Posts Tagged ‘ statistics ’

EM algorithm revisited

November 20, 2014
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EM algorithm revisited

On this Tuesday, Professor Xuming He presented their recent work on subgroup analysis, which is very interesting and useful in reality. Think about the following very much practical problem (since the drug is expensive or has certain amount of side effect): If you are given the drug response, some baseline covariates which have nothing to […]

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Christian Robert Shows that the Sample Median Cannot Be a Sufficient Statistic

Christian Robert Shows that the Sample Median Cannot Be a Sufficient Statistic

I am grateful to Christian Robert (Xi’an) for commenting on my recent Mathematical Statistics Lessons of the Day on sufficient statistics and minimally sufficient statistics. In one of my earlier posts, he wisely commented that the sample median cannot be a sufficient statistic.  He has supplemented this by writing on his own blog to show that […]

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Mathematical Statistics Lesson of the Day – Minimally Sufficient Statistics

Mathematical Statistics Lesson of the Day – Minimally Sufficient Statistics

In using a statistic to estimate a parameter in a probability distribution, it is important to remember that there can be multiple sufficient statistics for the same parameter.  Indeed, the entire data set, , can be a sufficient statistic – it certainly contains all of the information that is needed to estimate the parameter.  However, […]

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Nominal, Ordinal, Interval, Schmordinal

November 18, 2014
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Nominal, Ordinal, Interval, Schmordinal

Everyone wants to learn about ordinal data! I have a video channel with about 40 videos about statistics, and I love watching to see which videos are getting the most viewing each day. As the Fall term has recently started … Continue reading →

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Lucien Le Cam: “The Bayesians Hold the Magic”

November 18, 2014
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Lucien Le Cam: “The Bayesians Hold the Magic”

Today is the birthday of Lucien Le Cam (Nov. 18, 1924-April 25,2000): Please see my updated 2013 post on him.  Filed under: Bayesian/frequentist, Statistics

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Le Monde puzzle [#887bis]

November 15, 2014
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Le Monde puzzle [#887bis]

As mentioned in the previous post, an alternative consists in finding the permutation of {1,…,N} by “adding” squares left and right until the permutation is complete or no solution is available. While this sounds like the dual of the initial solution, it brings a considerable improvement in computing time, as shown below. I thus redefined […]

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Why the Law of Likelihood is bankrupt–as an account of evidence

November 15, 2014
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Why the Law of Likelihood is bankrupt–as an account of evidence

There was a session at the Philosophy of Science Association meeting last week where two of the speakers, Greg Gandenberger and Jiji Zhang had insightful things to say about the “Law of Likelihood” (LL)[i]. Recall from recent posts here and here that the (LL) regards data x as evidence supporting H1 over H0   iff Pr(x; H1) > Pr(x; H0). On many accounts, […]

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Le Monde puzzle [#887]

November 14, 2014
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Le Monde puzzle [#887]

A simple combinatorics Le Monde mathematical puzzle: N is a golden number if the sequence {1,2,…,N} can be reordered so that the sum of any consecutive pair is a perfect square. What are the golden numbers between 1 and 25? Indeed, from an R programming point of view, all I have to do is to […]

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Can we try to make an adjustment?

November 14, 2014
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Can we try to make an adjustment?

In most of our data science teaching (including our book Practical Data Science with R) we emphasize the deliberately easy problem of “exchangeable prediction.” We define exchangeable prediction as: given a series of observations with two distinguished classes of variables/observations denoted “x”s (denoting control variables, independent variables, experimental variables, or predictor variables) and “y” (denoting […] Related posts: Don’t use correlation to track prediction performance Reading the Gauss-Markov theorem Bad…

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How to Summarize a 2D Posterior Using a Highest Density Ellipse

November 13, 2014
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How to Summarize a 2D Posterior Using a Highest Density Ellipse

Making a slight digression from last month’s Probable Points and Credible Intervals here is how to summarize a 2D posterior density using a highest density ellipse. This is a straight forward extension of the highest density interval to the situati...

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