# Blog Archives

## Principal curves example (Elements of Statistical Learning)

April 21, 2016
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The bit of R code below illustrates the principal curves methods as described in The Elements of Statistical Learning, by Hastie, Tibshirani, and Friedman (Ch. 14; the book is freely available from the authors' website). Specifically, the code generates some bivariate data that have a nonlinear association, initializes the principal curve using the first (linear) principal … Continue reading...

## My Poster at Rocky 2015: Estimating parameters of the Hodgkin-Huxley cardiac cell model by integrating raw data from multiple types of voltage-clamp experiments

December 18, 2015
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I'm recently returned from the 2015 Rocky Mountain Bioinformatics Conference, where I presented the above poster. This is work with a colleague, Rick Gray, at the FDA. He and I collaborate on our NIH award "Optimal Design of Challenge-Response Experiments in Cardiac Electrophysiology" (HL118392) The (original) poster abstract is below, but the poster content is … Continue reading...

## Reference Chart for Precision of Wilson Binomial Proportion Confidence Interval

October 16, 2015
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I am often asked about the number of subjects needed to study a binary outcome, which usually leads to a discussion of confidence intervals for binary proportions, and the associated precision. Sometimes the precision is quantified as the width or half-width of a 95% confidence interval. For proportions, I like the Wilson score interval because … Continue reading...

## Delta Method Confidence Bands for Gaussian Mixture Density (Can Behave Badly)

October 9, 2015
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This post follows from a previous post (2798), in which the delta method was used to create an approximate pointwise 95% confidence band for a Gaussian density estimate. Note that the quality of this estimate was not assessed (e.g., whether the band has the correct pointwise coverage). Here we extend that approach to the Gaussian … Continue reading...

## Delta Method Confidence Bands for Gaussian Density

October 2, 2015
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During one of our Department's weekly biostatistics "clinics", a visitor was interested in creating confidence bands for a Gaussian density estimate (or a Gaussian mixture density estimate). The mean, variance, and two "nuisance" parameters, were simultaneously estimated using least-squares. Thus, the approximate sampling variance-covariance matrix (4x4) was readily available. The two nuisance parameters do not … Continue reading...

## Notes on Multivariate Gaussian Quadrature (with R Code)

September 25, 2015
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Statisticians often need to integrate some function with respect to the multivariate normal (Gaussian) distribution, for example, to compute the standard error of a statistic, or the likelihood function in of a mixed effects model. In many (most?) useful cases, these integrals are intractable, and must be approximated using computational methods. Monte-Carlo integration is one

## Recipe for Computing and Sampling Multivariate Kernel Density Estimates (and Plotting Contours for 2D KDEs).

September 19, 2015
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The code snippet below creates the above graphic: ## radially symmetric kernel (Gussian kernel) RadSym

## Recipe for Centered Horizontal Stacked Barplots (Useful for Likert scale responses)

September 8, 2015
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There is a nice package and paper about this here: http://www.jstatsoft.org/v57/i05/paper. However, the associated code is complex and uses lattice. Here's a brief recipe using base graphics that implements the above figure: set.seed(40) x

## Nested vs. Non-nested (crossed) Random Effects in R

June 13, 2015
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The R script below illustrates the nested versus non-nested (crossed) random effects functionality in the R packates lme4 and nlme. Note that crossed random effects are difficult to specify in the nlme framework. Thus, I've included a back-of-the-envelope (literally a scanned image of my scribble) interpretation of the 'trick' to specifying crossed random effects for

## Simulation-based power analysis using proportional odds logistic regression

May 22, 2015
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Consider planning a clinicial trial where patients are randomized in permuted blocks of size four to either a 'control' or 'treatment' group. The outcome is measured on an 11-point ordinal scale (e.g., the numerical rating scale for pain). It may be reasonable to evaluate the results of this trial using a proportional odds cumulative logit