Blog Archives

Quantifying uncertainty

April 13, 2015
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The primary way to quantify uncertainty is to use probability. Subject to certain axioms that aim to capture common-sense rules for quantifying uncertainty, probability theory is essentially the only way. (This is Cox’s theorem.) Other methods, such as fuzzy logic, may be useful, though they must violate common sense (at least as defined by Cox’s theorem) […]

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Why not statistics

April 9, 2015
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Jordan Ellenberg’s parents were both statisticians. In his interview with Strongly Connected Components Jordan explains why he went into mathematics rather than statistics. I tried. I tried to learn some statistics actually when I was younger and it’s a beautiful subject. But at the time I think I found the shakiness of the philosophical underpinnings […]

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Bayes factors vs p-values

March 31, 2015
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Bayesian analysis and Frequentist analysis often lead to the same conclusions by different routes. But sometimes the two forms of analysis lead to starkly different conclusions. The following illustration of this difference comes from a talk by Luis Pericci last week. He attributes the example to “Bernardo (2010)” though I have not been able to find the exact […]

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Pros and cons of the term “data science”

March 30, 2015
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I’ve resisted using the term “data science,” and enjoy poking fun at it now and then, but I’ve decided it’s not such a bad label after all. Here are some of the pros and cons of the term. (Listing “cons” first seems backward, but I’m currently leaning toward the pro side, so I thought I […]

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Replace data with measurements

March 26, 2015
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To tell whether a statement about data is over-hyped, see whether it retains its meaning if you replace data with measurements. So a request like “Please send me the data from your experiment” becomes “Please send me the measurements from your experiment.” Same thing. But rousing statements about the power of data become banal or even […]

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Fitting a triangular distribution

March 24, 2015
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Sometimes you only need a rough fit to some data and a triangular distribution will do. As the name implies, this is a distribution whose density function graph is a triangle. The triangle is determined by its base, running between points a and b, and a point c somewhere in between where the altitude intersects the base. […]

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A subtle way to over-fit

March 17, 2015
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If you train a model on a set of data, it should fit that data well. The hope, however, is that it will fit a new set of data well. So in machine learning and statistics, people split their data into two parts. They train the model on one half, and see how well it […]

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Finding the best dose

February 24, 2015
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In a dose-finding clinical trial, you have a small number of doses to test, and you hope find the one with the best response. Here “best” may mean most effective, least toxic, closest to a target toxicity, some combination of criteria, etc. Since your goal is to find the best dose, it seems natural to compare dose-finding […]

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Miscellaneous math resources

February 4, 2015
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Every Wednesday I’ve been pointing out various resources on my web site. So far they’ve all been web pages, but the following are all PDF files. Probability and statistics: How to test a random number generator Predictive probabilities for normal outcomes One-arm binary predictive probability Relating two definitions of expectation Illustrating the error in the […]

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Probability approximations

January 28, 2015
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This week’s resource post lists notes on probability approximations. Do we even need probability approximations anymore? They’re not as necessary for numerical computation as they once were, but they remain vital for understanding the behavior of probability distributions and for theoretical calculations. Textbooks often leave out details such as quantifying the error when discussion approximations. The […]

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