An immunoassay's minimal detectable concentration (MDC), the smallest analyte concentration the assay can reliably measure, is one of its most important properties. Bayes' theorem is used to unify the five current mathematical MDC definitions. The unified definition has significant implications for defining positive results for screening and diagnostic tests, setting criteria for immunoassay qu...

The concentration of measure phenomenon was first discovered in the 1930’s by Paul Lévy and has been investigated since then, with increasing intensity in recent decades. The probabilitytheoretic results have been gradually percolating throughout the mathematical community, finding applications in Banach space geometry, analysis of algorithms, statistics and machine learning. There are several ...

Radon, a naturally occurring radioactive element, was discovered in the year 1900, and high lung cancer rates among miners were recognized hundreds of years before that, but it wasn’t until the 1950s that researchers accepted that exposure to radon decay products was one of the major causes of the very high lung cancer rate among miners. Risks to the general population weren’t recognized until ...

The lossless codification of stationary memoryless binary sources using block coding is studied with the additional constraint of requiring only two codeword lengths. The fundamental coding scheme of Shannon based on the asymptotic equipartition property shows the existence of block codes of this type with average codeword lengths per source output converging to the binary entropy as the block ...

A weakly continuous near-action of a Polish group G on a standard Lebesgue measure space (X,μ) is whirly if for every A ⊆ X of strictly positive measure and every neighbourhood V of identity in G the set V A has full measure. This is a strong version of ergodicity, and locally compact groups never admit whirly actions. On the contrary, every ergodic near-action by a Polish Lévy group in the sen...

This text contains some of the material presented at the Summer

reliability. We had minor mechanical issues: capturing angle of smart device getting displaced; device getting knocked off the table; and charge cord dislodging. Auto-lock needs to be turned off on the capturing smart device. On one occasion, the camera app needed restarting due to automatic software update. These glitches were each corrected by a phone call to the nurse or by the provider in p...

2 Agnostic Learning We will proceed without making any assumptions on the distribution PXY . This situation is often termed as Agnostic Learning. The root of the word agnostic literally means not known. The term agnostic learning is used to emphasize the fact that often, perhaps usually, we may have no prior knowledge about PXY and f∗. The question then arises about how we can reasonably select...

We give an elementary algorithmic argument that sheds light on the concentration of measure phenomenon observed in the sum of independent random variables. Roughly speaking, we observe that without concentration of measure, it would be possible to predict the outcome of a fair coin toss with probability greater than 1/2. We use this idea to derive an alternative proof for a particular case of t...

The maximum a-posteriori (MAP) perturbation framework has emerged as a useful approach for inference and learning in high dimensional complex models. By maximizing a randomly perturbed potential function, MAP perturbations generate unbiased samples from the Gibbs distribution. Unfortunately, the computational cost of generating so many high-dimensional random variables can be prohibitive. More ...