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{
"metadata": {
"name": "LawOfLargeNumbers"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#Chapter 4\n",
"______\n",
"\n",
"##The greatest theorem never told\n",
"\n",
"\n",
"This chapter focuses on an idea that is always bouncing around our minds, but is rarely made explicit outside books devoted to statistics. In fact, we've been used this simple idea in every example thus far. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"###The Law of Large Numbers\n",
"\n",
"Let $Z_i$ be $N$ independent samples from some probability distribution. According to *the Law of Large numbers*, so long as the expected value $E[Z]$ is finite, the following holds,\n",
"\n",
"$$\\frac{1}{N} \\sum_{i=1}^N Z_i \\rightarrow E[ Z ], \\;\\;\\; N \\rightarrow \\infty.$$\n",
"\n",
"In words:\n",
"\n",
"> The average of a sequence of random variables from the same distribution converges to the expected value of that distribution.\n",
"\n",
"This may seem like a boring result, but it will be the most useful tool you use."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Intuition \n",
"\n",
"If the above Law is somewhat surprising, it can be made more clear be examining a simple example. \n",
"\n",
"Consider a random variable $Z$ that can take only two values, $c_1$ and $c_2$. Suppose we have a large number of samples of $Z$, denoting a specific sample $Z_i$. The Law says that we can approximate the expected value of $Z$ by averaging over all samples. Consider the average:\n",
"\n",
"\n",
"$$ \\frac{1}{N} \\sum_{i=1}^N \\;Z_i $$\n",
"\n",
"\n",
"By construction, $Z_i$ can only take on $c_1$ or $c_2$, hence we can partition the sum over these two values:\n",
"\n",
"\\begin{align}\n",
"\\frac{1}{N} \\sum_{i=1}^N \\;Z_i\n",
"& =\\frac{1}{N} \\big( \\sum_{ Z_i = c_1}c_1 + \\sum_{Z_i=c_2}c_2 \\big) \\\\\\\\[5pt]\n",
"& = c_1 \\sum_{ Z_i = c_1}\\frac{1}{N} + c_2 \\sum_{ Z_i = c_2}\\frac{1}{N} \\\\\\\\[5pt]\n",
"& = c_1 \\times \\text{ (approximate frequency of $c_1$) } \\\\\\\\ \n",
"& \\;\\;\\;\\;\\;\\;\\;\\;\\; + c_2 \\times \\text{ (approximate frequency of $c_2$) } \\\\\\\\[5pt]\n",
"& \\approx c_1 \\times P(Z = c_1) + c_2 \\times P(Z = c_2 ) \\\\\\\\[5pt]\n",
"& = E[Z]\n",
"\\end{align}\n",
"\n",
"\n",
"Equality holds in the limit, but we can get closer and closer by using more and more samples in the average. This Law holds for *any distribution*, minus some pathological examples that only mathematicians have fun with. \n",
"\n",
"##### Example\n",
"____\n",
"\n",
"\n",
"Below is a diagram of the Law of Large numbers in action for three different sequences of Poisson random variables. \n",
"\n",
" We sample `sample_size= 100000` Poisson random variables with parameter $\\lambda = 4.5$. (Recall the expected value of a Poisson random variable is equal to it's parameter.) We calculate the average for the first $n$ samples, for $n=1$ to `sample_size`. "
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"%pylab inline\n",
"\n",
"figsize( 12.5, 5 )\n",
"import pymc as mc\n",
"\n",
"sample_size = 100000\n",
"expected_value = lambda_ = 4.5\n",
"poi = mc.rpoisson\n",
"N_samples = range(1,sample_size,100)\n",
"\n",
"for k in range(3):\n",
"\n",
" samples = poi( lambda_, size = sample_size ) \n",
" \n",
" partial_average = [ samples[:i].mean() for i in N_samples ]\n",
" \n",
" plt.plot( N_samples, partial_average, lw=1.5,label=\"average \\\n",
" of $n$ samples; seq. %d\"%k)\n",
" \n",
"\n",
"plt.plot( N_samples, expected_value*np.ones_like( partial_average), \\\n",
" ls = \"--\", label = \"true expected value\", c = \"k\" )\n",
"\n",
"plt.ylim( 4.35, 4.65) \n",
"plt.title( \"Convergence of the average of \\n random variables to its \\\n",
"expected value\" )\n",
"plt.ylabel( \"average of $n$ samples\" )\n",
"plt.xlabel( \"# of samples, $n$\")\n",
"plt.legend()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "pyout",
"prompt_number": 3,
"text": [
"<matplotlib.legend.Legend at 0x615b6f0>"
]
},
{
"output_type": "display_data",
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}
],
"prompt_number": 3
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Looking at the above plot, it is clear that when the sample size is small, there is greater variation in the average (compare how *jagged and jumpy* the average is initially, then *smooths* out). All three paths *approach* the value 4.5, but just flirt with it as $N$ gets large. Mathematicians and statistician have another name for *flirting*: convergence. \n",
"\n",
"Another very relevant question we can ask is *how quickly am I converging to the expected value?* Let's plot something new. For a specific $N$, let's do the above trials thousands of times and compute how far away we are from the true expected value, on average. But wait &mdash; *compute on average*? This simply the law of large numbers again! For example, we are interested in, for a specific $N$, the quantity:\n",
"\n",
"$$D(N) = \\sqrt{ \\;E\\left[\\;\\; \\left( \\frac{1}{N}\\sum_{i=1}^NZ_i - 4.5 \\;\\right)^2 \\;\\;\\right] \\;\\;}$$\n",
"\n",
"(We take the square root so the dimensions of the above quantity and our random variables are the same). As the above is an expected value, it can be approximated using the law of large numbers: instead of averaging $Z_i$, we calculate the following multiple times and average them:\n",
"\n",
"$$ Y_k = \\left( \\;\\frac{1}{N}\\sum_{i=1}^NZ_i - 4.5 \\; \\right)^2 $$\n",
"\n",
"i.e., we consider the average\n",
"\n",
"$$ \\frac{1}{N_Y} \\sum_{k=1}^{N_Y} Y_k \\approx D(N) $$ where $N_Y$ is some suitably large number."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"figsize( 12.5, 4)\n",
"N_Y = 250\n",
"D_N_results = [] \n",
"N_array = np.arange( 0, 50000, 2500 )\n",
"lambda_ = 4.5\n",
"expected_value = 4.5\n",
"\n",
"def D_N( n ):\n",
" Z = poi( lambda_, size = (n, N_Y) )\n",
" average_Z = Z.mean(axis=0)\n",
" return np.sqrt( ( (average_Z - expected_value)**2 ).mean() )\n",
" \n",
" \n",
"for n in N_array:\n",
" D_N_results.append( D_N(n) )\n",
"\n",
"\n",
"plt.xlabel( \"$N$\" )\n",
"plt.ylabel( \"expected squared-distance from true value\" )\n",
"plt.plot(N_array, D_N_results, lw = 1, \n",
" label=\"expected distance between\\n\\\n",
"expected value and \\naverage of $N$ random variables.\")\n",
"plt.plot( N_array, np.sqrt(expected_value)/np.sqrt(N_array), lw = 3, ls = \"--\", \n",
" label = r\"$\\frac{\\sqrt{\\lambda}}{\\sqrt{N}}$\" )\n",
"plt.legend()\n",
"plt.title( \"How 'fast' is the sample average converging? \" )"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "pyout",
