Z)}$$\n",
|
||||
"$$p(x_i \\mid z) = \\frac{p(z \\mid x_i) p(x_i)}{p(z)}$$\n",
|
||||
"\n",
|
||||
"That looks ugly, but it is actually quite simple. Let's figure out what each term on the right means. First is $p(Z \\mid x_i)$. This is the the likelihood, or the probability for the measurement at every cell $x_i$. $p(x_i)$ is the *prior* - our belief before incorporating the measurements. We multiply those together. This is just the unnormalized multiplication in the `update()` function:\n",
|
||||
"That looks ugly, but it is actually quite simple. Let's figure out what each term on the right means. First is $p(z \\mid x_i)$. This is the the likelihood, or the probability for the measurement at every cell $x_i$. $p(x_i)$ is the *prior* - our belief before incorporating the measurements. We multiply those together. This is just the unnormalized multiplication in the `update()` function:\n",
|
||||
"\n",
|
||||
"```python\n",
|
||||
"def update(likelihood, prior):\n",
|
||||
" posterior = prior * likelihood # p(Z|x) * p(x)\n",
|
||||
" posterior = prior * likelihood # p(z|x) * p(x)\n",
|
||||
" return normalize(posterior)\n",
|
||||
"```\n",
|
||||
"\n",
|
||||
"The last term to consider is the denominator $p(Z)$. This is the probability of getting the measurement $Z$ without taking the location into account. It is often called the *evidence*. We compute that by taking the sum of $x$, or `sum(belief)` in the code. That is how we compute the normalization! So, the `update()` function is doing nothing more than computing Bayes theorem.\n",
|
||||
"The last term to consider is the denominator $p(z)$. This is the probability of getting the measurement $z$ without taking the location into account. It is often called the *evidence*. We compute that by taking the sum of $x$, or `sum(belief)` in the code. That is how we compute the normalization! So, the `update()` function is doing nothing more than computing Bayes' theorem.\n",
|
||||
"\n",
|
||||
"The literature often gives you these equations in the form of integrals. After all, an integral is just a sum over a continuous function. So, you might see Bayes' theorem written as\n",
|
||||
"\n",
|
||||
@@ -1464,9 +1553,9 @@
|
||||
"\n",
|
||||
"It's probable that the strength of Bayes' theorem is not yet fully apparent to you. We want to compute $p(x_i \\mid Z)$. That is, at step i, what is our probable state given a measurement. That's an extraordinarily difficult problem in general. Bayes' Theorem is general. We may want to know the probability that we have cancer given the results of a cancer test, or the probability of rain given various sensor readings. Stated like that the problems seem unsolvable.\n",
|
||||
"\n",
|
||||
"But Bayes' Theorem lets us compute this by using the inverse. \n",
|
||||
"But Bayes' Theorem lets us compute this by using the inverse $p(Z\\mid x_i)$, which is often straightforward to compute\n",
|
||||
"\n",
|
||||
"$$p(A \\mid B) \\propto p(B \\mid A)\\, p(A)$$\n",
|
||||
"$$p(x_i \\mid Z) \\propto p(Z\\mid x_i)\\, p(x_i)$$\n",
|
||||
"\n",
|
||||
"That is, to compute how likely it is to rain given specific sensor readings we only have to compute the likelihood of the sensor readings given that it is raining! That's a ***much*** easier problem! Well, weather prediction is still a difficult problem, but Bayes makes it tractable. \n",
|
||||
"\n",
|
||||
@@ -1506,9 +1595,9 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 35,
|
||||
"execution_count": 36,
|
||||
"metadata": {
|
||||
"scrolled": true
|
||||
"scrolled": false
|
||||
},
|
||||
"outputs": [
|
||||
{
|
||||
@@ -1536,7 +1625,7 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 36,
|
||||
"execution_count": 37,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
@@ -1565,16 +1654,16 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 37,
|
||||
"execution_count": 38,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"[ 6.306 -1.309 -0.207 5.673 1.932 0.207 1.143\n",
|
||||
" -1.608 -0.85 -1.997 4.806 4.715 5.264 3.575\n",
|
||||
" 2.208]\n"
|
||||
"[ 5.912 -2.009 -2.718 1.266 -1.085 3.941 3.499\n",
|
||||
" 5.626 -0.137 1.396 4.562 2.127 8.176 1.794\n",
|
||||
" 1.829]\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
@@ -1592,7 +1681,7 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 38,
|
||||
"execution_count": 39,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
@@ -1617,7 +1706,7 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 39,
|
||||
"execution_count": 40,
|
||||
"metadata": {
|
||||
"scrolled": true
|
||||
},
|
||||
@@ -1657,14 +1746,14 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 40,
|
||||
"execution_count": 41,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"image/png": 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truncated
|
||||
"image/png": "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 truncated
