Handouts for 2017

The TA will have some material for the ** tutorial**. The handouts used for the tutorial are here .

**Old term tests and
exams** are posted here in a password protected
site. The password will be given in a
lecture class.

**Handouts used in the lectures.**

Jan 6, 2017 : course outline and ch8-2intro.pdf

This uses data from the text, It comes with a CD with the text. The data set is also available from http://www.stat.berkeley.edu/~rice/Book3ed/ where you click on the Data Sets link. It comes in various formats. Often csv format is most useful as many statsitical packages can read these, including R. ASCII is also a useful version in the same sense.

illinois60.txt this is a data set that we use for some gamma fit data examples later in the course.

Jan 9, 2017 : Ch8-StatModels.pdf This handout is mostly material not from the text. It gives some background ideas and discussion of statistical modeling and some settings for which it is useful.

Jan 11 : continue with Jan 9 handouts + ch8-3-estimator-prop.pdf

for Jan 13 or 16 2017 : ch8-3-Consistency-ContinuousFunctions.pdf

Jan 18, 2017 : continue with additional comments on simulation.

Ch8-4MethodofMoments.pdf and Ch8-5-MLE-I.pdf These handouts are used for a few lectures.

Jan 20, 2017 : Gamma-Method-of-Moments.R

and data for the gamma fitting example : Data\illinois60.txt , Data\illinois61.txt , Data\illinois62.txt , Data\illinois63.txt , Data\illinois64.txt

In earlier courses
students studied these as ** point estimators** but for statistical
inference we will also require the distribution of these estimators. Sometimes we can obtain the distribution but
more often we will need an approximation to the distribution. Algebraic forms for these approximations is
often the most useful.

For upcoming lectures : distribution of estimators DeltaMethod.pdf (this is an extension of the moment approximation idea from Section 4.6) and Ch8-5-MLE-II.pdf

Jan 23 and 25, 2017 : Continue with MLE-1. Next consider the sampling distribution of the method of moments and MLE estimators. Delta method and continue with MLE. Example in R gamma-mle.r

January 30, 2017 : The first term test is next week, on February 8, during the tutorial time.

The exam will also include a formula sheet formulae-Stat3858.pdf which includes some information on the various distributions.

The material covered on this test is the material in the handouts, which includes corresponding material for Rice Sections 8.2, 8.3, 8.4 + Delta method, 8.5 (we should finish this material by Friday).

The refers to something called the parametric bootstrap. This will not be on the test.

February 1, 2017 : continue with regular MLE.

February 3, 2017 : The regular MLE case allows us to find an approximation for the distribution of the MLE.

The text also discusses a simulation method called the parametric bootstrap. We see how to implement this in parametricboot.r and its relation to the simulation method discussed

Feb 6, 2017 : parametric bootstrap

Ch8-7and8-CramerRao-SufficientStats This material is not covered on Test 1, but the notion of sufficient statistics is helpful in simplifying the likelihood or log likelihood for most of the regular statistical models.

Feb 8, 201 7 : desk measurements in cm DeskFeb2017.csv One of the interesting things about this data set is one point seems to ber very different. Is it an outlier or some type of invalid data point?

February 10, 2017 : today finish discussion about Cramer-Rao and Rao-Blackwell. Then begin the material related to hypothesis testing etc in Chapter 9. ch9-LR-1.pdf . This file is updated as of March 8, 2017 , so that the power function in terms of beta is now the same as in the Rice text.

February 13, 2017 : np-lemma.pdf and continue with Likelihood ratio decision rules. This file is updated as of March 8, 2017 , so that the power function in terms of beta is now the same as in the Rice text.

February 15, 2017 : continue with generalized likelihood ratio. Two additional examples

exponential ExponentialLikelihoodRatio.pdf

February 17, 2017 : continue with the exponential example

Multinomial MultinomialLikelihoodRatio.pdf from the material in Section 8.5.1

Brief solutions for the Feb 2017 are posted in the old exams folder (password protected).

February 27, 2017 : Return test 1.

Continue with Multinomial GLR from before break week and the material from Chapter 13.3 and 13.4 ContingencyTables.pdf

Feb 27, 2017 : Histogram of first term test grades Feb2017.pdf The marks for the three questions are 16, 17 and 17.

Boxplots for the 3 questions : boxplotFeb2017.pdf

Summary for test 1 :

Min. 1st Qu. Median Mean 3rd Qu. Max.