"prompt_number": 4,
"text": [
"<matplotlib.text.Text at 0x12098e10>"
]
},
{
"output_type": "display_data",
"png": 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6OtKvXz+ddA4fPkyTJk2wt7dn6tSpCCHyfXh//Pgx48ePx9HRkWbNmnH27Fmd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6s+n3zyCZ599lkAQHx8PK5fv47Gxsa7nitjESYiWaqrq+1dAo0jzAvJxayQLZgXGgtk3UF45pln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\nAABJRU5ErkJggg==\n"
}
],
"prompt_number": 4
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"As expected, the expected distance between our sample average and the actual expected value shrinks as $N$ grows large. But also notice that the *rate* of convergence decreases, that is, we need only 10 000 additional samples to move from 0.020 to 0.015, a difference of 0.005, but *20 000* more samples to again decrease from 0.015 to 0.010, again only a 0.005 decrease.\n",
"\n",
"\n",
"It turns out we can measure this rate of convergence. Above I have plotted a second line, the function $\\sqrt{\\lambda}/\\sqrt{N}$. This was not chosen arbitrarily. In most cases, given a sequence of random variable distributed like $Z$, the rate of converge to $E[Z]$ of the Law of Large Numbers is \n",
"\n",
"$$ \\frac{ \\sqrt{ \\; Var(Z) \\; } }{\\sqrt{N} }$$\n",
"\n",
"This is useful to know: for a given large $N$, we know (on average) how far away we are from the estimate. On the other hand, in a Bayesian setting, this can seem like a useless result: Bayesian analysis is OK with uncertainty so what's the *statistical* point of adding extra precise digits? Though drawing samples can be so computationally cheap that having a *larger* $N$ is fine too. \n",
"\n",
"### How do we compute $Var(Z)$ though?\n",
"\n",
"The variance is simply another expected value that can be approximated! Consider the following, once we have the expected value (by using the Law of Large Numbers to estimate it, denote it $\\mu$), we can estimate the variance:\n",
"\n",
"$$ \\frac{1}{N}\\sum_{i=1}^N \\;(Z_i - \\mu)^2 \\rightarrow E[ \\;( Z - \\mu)^2 \\;] = Var( Z )$$\n",
"\n",
"### Expected values and probabilities \n",
"There is an even less explicit relationship between expected value and estimating probabilities. Define the *indicator function*\n",
"\n",
"$$\\mathbb{1}_A(x) = \n",
"\\begin{cases} 1 & x \\in A \\\\\\\\\n",
" 0 & else\n",
"\\end{cases}\n",
"$$\n",
"Then, by the law of large numbers, if we have many samples $X_i$, we can estimate the probability of an event $A$, denoted $P(A)$, by:\n",
"\n",
"$$ \\frac{1}{N} \\sum_{i=1}^N \\mathbb{1}_A(X_i) \\rightarrow E[\\mathbb{1}_A(X)] = P(A) $$\n",
"\n",
"Again, this is fairly obvious after a moments thought: the indicator function is only 1 if the event occurs, so we are summing only the times the event occurs and dividing by the total number of trials (consider how we usually approximate probabilities using frequencies). For example, suppose we wish to estimate the probability that a $Z \\sim Exp(.5)$ is greater than 10, and we have many samples from a $Exp(.5)$ distribution. \n",
"\n",
"\n",
"$$ P( Z > 10 ) = \\sum_{i=1}^N \\mathbb{1}_{z > 10 }(Z_i) $$\n"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import pymc as mc\n",
"\n",
"N = 10000\n",
"print np.mean( [ mc.rexponential( 0.5 )>10 for i in range(N) ] )"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"0.0058\n"
]
}
],
"prompt_number": 4
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### What does this all have to do with Bayesian statistics? \n",
"\n",
"\n",
"*Point estimates*, to be introduced in the next chapter, in Bayesian inference are computed using expected values. In more analytical Bayesian inference, we would have been required to evaluate complicated expected values represented as multi-dimensional integrals. No longer. If we can sample from the posterior distribution directly, we simply need to evaluate averages. Much easier. If accuracy is a priority, plots like the ones above show how fast you are converging. And if further accuracy is desired, just take more samples from the posterior. \n",
"\n",
"When is enough enough? When can you stop drawing samples from the posterior? That is the practitioners decision, and also dependent on the variance of the samples (recall from above a high variance means the average will converge slower). \n",
"\n",
"We also should understand when the Law of Large Numbers fails. As the name implies, and comparing the graphs above for small $N$, the Law is only true for large sample sizes. Without this, the asymptotic result is not reliable. Knowing in what situations the Law fails can give use *confidence in how unconfident we should be*. The next section deals with this issue."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## The Disorder of Small Numbers\n",
"\n",
"The Law of Large Numbers is only valid as $N$ gets *infinitely* large: never truly attainable. While the law is a powerful tool, it is foolhardy to apply it liberally. Our next example illustrates this.\n",
"\n",
"\n",
"##### Example: Aggregated geographic data\n",
"\n",
"\n",
"Often data comes in aggregated form. For instance, data may be grouped by state, county, or city level. Of course, the population numbers vary per geographic area. If the data is an average of some characteristic of each the geographic areas, we must be conscious of the Law of Large Numbers and how it can *fail* for areas with small populations.\n",
"\n",
"We will observe this on a toy dataset. Suppose there are five thousand counties in our dataset. Furthermore, population number in each state are uniformly distributed between 100 and 1500. The way the population numbers are generated is irrelevant to the discussion, so we do not justify this. We are interested in measuring the average height of individuals per county. Unbeknownst to the us, height does **not** vary across county, and each individual, regardless of the county he or she is currently living in, has the same distribution of what their height may be:\n",
"\n",
"$$ \\text{height} \\sim \\text{Normal}(150, 15 ) $$\n",
"\n",
"We aggregate the individuals at the county level, so we only have data for the *average in the county*. What might our dataset look like?"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"figsize( 12.5, 4) \n",
"std_height = 15\n",
"mean_height = 150\n",
"\n",
"n_counties = 5000\n",
"pop_generator = mc.rdiscrete_uniform\n",
"norm = mc.rnormal\n",
"\n",
"#generate some artificial population numbers\n",