|
||||
"text/plain": [
|
||||
"<Figure size 900x400 with 1 Axes>"
|
||||
"<matplotlib.figure.Figure at 0x1d91793a518>"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
@@ -1692,7 +1781,7 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 41,
|
||||
"execution_count": 42,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
@@ -1710,14 +1799,14 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 42,
|
||||
"execution_count": 43,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"image/png": "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 truncated
|
||||
"image/png": "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 truncated
|
||||
"text/plain": [
|
||||
"<Figure size 900x400 with 1 Axes>"
|
||||
"<matplotlib.figure.Figure at 0x1d91740e320>"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
@@ -1740,7 +1829,7 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 43,
|
||||
"execution_count": 44,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
@@ -1759,14 +1848,14 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 44,
|
||||
"execution_count": 45,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"image/png": 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truncated
|
||||
"image/png": "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 truncated
|
||||
"text/plain": [
|
||||
"<Figure size 900x400 with 1 Axes>"
|
||||
"<matplotlib.figure.Figure at 0x1d9173e6c88>"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
@@ -1802,16 +1891,16 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 45,
|
||||
"execution_count": 46,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"DescribeResult(nobs=5000, minmax=(0.7521655375313596, 20.12956908425545), mean=10.02056777098, variance=2.715020215603436, skewness=0.08832633839087363, kurtosis=1.5874986019432313)"
|
||||
"DescribeResult(nobs=5000, minmax=(1.888855071015895, 19.03723274712268), mean=10.01034378048552, variance=2.7776404133106123, skewness=0.009548424333982227, kurtosis=1.4807836826747778)"
|
||||
]
|
||||
},
|
||||
"execution_count": 45,
|
||||
"execution_count": 46,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
@@ -1830,16 +1919,18 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 46,
|
||||
"metadata": {},
|
||||
"execution_count": 47,
|
||||
"metadata": {
|
||||
"scrolled": true
|
||||
},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"DescribeResult(nobs=10, minmax=(-0.9998998256891874, 0.9895966170353847), mean=-0.20889859670553768, variance=0.415215914064243, skewness=0.6414173152025241, kurtosis=-0.8094358398006518)\n",
|
||||
"DescribeResult(nobs=10, minmax=(-1.8942931152842175, 0.49750728125905835), mean=-0.10563915941786776, variance=0.4841165908890319, skewness=-1.8464582995970673, kurtosis=2.5452896197893757)\n",
|
||||
"\n",
|
||||
"DescribeResult(nobs=300000, minmax=(-4.441381784212609, 5.266318154694646), mean=-0.0007561587947956754, variance=0.9993482527217467, skewness=0.0012861120678718861, kurtosis=-0.013345063233251686)\n"
|
||||
"DescribeResult(nobs=300000, minmax=(-4.772620736872989, 4.446895068081072), mean=-0.0006837046884366415, variance=0.9995353806594786, skewness=0.002331471754136653, kurtosis=0.007185223820032061)\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
@@ -2072,7 +2163,7 @@
|
||||
"name": "python",
|
||||
"nbconvert_exporter": "python",
|
||||
"pygments_lexer": "ipython3",
|
||||
"version": "3.6.5"
|
||||
"version": "3.6.4"
|
||||
},
|
||||
"widgets": {
|
||||
"application/vnd.jupyter.widget-state+json": {
|
||||
|
||||
@@ -24,7 +24,7 @@
|
||||
"\n",
|
||||
"Introduces the discrete Bayes filter. From this you will learn the probabilistic (Bayesian) reasoning that underpins the Kalman filter in an easy to digest form.\n",
|
||||
"\n",
|
||||
"[**Chapter 3: Gaussian Probabilities**](http://nbviewer.ipython.org/urls/raw.github.com/rlabbe/Kalman-and-Bayesian-Filters-in-Python/master/03-Gaussians.ipynb)\n",
|
||||
"[**Chapter 3: Probabilities, Gaussians, and Bayes' Theorem**](http://nbviewer.ipython.org/urls/raw.github.com/rlabbe/Kalman-and-Bayesian-Filters-in-Python/master/03-Gaussians.ipynb)\n",
|
||||
"\n",
|
||||
"Introduces using Gaussians to represent beliefs in the Bayesian sense. Gaussians allow us to implement the algorithms used in the discrete Bayes filter to work in continuous domains.\n",
|
||||
"\n",
|
||||
@@ -149,9 +149,7 @@
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 1,
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
},
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
@@ -417,9 +415,9 @@
|
||||
"name": "python",
|
||||
"nbconvert_exporter": "python",
|
||||
"pygments_lexer": "ipython3",
|
||||
"version": "3.5.1"
|
||||
"version": "3.6.5"
|
||||
}
|
||||
},
|
||||
"nbformat": 4,
|
||||
"nbformat_minor": 0
|
||||
"nbformat_minor": 1
|
||||
}
|
||||
Reference in new issue
Block a user