A Primer on Probability

Probability Primer 1 Running head: PROBABILITY PRIMER A Primer on Probabilistic Inference

A Primer on Discrete Probability

1 Probability Theory over Countable Spaces Definition 1 (Countable Probability Space). A Countable Probability Space is composed of the tuple (Ω,Pr). • Countable Sample Space Ω The sample space is a set of outcomes for a particular experiment. “Countable” means that either the size of Ω is finite or there is a one-to-one and onto correspondence between the the elements of Ω and the set of Natur...

A Primer on Probability

Example 3 A coin toss is an example of a Bernoulli trial, which in general is an experiment with only two possible outcomes: success, which occurs with probability p; and failure, which occurs with probability q := 1−p. Of course, success and failure are arbitrary names, which can be changed as convenient. In the case of a coin, we might associate success with the outcome that the coin comes up...

A Primer on Probability

Example 3 A coin toss is an example of a Bernoulli trial, which in general is an experiment with only two possible outcomes: success, which occurs with probability p; and failure, which occurs with probability q := 1−p. Of course, success and failure are arbitrary names, which can be changed as convenient. In the case of a coin, we might associate success with the outcome that the coin comes up...

A Primer on Bayesian Approaches to Hypothesis-testing

The Bayesian approach to testing hypotheses has two critical elements. First, a Bayesian approach stands the classical (by which I mean frequentist but I can’t bring myself to type these “ist” designations) approach on its head. In the classical approach, our questions revolve around the probability of the data, given a specific hypothesis. In the Bayesian approach, our questions revolve around...

Primer Design and Marker Clustering for Multiplex SNP-IT Primer Extension Genotyping Assay using Statistical Modeling

MOTIVATION The optimization of the primer design is critical for the development of high-throughput SNP genotyping methods. Recently developed statistical models of the SNP-IT primer extension genotyping reaction allow further improvement of primer quality for the assay. RESULTS Here we describe how the statistical models can be used to improve primer design for the assay. We also show how to...