"population = pop_generator(100, 1500, size = n_counties )\n",
"\n",
"average_across_county = np.zeros( n_counties )\n",
"for i in range( n_counties ):\n",
" #generate some individuals and take the mean\n",
" average_across_county[i] = norm(mean_height, 1./std_height**2,\n",
" size=population[i] ).mean()\n",
" \n",
"\n",
"#where are the extreme populations?\n",
"i_min = np.argmin( average_across_county )\n",
"i_max = np.argmax( average_across_county )\n",
"\n",
"#plot population vs. average\n",
"plt.scatter( population, average_across_county, alpha = 0.5, c=\"#7A68A6\")\n",
"plt.scatter( [ population[i_min], population[i_max] ], \n",
" [average_across_county[i_min], average_across_county[i_max] ],\n",
" s = 60, marker = \"o\", facecolors = \"none\",\n",
" edgecolors = \"#A60628\", linewidths = 1.5, \n",
" label=\"extreme heights\")\n",
"\n",
"plt.xlim( 100, 1500 )\n",
"plt.title( \"Average height vs. County Population\")\n",
"plt.xlabel(\"County Population\")\n",
"plt.ylabel(\"Average height in county\")\n",
"plt.plot( [100, 1500], [150, 150], color = \"k\", label = \"true expected \\\n",
"height\", ls=\"--\" )\n",
"plt.legend(scatterpoints = 1)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "pyout",
"prompt_number": 20,
"text": [
"<matplotlib.legend.Legend at 0xc5cb030>"
]
},
{
"output_type": "display_data",
"png": 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lGI1GHnroIZ5//nnefPNNMjMzef/99x2Of/vttykuLub06dMsXbqU0aNHAzBl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cgPdVOTM+QPrOVsQxSknL0SuU2WZbQ65T/IHk+SFDL5+qIqyNi91fig8Vo3NO4+7jEZrFCQxoZp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\nKdcdtqhx/maKpmsEG79AfUbxu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br//T9knZycoH8Slxx201bL7vo3F3XPaVPSdCpEvRV1DY5vNfHq2Rija4+i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8yf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\n"
}
],
"prompt_number": 20
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"What do we observe? *Without accounting for population sizes* we run the risk of making an enormous inference error: if we ignored population size, we would say that the county with the shortest and tallest individuals have been correctly circled. But this inference is wrong for the following reason. These two counties do *not* necessarily have the most extreme heights. The error is that the calculated average of the small population is not a good reflection of the true expected value of the population (which should be $\\mu =150$). The sample size/population size/$N$, whatever you wish to call it, is simply too small to invoke the Law of Large Numbers effectively. \n",
"\n",
"We provide more damning evidence against this inference. Recall the population numbers were uniformly distributed over 100 to 1500. Our intuition should tell us that the counties with the most extreme population heights should also be uniformly spread over 100 to 4000, and certainly independent of the county's population. Not so. Below are the population sizes of the counties with the most extreme heights."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"print \"Population sizes of 10 'shortest' counties: \"\n",
"print population[ np.argsort( average_across_county )[:10] ]\n",
"print\n",
"print \"Population sizes of 10 'tallest' counties: \"\n",
"print population[ np.argsort( -average_across_county )[:10] ]"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Population sizes of 10 'shortest' counties: \n",
"[181 168 229 110 156 123 222 154 498 375]\n",
"\n",
"Population sizes of 10 'tallest' counties: \n",
"[105 114 111 236 373 244 183 278 234 268]\n"
]
}
],
"prompt_number": 11
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Not at all uniform over 100 to 1500. This is an absolute failure of the Law of Large Numbers. \n",
"\n",
"##### Example: Kaggle's *U.S. Census Return Rate Challenge*\n",
"\n",
"Below is data from the 2010 US census, which partitions populations beyond counties to the level of block groups (which are aggregates of city blocks or equivalents). The dataset is from a Kaggle machine learning competition some colleagues and I participated in. The objective was to predict the census letter mail-back rate of a group block, measured between 0 and 100, using census variables (median income, number of females in the block-group, number of trailer parks, average number of children etc.). Below we plot the census mail-back rate versus block group population:"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"figsize( 12.5, 6.5 )\n",
"data = np.genfromtxt( \"./data/census_data.csv\", skip_header=1, \n",
" delimiter= \",\")\n",
"plt.scatter( data[:,1], data[:,0], alpha = 0.5, c=\"#7A68A6\")\n",
"plt.title(\"Census mail-back rate vs Population\")\n",
"plt.ylabel(\"Mail-back rate\")\n",
"plt.xlabel(\"population of block-group\")\n",
"plt.xlim(-100, 15e3 )\n",
"plt.ylim( -5, 105)\n",
"\n",
"i_min = np.argmin( data[:,0] )\n",
"i_max = np.argmax( data[:,0] )\n",
"\n",
" \n",
"plt.scatter( [ data[i_min,1], data[i_max, 1] ], \n",
" [ data[i_min,0], data[i_max,0] ],\n",
" s = 60, marker = \"o\", facecolors = \"none\",\n",
" edgecolors = \"#A60628\", linewidths = 1.5, \n",
" label=\"most extreme points\")\n",
"\n",
"plt.legend(scatterpoints = 1);\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "display_data",
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}
],
"prompt_number": 89
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The above is a classic phenomenon in statistics. I say *classic* referring to the \"shape\" of the scatter plot above. It follows a classic triangular form, that tightens as we increase the sample size (as the Law of Large Numbers becomes more exact). \n",
"\n",
"I am perhaps overstressing the point and maybe I should have titled the book *\"You don't have big data problems!\"*, but here again is an example of the trouble with *small datasets*, not big ones. Simply, small datasets cannot be processed using the Law of Large Numbers. Compare with applying the Law without hassle to big datasets (ex. big data). I mentioned earlier that paradoxically big data prediction problems are solved by relatively simple algorithms. The paradox is partially resolved by understanding that the Law of Large Numbers creates solutions that are *stable*, i.e. adding or subtracting a few data points will not affect the solution much. On the other hand, adding or removing data points to a small dataset can create very different results. \n",
"\n",
