# Physics 391 Fall 2010Schedule

I will include here relevant readings, documents and links for each lecture. Always under construction! This page is subject to modification as the semester progresses-- often topics can take longer than initially planned, and we may make interesting diversions if opportunities arise. The likely material to be covered can be found here. Readings (if there are any) and more details for a given lecture will appear at a day or two before the lecture, and I may also add notes and links after a given lecture has taken place.

## Monday, September 27: Lecture 1   Introduction and Review

This lecture will be review for most people. I will cover some basic concepts and definitions: interpreting uncertainties, statistical and systematic uncertainties, mean and variance of a distribution, propagation of uncertainties.

• I expect everyone to already have a grasp of experimental error analysis at the level of the links below:
• WUN2K 1
• FAQ 1

Optional Homework 1 available; this one need not be handed in.

## Monday, October 4: Lecture 2   Probability, Probability Distributions

I will review some basic ideas of probability, including Bayes' Law. Then I will go through some common and useful probability distributions and their properties: binomial, Poisson and Gaussian distributions. The latter two represent different limits of the binomial distribution.

## Tuesday, October 5: Lecture 3   Estimating Means and Uncertainties

During the first part of the lecture, I will cover estimation of the mean of a distribution and the uncertainty on the mean (the "error on the mean") assuming Gaussian errors. In the second part, I will start to discuss error matrices; this topic will be continued after the break.

Homework 2 available

## Monday, October 18: Lecture 4   Correlations, Error Ellipses and Error Matrices

After a brief review of covariance in error propagation (introducing one new quantity, the dimensionless "correlation coefficient"), I will pick up where we left off last class. We will discuss properties of error ellipses and error matrices for the case when random variables are correlated with each other. Finally I will enumerate practical uses of error matrices; we will go through a number of examples next class.

## Tuesday, October 19: Lecture 5   Error Matrices: Examples

I will cover several examples of the use of error matrices.

## Monday, October 25: Lecture 6   Parameter Estimation

I will cover two useful methods of parameter estimation. The "maximum likelihood" method is quite general and powerful, although can have some practical drawbacks. The "least squares" method, which can be considered a special case of the likelihood method, works well in many common cases.

Homework 3 available

## Monday, November 1: Lecture 7   Uncertainties on Estimated Parameters

I will first discuss how one determines uncertainties on parameters estimated by the maximum likelihood method. Then we'll turn attention to least squares: I will cover estimation of parameters by a matrix method for the linear case (least squares fit to functions linear in the parameters) and determination of the uncertainties in this case.

• Correction to lecture notes: for a linear transformation x' = Bx, the error matrix transforms as M' = B M B^T, not M' = B^T M B (to see this, write out entries for a 2x2 matrix).
• WUN2K 7
• FAQ 7
• Fit example

## Tuesday, November 2: Lecture 8   Confidence Intervals and Hypothesis Testing

I will first discuss how one determines confidence intervals for measured parameters: this can usually be done using a "Neyman construction". Next I will cover the basics of hypothesis testing using chi-squared.