Posts Tagged ‘ Probability and Statistics ’

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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More data, less accuracy

January 27, 2015
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Statistical methods should do better with more data. That’s essentially what the technical term “consistency” means. But with improper numerical techniques, the the numerical error can increase with more data, overshadowing the decreasing statistical error. There are three ways Bayesian posterior probability calculations can degrade with more data: Polynomial approximation Missing the spike Underflow Elementary numerical integration algorithms, […]

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Random probability tweets

December 3, 2014
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For the next few weeks, I’ve scheduled @ProbFact tweets to come out at random times. They will follow a Poisson distribution with an average of two per day. (Times are truncated to multiples of 5 minutes because my scheduling software requires that.)  

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First two impressions of statistics

November 25, 2014
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When I was a postdoc I asked a statistician a few questions and he gave me an overview of his subject. (My area was PDEs; I knew nothing about statistics.) I remember two things that he said. A big part of being a statistician is knowing what to do when your assumptions aren’t met, because […]

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Blue Bonnet Bayes

October 28, 2014
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Blue Bonnet Bayes

Blue Bonnet™ used to run commercials with the jingle “Everything’s better with Blue Bonnet on it.” Maybe they still do. Perhaps in reaction to knee-jerk antipathy toward Bayesian methods, some statisticians have adopted knee-jerk enthusiasm for Bayesian methods. Everything’s better with Bayesian analysis on it. Bayes makes it better, like a little dab of margarine […]

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Common sense and statistics

September 18, 2014
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College courses often begin by trying to weaken your confidence in common sense. For example, a psychology course might start by presenting optical illusions to show that there are limits to your ability to perceive the world accurately. I’ve seen at least one physics textbook that also starts with optical illusions to emphasize the need […]

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Intuition and Data at KeenCON

August 14, 2014
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Intuition and Data at KeenCON

I will be giving a talk “Bayesian statistics as a way to integrate intuition and data” at KeenCon, September 11, 2014 in San Francisco. Update: Use promo code KeenCon-JohnCook to get 75% off registration.

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Chances of being picked twice for drug testing

June 18, 2014
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Chances of being picked twice for drug testing

Suppose in a company of N employees, m are chosen randomly for drug screening [1]. In two independent screenings, what is the probability that someone will be picked both times? It may be unlikely that any given individual will be picked twice, while being very likely that someone will be picked twice. Imagine m employees […]

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