"For further reading on the hidden dangers of the Law of Large Numbers, I would highly recommend the excellent manuscript [The Most Dangerous Equation](http://nsm.uh.edu/~dgraur/niv/TheMostDangerousEquation.pdf). "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##### Example: How Reddits ranks comments\n",
"\n",
"You may have disagreed with the original statement that the Law of Large numbers is known to everyone, but only implicitly in our subconscious decision making. Consider ratings on online products: how often do you trust an average 5-star rating if there is only 1 reviewer? 2 reviewers? 3 reviewers? We implicitly understand that with such few reviewers that the average rating is **not** a good reflection of the true value of the product.\n",
"\n",
"This has created flaws in how we sort items, and more generally, how we compare items. Many people have realized that sorting online search results by their rating, whether the objects be books, videos, or online comments, return poor results. Often the seemingly top videos or comments have perfect ratings only from a few enthusiastic fans, and truly more quality videos or comments are hidden in later pages with *falsely-substandard* ratings of around 4.8. How can we correct this?\n",
"\n",
"Consider the popular site Reddit (I purposefully did not link to the website as you would never come back). The site hosts links to stories or images, and a very popular part of the site are the comments associated with each link. Redditors can vote up or down on each comment (called upvotes and downvotes). Reddit, by default, will sort comments by Top, that is, the best comments.\n",
"\n",
"<img src=\"http://i.imgur.com/QjtUF3x.png\" />\n",
"\n",
"\n",
"How would you determine which comments are the best? There are a number of ways to achieve this:\n",
"\n",
"1. *Popularity*: A comment is considered good if it has many upvotes. A problem with this model is that a comment with hundreds of upvotes, but thousands of downvotes. While being very *popular*, the comment is likely more controversial than best.\n",
"2. *Difference*: Using the *difference* of upvotes and downvotes. This solves the above problem, but fails when we consider the temporal nature of comments. Comments can be posted many hours after the original link submission. The difference method will bias the *Top* comments to be the oldest comments, which have accumulated more upvotes than newer comments, but are not necessarily the best.\n",
"3. *Time adjusted*: Consider using Difference divided by the age of the comment. This creates a *rate*, something like *difference per second*, or *per minute*. An immediate counter example is, if we use per second, a 1 second old comment with 1 upvote would be better than a 100 second old comment with 99 upvotes. One can avoid this by only considering at least t second old comments. But what is a good t value? Does this mean no comment younger than t is good? We end up comparing unstable quantities with stable quantities (young vs. old comments).\n",
"3. *Ratio*: Rank comments by the ratio of upvotes to total number of votes (upvotes plus downvotes). This solves the temporal issue, such that new comments who score well can be considered Top just as likely as older comments, provided they have many upvotes to total votes. The problem here is that a comment with a single upvote (ratio = 1.0) will beat a comment with 999 upvotes and 1 downvote (ratio = 0.999), but clearly the latter comment is *more likely* to be better.\n",
"\n",
"I used the phrase *more likely* for good reason. It is possible that the former comment, with a single upvote, is in fact a better comment than the later with 999 upvotes. The hesitation to agree with this is because we have not seen the other 999 potential votes the former comment might get. Perhaps it will achieve an additional 999 upvotes and 0 downvotes and be considered better than the latter, though not likely.\n",
"\n",
"What we really want is an estimate of the *true upvote ratio*. Note that the true upvote ratio is not the same as the observed upvote ratio: the true upvote ratio is hidden, and we only observe upvotes vs. downvotes (one can think of the true upvote ratio as \"what is the underlying probability someone gives this comment a upvote, versus a downvote\"). So the 999 upvote/1 downvote comment probably has a true upvote ratio close to 1, which we can assert with confidence thanks to the Law of Large Numbers, but on the other hand we are much less certain about the true upvote ratio of the comment with only a single upvote. Sounds like a Bayesian problem to me.\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"One way to determine a prior on the upvote ratio is that look at the historical distribution of upvote ratios. This can be accomplished by scrapping Reddit's comments and determining a distribution. There are a few problems with this technique though:\n",
"\n",
"1. Skewed data: The vast majority of comments have very few votes, hence there will be many comments with ratios near the extremes (see the \"triangular plot\" in the above Kaggle dataset), effectively skewing our distribution to the extremes. One could try to only use comments with votes greater than some threshold. Again, problems are encountered. There is a tradeoff between number of comments available to use and a higher threshold with associated ratio precision. \n",
"2. Biased data: Reddit is composed of different subpages, called subreddits. Two examples are *r/aww*, which posts pics of cute animals, and *r/politics*. It is very likely that the user behaviour towards comments of these two subreddits are very different: visitors are likely friend and affectionate in the former, and would therefore upvote comments more, compared to the latter, where comments are likely to be controversial and disagreed upon. Therefore not all comments are the same. \n",
"\n",
"\n",
"In light of these, I think it is better to use a `Uniform` prior.\n",
"\n",
"\n",
"With our prior in place, we can find the posterior of the true upvote ratio. The Python script `comments_for_top_reddit_pic.py` will scrap the comments from the current top picture on Reddit. Below is the picture, and some comments:"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from IPython.core.display import Image\n",
"#adding a number to the end of the %run call with get the ith top photo.\n",
"%run top_pic_comments.py 2\n",
"\n",
"Image(top_post_url)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Version 2.0.14 of praw is outdated. Version 2.0.15 was released Saturday April 06, 2013.\n",
