Applied Math Seminar: Measurement Error Modeling using Empirical Phase Functions (Prof. Cornelis Potgieter, Southern Methodist University)

Measurement error, formally defined as the difference between the measured value and the true value of a quantity of interest, is ubiquitous. When a doctor takes your blood pressure, the instrumentation may not be properly calibrated and the reading is subject to error. When completing an online Harry Potter Sorting Hat quiz, you may accidentally click the wrong option for a specific question and find yourself in House Slytherin!. The effect of measurement error is sometimes insignificant, but there are instances where ignored measurement error can be rather consequential. You definitely do not want your doctor to put you on a long-term medication for managing high BP due to an erroneous measurement!

In this talk, I will discuss two problems frequently encountered when measurement error is present in sampled data. The first of these is known as density deconvolution, which involves estimating the density function of the population of interest. When measurement error is present, a density function estimated from the sample will have inflated variance, and interesting population features may be obscured. The second problem relates to regression modeling when the predictor variable is subject to measurement error. Here, when using the contaminated data to estimate the regression model, parameter estimates will be biased unless measurement error is properly adjusted for. I will show how the empirical phase functions, a transformation of the sample data to the complex plane, can be used to find solutions to both of these problems.

Oh, and don’t worry too much about your doctor unnecessarily prescribing blood pressure medication. She is well aware that measurement error exists, and will re-take the measurement, and also perform other tests before making a diagnosis. Being sorted into House Slytherin though, there you are on your own…