From 38e7a285e2ca7b35f91dd744f9a044b0983fd2d3 Mon Sep 17 00:00:00 2001 From: Reuven Y Date: Sat, 27 Apr 2019 22:06:23 +0300 Subject: [PATCH 1/2] Correct reference number to Huber book --- 03-Gaussians.ipynb | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/03-Gaussians.ipynb b/03-Gaussians.ipynb index 35b7d2e..04439e8 100644 --- a/03-Gaussians.ipynb +++ b/03-Gaussians.ipynb @@ -782,7 +782,7 @@ "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." ] From 155290182bf43dfe6f32a99203a0865b18ff5159 Mon Sep 17 00:00:00 2001 From: Reuven Y Date: Sat, 27 Apr 2019 22:07:58 +0300 Subject: [PATCH 2/2] Update 03-Gaussians.ipynb Typo - missing "that" --- 03-Gaussians.ipynb | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/03-Gaussians.ipynb b/03-Gaussians.ipynb index 04439e8..875e495 100644 --- a/03-Gaussians.ipynb +++ b/03-Gaussians.ipynb @@ -1393,7 +1393,7 @@ "source": [ "## Putting it all Together\n", "\n", - "Now we are ready to talk about Gaussians can be used in filtering. In the next chapter we will implement a filter using Gaussins. Here I will explain why we would want to use Gaussians.\n", + "Now we are ready to talk about Gaussians that can be used in filtering. In the next chapter we will implement a filter using Gaussins. Here I will explain why we would want to use Gaussians.\n", "\n", "In the previous chapter we represented probability distributions with an array. We performed the update computation by computing the element-wise product of that distribution with another distribution representing the likelihood of the measurement at each point, like so:" ]