"Title of submission: \n"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"3 Wolves in Quebec, Canada\n",
"http://i.imgur.com/aHes4aF.jpg\n"
]
},
{
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BKsxDglRsQntZ/ePP+SpZJq34TasXTZs6TKCUCX4ak552e4y7JA3UXN3s3ePX+NhtHXj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\nMsBiVEs5AOjaFzq8ao7AZrHOGUIUElwcoV1fNpp6Q31Af//Z\n",
"output_type": "pyout",
"prompt_number": 1,
"text": [
"<IPython.core.display.Image at 0x8753438>"
]
}
],
"prompt_number": 1
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\"\"\"\n",
"contents: an array of the text from all comments on the pic\n",
"votes: a 2d numpy array of upvotes, downvotes for each comment.\n",
"\"\"\"\n",
"n_comments = len(contents )\n",
"comments = np.random.randint( n_comments, size=4)\n",
"print \"Some Comments (out of %d total) \\n-----------\"%n_comments\n",
"for i in comments:\n",
" print '\"' + contents[i] + '\"'\n",
" print\"upvotes/downvotes: \",votes[i,:]\n",
" print"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Some Comments (out of 49 total) \n",
"-----------\n",
"\"Shaggydog, Nymeria, and Ghost?\""
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"upvotes/downvotes: [134 17]\n",
"\n",
"\"I call bullshit. Not one of them is howling, nor is there a moon present.\"\n",
"upvotes/downvotes: [80 13]\n",
"\n",
"\"That would make a badass t shirt.\"\n",
"upvotes/downvotes: [10 0]\n",
"\n",
"\"That is the alpha male and he is alerting his pack that he has found a Tim Hortons.\"\n",
"upvotes/downvotes: [2 0]\n",
"\n"
]
}
],
"prompt_number": 43
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" For a given true upvote ratio $p$ and $N$ votes, the number of upvotes will look like a Binomial random variable with parameters $p$ and $N$. (This is because of the equivalence between upvote ratio and probability of upvoting versus downvoting, out of $N$ possible votes/trials). We create a function that performs Bayesian inference on $p$, for a particular comment's upvote/downvote pair."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import pymc as mc\n",
"\n",
"def posterior_upvote_ratio( upvotes, downvotes, samples = 20000):\n",
" N = upvotes + downvotes\n",
" upvote_ratio = mc.Uniform( \"upvote_ratio\", 0, 1 )\n",
" observations = mc.Binomial( \"obs\", N, upvote_ratio, value = upvotes, observed = True)\n",
" \n",
" model = mc.Model( [upvote_ratio, observations ]) \n",
" map_ = mc.MAP(model).fit()\n",
" mcmc = mc.MCMC(model)\n",
" \n",
" mcmc.sample(samples, samples/4)\n",
" \n",
" return mcmc.trace(\"upvote_ratio\")[:]\n",
" "
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 44
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Below are the resulting posterior distributions."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"figsize( 11., 8)\n",
"posteriors = []\n",
"colours = [\"#348ABD\", \"#A60628\", \"#7A68A6\", \"#467821\", \"#CF4457\"]\n",
"for i in range(len(comments)):\n",
" j = comments[i]\n",
" posteriors.append( posterior_upvote_ratio( votes[j, 0], votes[j,1] ) )\n",
" plt.hist( posteriors[i], bins = 18, normed = True, alpha = .9, \n",
" histtype=\"step\",color = colours[i%5], lw = 3,\n",
" label = '(%d up:%d down)\\n%s...'%(votes[j, 0], votes[j,1], contents[j][:50]) )\n",
" plt.hist( posteriors[i], bins = 18, normed = True, alpha = .2, \n",
" histtype=\"stepfilled\",color = colours[i], lw = 3, )\n",
" #plt.title( 'upvotes:downvotes: %d:%d'%(votes[j,0], votes[j,1]) )\n",
"\n",
" \n",
"plt.legend(loc=\"upper left\")\n",
"plt.xlim( 0, 1)\n",
"plt.title(\"Posterior distributions of upvote ratios on different comments\");\n",
"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
" \r",
"[****************100%******************] 20000 of 20000 complete"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n"
]
},
{
"output_type": "display_data",
"png": 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FOH78OBeenJwMW1vbeskOlFsLa7sY/syZM3BxcUGPHj0gKyuL5cuX86yUwcHB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\ncFy+DEcYU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}
],
"prompt_number": 45
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Some distributions are very tight, others have very long tails (relatively speaking), expressing our uncertainty with what the true upvote ratio might be.\n",
"\n",
"### Sorting!\n",
"\n",
"We have been ignoring the goal of this exercise: how do we sort the comments from *best to worst*? Of course, we cannot sort distributions, we must sort scalar numbers. There are many ways to distill a distribution down to a scalar: expressing the distribution through its expected value, or mean, is one way. Choosing the mean bad choice though. This is because the mean does not take into account the uncertainty of distributions.\n",
"\n",
"I suggest using the *95% least plausible value*, defined as the value such that there is only a 5% chance the true parameter is lower (think of the lower bound on the 95% credible region). Below are the posterior distributions with the 95% least-plausible value plotted:"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"N = posteriors[0].shape[0]\n",
"lower_limits = []\n",
"\n",
"for i in range(len(comments)):\n",
" j = comments[i]\n",
" plt.hist( posteriors[i], bins = 20, normed = True, alpha = .9, \n",
" histtype=\"step\",color = colours[i], lw = 3,\n",
" label = '(%d up:%d down)\\n%s...'%(votes[j, 0], votes[j,1], contents[j][:50]) )\n",
" plt.hist( posteriors[i], bins = 20, normed = True, alpha = .2, \n",
" histtype=\"stepfilled\",color = colours[i], lw = 3, )\n",
" v = np.sort( posteriors[i] )[ int(0.05*N) ]\n",
" #plt.vlines( v, 0, 15 , color = \"k\", alpha = 1, linewidths=3 )\n",
" plt.vlines( v, 0, 10 , color = colours[i], linestyles = \"--\", linewidths=3 )\n",
" lower_limits.append(v)\n",
" plt.legend(loc=\"upper left\")\n",
"\n",
" \n",
"plt.legend(loc=\"upper left\")\n",
"\n",
"plt.title(\"Posterior distributions of upvote ratios on different comments\");\n",
"order = argsort( -np.array( lower_limits ) )\n",
"print order, lower_limits\n",
"\n",
" "
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"[0 1 2 3] [0.83778530918250105, 0.78945340111675133, 0.7676689367397137, 0.36240895835250453]\n"
]
},
{
"output_type": "display_data",
"png": 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CERERuHHjBidXjx49uGnvy5cvw9jYGFeuXAEAXLlyhTfdHRMTAwsLCyQlJWHO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\nrkJggg==\n"
}
],
"prompt_number": 46
