Math and statistics articles by category
This page categorizes my informal math and statistics articles and blog posts. See this page for informal articles on other topics such as programming. See also journal articles and technical reports.
Categories
Elementary
Preventing and detecting errors
Interpreting and misinterpreting probabilities
Modeling
Clinical trials
Mathematical statistics
Random number generation
Practicalities
Pure math
Elementary
Tukey
tallying
Honeybee geneology
Coping with exponential growth
Selection bias and bombers
Canonical example of Bayes' theorem in detail
Linear
interpolation
Quadratic interpolation
Preventing and detecting errors
In praise of tedious proofs
Coloring numbers
Proofs of false statements
Literate programming and statistics
Irreproducible analysis
Programming the last mile
Complementary validation
Troubleshooting
Sweave
Preventing an unpleasant Sweave surprise
Interpreting and misinterpreting probabilities
Plausible reasoning
How
loud is the evidence?
Learning is not the same as gaining information
Laws of large numbers and small numbers
The law of small numbers
Probability and information
Example of the law of small numbers
What a probability means
Irrelevant uncertainty
False positives for medical papers
False positives for medical tests
Most published research results are false
Musicians, drunks, and Oliver Cromwell
Modeling
Thick tails
Why heights are normally distributed
Why heights are not normally distributed
How to linearize data for regression
Approximate problems and approximate solutions
Wine, Beer, and Statistics
Clinical trials
Stopping trials of ineffective drugs earlier
Three ways of tuning an adaptively randomized trial
Galen and clinical trials
Dose-finding: why start at the lowest dose?
Innovation II
(scurvy trial from 1601)
Most published research results are false
False positives for medical papers
Population
drift
Randomized trials of parachute use
Small effective sample size does not mean uninformative
Mathematical statistics
Clickable chart of distribution relationships
Conjugate prior relationships
Robust priors
Quantifying the error in the central limit theorem
Four characterizations of the normal distribution
Random inequalities
I,
II,
III,
IV,
V,
VI,
VII
Estimating Cauchy distribution location
parameter
Inverse gamma distribution
Negative binomial distribution
Relating two definitions of expectation
Bias
Four types of errors
Stochastic independence
Normal approximation details:
beta
binomial
gamma
Poisson
Student-t
Poisson approximation to binomial
Relative error in normal
approximations
Stable distributions
Unbiased estimators can be terrible
Random number generation
Pitfalls in Random Number Generation
Simple random number generation
Random number generator controversy
Random number generation in C++ TR1
Practicalities
IEEE arithmetic exceptions in C++
Computing standard deviation
Fibonacci numbers at work (numerical integration)
Computing the inverse of the normal CDF
Approximate problems and approximate solutions
How to calculate binomial probabilities
Calculating
percentiles in memory-bound applications
Avoiding
overflow, underflow, and loss of precision
Overflow and loss of precision
What to make “u” in integration by parts
Integration and pragmatism
Quick TeX to graphic utility
LaTeX on Windows
Everything begins with “p”
Asymptotic notation
R for Programmers coming from other languages
Step size for
numerical differential equations
The error function and the normal distribution
Working with distributions in
Mathematica and R/S-PLUS
Random number generation in C++
Innovation IV
(Tukey on efficiency)
Pure math
Modes of convergence
Binomial coefficient generalizations
Multi-index notation
Computing binomial coefficients
Selecting with replacement (Stanley's
symbol)
Jenga
mathematics
What is the cosine of a matrix
Orthogonal polynomials
Chebyshev polynomials
Hypergeometric functions