Merge pull request #296 from robi-y/master

Typos: ref. number and missing words
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Roger Labbe 2020-04-26 18:19:38 -07:00 committed by GitHub
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"source": [
"Is this \"correct\"? You tell me. Without the outlier of 100 we get $\\sigma^2=2.03$, which accurately reflects how $X$ is varying absent the outlier. The one outlier swamps the variance computation. Do we want to swamp the computation so we know there is an outlier, or robustly incorporate the outlier and still provide an estimate close to the value absent the outlier? Again, you tell me. Obviously it depends on your problem.\n",
"\n",
"I will not continue down this path; if you are interested you might want to look at the work that James Berger has done on this problem, in a field called *Bayesian robustness*, or the excellent publications on *robust statistics* by Peter J. Huber [3]. In this book we will always use variance and standard deviation as defined by Gauss.\n",
"I will not continue down this path; if you are interested you might want to look at the work that James Berger has done on this problem, in a field called *Bayesian robustness*, or the excellent publications on *robust statistics* by Peter J. Huber [4]. In this book we will always use variance and standard deviation as defined by Gauss.\n",
"\n",
"The point to gather from this is that these *summary* statistics always tell an incomplete story about our data. In this example variance as defined by Gauss does not tell us we have a single large outlier. However, it is a powerful tool, as we can concisely describe a large data set with a few numbers. If we had 1 billion data points we would not want to inspect plots by eye or look at lists of numbers; summary statistics give us a way to describe the shape of the data in a useful way."
]