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The best comments, according to our procedure, are the comments that are *most-likely* to score a high percentage of upvotes. Visually those are the comments with the 95% least plausible value close to 1.\n",
"\n",
"Why is sorting based on this quantity a good idea? By ordering by the 95% least plausible value, we are being the most conservative with what we think is best. That is, even in the worst case scenario, when we have severely overestimated the upvote ratio, we can be sure the best comments are still on top. Under this ordering, we impose the following very natural properties:\n",
"\n",
"1. given two comments with the same observed upvote ratio, we will assign the comment with more votes as better (since we are more confident it has a higher ratio).\n",
"2. given two comments with the same number of votes, we still assign the comment with more upvotes as *better*.\n",
"\n",
"### But this is too slow for real-time!\n",
"\n",
"I agree, computing the posterior of every comment takes a long time, and by the time you have computed it, likely the data has changed. I delay the mathematics to the appendix, but I suggest using the following formula to compute the lower bound very fast.\n",
"\n",
"$$ \\frac{a}{a + b} - 1.65\\sqrt{ \\frac{ab}{ (a+b)^2(a + b +1 ) } }$$\n",
"\n",
"where \n",
"\\begin{align}\n",
"& a = 1 + u \\\\\\\\\n",
"& b = 1 + d \\\\\\\\\n",
"\\end{align}\n",
"\n",
"$u$ is the number of upvotes, and $d$ is the number of downvotes. The formula is a shortcut in Bayesian inference, which will be further explained in Chapter 6 when we discuss priors in more detail.\n"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def intervals(u,d):\n",
" a = 1. + u\n",
" b = 1. + d\n",
" mu = a/(a+b)\n",
" std_err = 1.65*np.sqrt( (a*b)/( (a+b)**2*(a+b+1.) ) )\n",
" return ( mu, std_err )\n",
"\n",
"\n",
"print \"Approximate lower bounds:\"\n",
"posterior_mean, std_err = intervals(votes[:,0],votes[:,1])\n",
"lb = posterior_mean - std_err\n",
"print lb\n",
"print\n",
"\n",
"print \"Top 40 Sorted according to approximate lower bounds:\"\n",
"print\n",
"order = np.argsort( -lb )\n",
"ordered_contents = []\n",
"for i in order[:40]:\n",
" ordered_contents.append( contents[i] )\n",
" print votes[i,0], votes[i,1], contents[i]\n",
" print \"-------------\"\n",
"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Approximate lower bounds:\n",
"[ 0.85943711 0.83951434 0.8458571 0.84536604 0.86388258 0.83651439\n",
" 0.89239065 0.7929375 0.85447643 0.70806405 0.79018506 0.82545948\n",
" 0.70408053 0.79198214 0.60100251 0.6931046 0.6931046 0.6530083\n",
" 0.7137931 0.60091591 0.60091591 0.60091591 0.60091591 0.60091591\n",
" 0.52182581 0.60100251 0.53055613 0.53055613 0.53055613 0.56085485\n",
" 0.51184301 0.4722123 0.43047887 0.43047887 0.43047887 0.53055613\n",
" 0.43047887 0.43047887 0.43047887 0.53055613 0.43047887 0.43047887\n",
" 0.43047887 0.43047887 0.43047887 0.43047887 0.43047887 0.43047887\n",
" 0.43047887]"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"\n"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Top 40 Sorted according to approximate lower bounds:\n",
"\n"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"22 0 Being as an ocean?\n",
"-------------\n",
"354 43 Ok, three-wolf-joke-in-my-second-language time:\n",
"\n",
"Un jours trois loups chassent ensemble dans la for\u00eat: un Qu\u00e9b\u00e9cois, un Franco-Ontarien et un Fran\u00e7ais. Soudainement, **PAF!**, ils tombent dans un pi\u00e8ge \u00e0 loup et ont chacun une patte poigner. \n",
"\n",
"\"Oh ben *tabarnak*\" dit le Franco-Ontarien. \"L\u00e0 on fait quoi, crisse? Les chasseurs vont nous tuer!\"\n",
"\n",
"\"J'ai une id\u00e9e!\" exclame le Qu\u00e9b\u00e9cois. \"Si on s'mange une patte on pourrait nous lib\u00e9rer. C'est ben plate, mais on n'a pas le choix.\" Aussit\u00f4t dit, aussit\u00f4t fait, et Qu\u00e9b\u00e9cois et le Franco-Ontarien s'en sortent. Alors qu'ils allaient sortir de la for\u00eat, le Franco-Ontarien dit \"Hey! Y'est o\u00f9 le Fran\u00e7ais d'abord?\"\n",
"\n",
"\"Osti d'sapp\u00e9,\" r\u00e9pond le Qu\u00e9b\u00e9cois, \"l\u00e0 on va avoir \u00e0 le sauver!\" Les deux retournent sur le lieu de leur capture et voient le Fran\u00e7ais, toujours emprisonn\u00e9, qui leur dit\n",
"\n",
"\"Bordel, vous avez fait comment les mecs? Je m'suis d\u00e9j\u00e0 bouff\u00e9 trois pattes et je suis encore bloqu\u00e9!\"\n",
"-------------\n",
"362 46 This was done by photographer Daniel Parent. [[Source](http://500px.com/photo/7505677?from=set/285118)] -- [Check out his collection of wolf photos here](http://500px.com/djlparent99/sets/wolves)\n",
"\n",
"Here are some of my favorites from the collection:\n",
"\n",
"- OP's one, called [\"Three Weary Wolves\"](http://i.imgur.com/dW2bsks.jpg) [707 x 900 Version]\n",
"\n",
"- [\"The Crossing\" (with 12 wolves)](http://i.imgur.com/J5bKJsu.jpg)\n",
"\n",
"- [\"Above and Beyond\"](http://i.imgur.com/bJHbrNa.jpg)\n",
"\n",
"- [\"On Patrol\"](http://i.imgur.com/TKyST9h.jpg)\n",
"-------------\n",
"44 3 Are they also in a Christian hard rock band?\n",
"-------------\n",
"33 2 Princess Mononoke?\n",
"-------------\n",
"805 126 / \\ _-' \n",
" _/| \\-''- _ / /\\__/\\ \n",
" __~' { | \\ / \\ \n",
" / \\ | - - | \n",
" / \"\u0ca0. |\u0ca0 } \\ /| \n",
" | \\ ; \\ T / |\\ \n",
" ', | \n",
" \\_ __\\ \n",
" ''-_ \\.// \n",
" / '-____' \n",
" / n, Sorry.\n",
" / _/ | _ \n",
" _' /' `'/ \n",
" _-' &lt;~ .' \n",
" .' | \n",
" _/ | \n",
" _/ `.`. \n",
" / ' \\__ | | \n",
" ___/ /__\\ \\ \\ \n",
" (___.'\\_______)\\_|_| \n",
"\n",
"-------------\n",
"134 17 Shaggydog, Nymeria, and Ghost?\n",
"-------------\n",
"106 13 [Was this picture taken in Rivi\u00e8re-du-Loup?](http://www.badumtss.net/) \n",
"-------------\n",
"21 1 Dire Wolves. Fucking sexy ass Dire Wolves. \n",
"-------------\n",
"80 13 I call bullshit. Not one of them is howling, nor is there a moon present.\n",
"-------------\n",
"17 1 Yayy Quebec on the front page :)\n",
"-------------\n",
"10 0 That would make a badass t shirt.\n",
"-------------\n",
"23 4 where's moon moon?\n",
"-------------\n",
"11 1 Good Ol' Quebec, Canada. Land of wolves, maple syrup and Labatt 50. \n",
"-------------\n",
"22 4 No retarded comment from me. This is a nice picture!\n",
"-------------\n",
"6 0 I recognize this from a Being As An Ocean band t-shirt.\n",
"\n",
"Such a cool picture. \n",
"-------------\n",
"6 0 Looks like a boy band posing for their new album cover.\n",
"-------------\n",
"5 0 Is that Wolf+1's new album cover?\n",