9.0 29.8 35.5 35.8 42.0 50.0

March 1, 2017 : continue with contingency table, just test of independence for now. Cold data example cold-eg.r

Chapter 11 two sample normal (sections 11.2.1 and 11.2.2) twosamp-normal.pdf

After this return to contingency table to two and multiple independent samples.

March 3, 2017 : continue with two sample normal. Also consider some two sample non normal settings.

Continue either today or Monday with contingency tables, but with data generated from independent samples. This will be the analogue or two or multiple independent samples problems.

JaneAusten-eg.r and the associated data Sec13-3-JAustenData.txt

March 6, 2017 : Continue with contingency tables and the multiple independent samples problem.

March 8, 2017 : The exam link now contains the previous two years term test 2.

Throughout the course we have mentioned the need for model checking. We now consider some of these ideas and in particular the construction of QQ plots.

Momapprox.pdf This is a handout from Stat 3657, but the last section of this discusses QQ plots. It deals with normal QQ plots plus some other QQ plots.

Rscript to construct some qq plots qqplotsintro.r

Some other miscellaneous goodness of fit tests normtest.r Sec 9.9 Jarque-Bera and Kolmogorov-Smirnov statistic

**Assignment 3 is due
on March 15, 2017. Correction to
Assignment**

**9.11.4 : do
only parts (a), (b)**

**11.6.21 : skip part (b) (non parametric method)**

March 13, 2017 : Continue with the model checking methods and QQ plots.

March 15, 2017 : Last
comments on various aspect of model diagnostics. Data sometimes need *cleaning*, a topic that is
dealt with more in a data analysis course.
We can look at one aspect using the in class experiment of the desk
measurement.

DeskFeb2017.xlsx desk measurement data from class in February

DeskFeb2017.r R script file for analysis of this data.

Power of a test is a topic related to hypothesis testing. We will spend only a brief amount of time on this topic.

March 17, 2017 : Up to this point we have dealt with parametric models and inference for these models. Modern statistical methods includes the nonparametric bootstrap, usually simply called the bootstrap.

The bootstrap method is not discussed in Rice. Here is a brief introduction to the bootstrap.

March 20, 2017

First implement the bootstrap for a specific example using our own code boot-1.r

For the example in boot-1 I used some data from a particular model, which is not needed or used in the bootstrap. We compare the correct (but usually unknown model) distribution with the bootstrap distribution of a particular r.v. needed for a confidence interval calculation. boot-1B.r

There are two often used packages for nonparametric bootstrap. We use these in the following examples

boot-2.r Uses a package written by A Canty, McMaster University

boot-ET.r Uses a package by Efron (modern originator of the bootstrap) and Tibshirani (a Canadian, former professor at Toronto and now at Stanford)

boot-realdata examples.r Apply the bootstrap method to two data sets that we looked at earlier in the course.

A two sample problem similar to one of the homework problems to estimate P(X>Y) based on two independent random samples boot-2samp.r - corrected from class and some comments added (March 24, 2017)

March 24, 2017 : A few additional comments on bootstrap.

Bayesian methods introduction BayesMethods.pdf

March 27, 2017 : Office hours are cancelled for today.

Continue with Bayesian methods. We also look at one non-conjugate prior example BayesEgnonconjugate.pdf for which we can obtain algebraic answers, that is a formula.

March 31, 2017 and April 3 : Bayes examples in R

Bayes-3.R Binomial example

Bayes-2.R Poisson example

cointipping2.r Coin tipping; we only use the first part of this R script, and omit how to simulate from this prior. Corrected from class to give the normal approximation for the posterior. (corrected for h = increment in Riemann partial sum to approximated the integrals as needed.)

cointipping.r Use a few different priors, some of which are not conjugate prior

and coin tipping data cointipping.csv The coin tipping data is from a class several years ago where Dr Murdoch had students do the coin tipping and record the data. These examples include using a conjugate and some non-conjugate priors.

April 5, 2017 : Classes end on Friday April 7. Today review and questions.

I will hold an extra office hour today from 2:30-3:30 PM. There will be an office hour as per usual on Thursday 2:30-3:30 PM. Friday will be taken up with grad student meetings, administrative details and exam printing, so I will not have a Friday office hour.

There is a tutorial today, the last one before the exam.