"-------------\n",
"7 1 On a tu pris ces photos \u00e0 Rivi\u00e8re-du-Loup ?? :-)\n",
"-------------\n",
"7 1 Mon tabarnac c'est dont ben des beaux loups esti!\n",
"\n",
"-------------\n",
"4 0 This image has actually been reprinted into a REALLY nice shirt by the band Being As An Ocean\n",
"\n",
"http://merchnow.com/products/149014/alpine-wolf-white\n",
"-------------\n",
"4 0 where, specifically in Quebec was that photo taken?\n",
"-------------\n",
"4 0 I like this one, one wolf is facing one way another facing the other way and the wolf in the back is like whaddya want from me\n",
"-------------\n",
"4 0 reminds me of princess mononoke\n",
"-------------\n",
"4 0 [As a Magic: The Gathering card](http://i.imgur.com/KI74xCc.jpg)\n",
"-------------\n",
"6 1 Winter is coming.\n",
"-------------\n",
"3 0 I suppose this is the time to post [this](http://www.reddit.com/r/pics/comments/1d1qs4/i_wrestled_those_wolves_in_quebec_canada/) picture.\n",
"\n",
"Me, in Quebec, joking around with some wolves.\n",
"-------------\n",
"3 0 Looks like the Christ + 1 album cover.\n",
"-------------\n",
"3 0 Where exactly was it taken?\n",
"-------------\n",
"3 0 J'adore!\n",
"-------------\n",
"3 0 Looks like Cartman tried to make an christian rock album cover\n",
"-------------\n",
"9 3 Did Eric Cartman stage this for an album cover?\n",
"-------------\n",
"5 1 [3 Wolf River](http://i.imgur.com/W01N0G4.png) saved my marriage! I used to wear boring 3-piece suits and platinum cufflinks, but my lady got tired of my buttoned-down looks; she wanted a wildman.\n",
"\n",
"Cue 3 Wolf River: this magnificent fucking shirt has not one, NOT TWO, BUT *THREE* stunning, predatory killing machines featured in a sharp art-deco arrangement. Also there's an awesome river, full of water and freshwater crabs and shit. My lady saw me sporting this bad boy and we had to send the kids away. Not for the weekend; *forever.*\n",
"\n",
"The amount of sheer manliness contained within these threads was not meant for mortal men, and yet *you* could own one of these majestic chest-hiders for *only $24.99!*\n",
"-------------\n",
"9 4 I hope those Stark kids pick up after them.\n",
"-------------\n",
"2 0 Dude i love how quebec looks, lived there nearly my entire life\n",
"-------------\n",
"2 0 3 wolf canada...\n",
"-------------\n",
"2 0 MAJESTIC AS FUCK!\n",
"-------------\n",
"2 0 For those of you who were wondering where those pictures came from, a lot of them were taken at Park Omega (http://www.parc-omega.com/)\n",
"-------------\n",
"2 0 That is the alpha male and he is alerting his pack that he has found a Tim Hortons.\n",
"-------------\n",
"2 0 Like an all wolf [Christian rock band](http://imgur.com/9yR3V6R.jpg)\n",
"-------------\n"
]
}
],
"prompt_number": 52
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can view the ordering visually by plotting the posterior mean and bounds, and sorting by the lower bound. In the plot below, notice that the left error-bar is sorted (as we suggested this is the best way to determine an ordering), so the means, indicated by dots, do not follow any strong pattern. "
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"r_order = order[::-1][:40]\n",
"plt.errorbar( posterior_mean[r_order], np.arange( len(r_order) ), \n",
" xerr=std_err[r_order],xuplims=True, capsize=0, fmt=\"o\",\n",
" color = \"#7A68A6\")\n",
"plt.xlim( 0.3, 1)\n",
"plt.yticks( np.arange( len(r_order)-1,-1,-1 ), map( lambda x: x[:30], ordered_contents) );\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "display_data",
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}
],
"prompt_number": 53
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In the graphic above, you can see why sorting by mean would be sub-optimal."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Conclusion\n",
"\n",
"While the Law of Large Numbers is cool, it is only true so much as its name implies: with large sample sizes only. We have seen how our inference can be affected by not considering *how the data is shaped*. \n",
"\n",
"1. By (cheaply) drawing many samples from the posterior distributions, we can ensure that the Law of Large Number applies as we approximate expected values (which we will do in the next chapter).\n",
"\n",
"2. Bayesian inference understands that with small sample sizes, we can observe wild randomness. Our posterior distribution will reflect this by being more spread rather than tightly concentrated. Thus, our inference should be correctable.\n",
"\n",
"3. There are major implications of not considering the sample size, and trying to sort objects that are unstable leads to pathological orderings. The method provided above solves this problem.\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Appendix\n",
"\n",
"##### Derivation of sorting comments formula\n",
"\n",
"Basically what we are doing is using a Beta prior (with parameters $a=1, b=1$, which is a uniform distribution), and using a Binomial likelihood with observations $u, N = u+d$. This means our posterior is a Beta distribution with parameters $a' = 1 + u, b' = 1 + (N - u) = 1+d$. We then need to find the value, $x$, such that 0.05 probability is less than $x$. This is usually done by inverting the CDF ([Cumulative Distribution Function](http://en.wikipedia.org/wiki/Cumulative_Distribution_Function)), but the CDF of the beta, for integer parameters, is known but is a large sum [3]. \n",
"\n",
"We instead using a Normal approximation. The mean of the Beta is $\\mu = a'/(a'+b')$ and the variance is \n",
"\n",
"$$\\sigma^2 = \\frac{a'b'}{ (a' + b')^2(a'+b'+1) }$$\n",
"\n",
"Hence we solve the following equation for $x$ and have an approximate lower bound. \n",
"\n",
"$$ 0.05 = \\Phi\\left( \\frac{(x - \\mu)}{\\sigma}\\right) $$ \n",
"\n",
"$\\Phi$ being the [cumulative distribution for the normal distribution](http://en.wikipedia.org/wiki/Normal_distribution#Cumulative_distribution)\n",
"\n",
"\n",
"\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##### Exercises\n",
"\n",
"1\\. How would you estimate the quantity $E\\left[ \\cos{X} \\right]$, where $X \\sim \\text{Exp}(4)$? What about $E\\left[ \\cos{X} | X \\lt 1\\right]$, i.e. the expected value *given* we know $X$ is less than 1? Would you need more samples than the original samples size to be equally as accurate?"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"## Enter code here\n",
"import scipy.stats as stats\n",
"exp = stats.expon( scale=4 )\n",
"N = 1e5\n",
"X = exp.rvs( N )\n",
"## ..."
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 14
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"2\\. The following table was located in the paper \"Going for Three: Predicting the Likelihood of Field Goal Success with Logistic Regression\" [2]. The table ranks football field-goal kickers by there percent of non-misses. What mistake have the researchers made?\n",
"\n",
"-----\n",
"\n",
"#### Kicker Careers Ranked by Make Percentage\n",
"<table><tbody><tr><th>Rank </th><th>Kicker </th><th>Make % </th><th>Number of Kicks</th></tr><tr><td>1 </td><td>Garrett Hartley </td><td>87.7 </td><td>57</td></tr><tr><td>2</td><td> Matt Stover </td><td>86.8 </td><td>335</td></tr><tr><td>3 </td><td>Robbie Gould </td><td>86.2 </td><td>224</td></tr><tr><td>4 </td><td>Rob Bironas </td><td>86.1 </td><td>223</td></tr><tr><td>5</td><td> Shayne Graham </td><td>85.4 </td><td>254</td></tr><tr><td>\u2026 </td><td>\u2026 </td><td>\u2026</td><td> </td></tr><tr><td>51</td><td> Dave Rayner </td><td>72.2 </td><td>90</td></tr><tr><td>52</td><td> Nick Novak </td><td>71.9 </td><td>64</td></tr><tr><td>53 </td><td>Tim Seder </td><td>71.0 </td><td>62</td></tr><tr><td>54 </td><td>Jose Cortez </td><td>70.7</td><td> 75</td></tr><tr><td>55 </td><td>Wade Richey </td><td>66.1</td><td> 56</td></tr></tbody></table>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### References\n",
"\n",
"1. Wainer, Howard. *The Most Dangerous Equation*. American Scientist, Volume 95.\n",
"2. Clarck, Torin K., Aaron W. Johnson, and Alexander J. Stimpson. \"Going for Three: Predicting the Likelihood of Field Goal Success with Logistic Regression.\" (2013): n. page. Web. 20 Feb. 2013.\n",
"3. http://en.wikipedia.org/wiki/Beta_function#Incomplete_beta_function"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from IPython.core.display import HTML\n",
"def css_styling():\n",
" styles = open(\"../styles/custom.css\", \"r\").read()\n",
" return HTML(styles)\n",
"css_styling()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"html": [
"<style>\n",
" @font-face {\n",
" font-family: \"Computer Modern\";\n",
" src: url('http://mirrors.ctan.org/fonts/cm-unicode/fonts/otf/cmunss.otf');\n",
" }\n",
" div.cell{\n",
" width:800px;\n",
" margin-left:16% !important;\n",
" margin-right:auto;\n",
" }\n",
" h1 {\n",
" font-family: Helvetica, serif;\n",
" }\n",
" h4{\n",
" margin-top:12px;\n",
" margin-bottom: 3px;\n",
" }\n",
" div.text_cell_render{\n",
" font-family: Computer Modern, \"Helvetica Neue\", Arial, Helvetica, Geneva, sans-serif;\n",
" line-height: 145%;\n",
" font-size: 130%;\n",
" width:800px;\n",
" margin-left:auto;\n",
" margin-right:auto;\n",
" }\n",
" .CodeMirror{\n",
" font-family: \"Source Code Pro\", source-code-pro,Consolas, monospace;\n",
" }\n",
" .prompt{\n",
" display: None;\n",
" }\n",
" .text_cell_render h5 {\n",
" font-weight: 300;\n",
" font-size: 16pt;\n",
" color: #4057A1;\n",
" font-style: italic;\n",
" margin-bottom: .5em;\n",
" margin-top: 0.5em;\n",
" display: block;\n",
" }\n",
" \n",
" .warning{\n",
" color: rgb( 240, 20, 20 )\n",
" } \n",
"</style>\n",
"<script>\n",
" MathJax.Hub.Config({\n",
" TeX: {\n",
" extensions: [\"AMSmath.js\"]\n",
" },\n",
" tex2jax: {\n",
" inlineMath: [ ['$','$'], [\"\\\\(\",\"\\\\)\"] ],\n",
" displayMath: [ ['$$','$$'], [\"\\\\[\",\"\\\\]\"] ]\n",
" },\n",
" displayAlign: 'center', // Change this to 'center' to center equations.\n",
" \"HTML-CSS\": {\n",
" styles: {'.MathJax_Display': {\"margin\": 4}}\n",
" }\n",
" });\n",
"</script>"
],
"output_type": "pyout",
"prompt_number": 1,
"text": [
"<IPython.core.display.HTML at 0x5183f28>"
]
}
],
"prompt_number": 1
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<style>\n",
" img{\n",
" max-width:800px}\n",
"</style>"
]
}
],
"metadata": {}
}
]
}
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