- 16.16.1: Refer to the results of Example 16.2 given in Table 16.1. a Which o...
- 16.16.2: Define each of the following: a Prior distribution for a parameter ...
- 16.16.3: Applet Exercise The applet Binomial Revision can be used to explore...
- 16.16.4: Applet Exercise Scroll down to the section Applet with Controls on ...
- 16.16.5: Repeat the directions in Exercise 16.4, using a beta prior with = 1...
- 16.16.6: Suppose that Y is a binomial random variable based on n trials and ...
- 16.16.7: In Section 16.1 and Exercise 16.6, we considered an example where t...
- 16.16.8: Refer to Exercise 16.6. If Y is a binomial random variable based on...
- 16.16.9: Suppose that we conduct independent Bernoulli trials and record Y ,...
- 16.16.11: Let Y1, Y2,..., Yn denote a random sample from a Poisson-distribute...
- 16.16.12: Let Y1, Y2,..., Yn denote a random sample from a normal population ...
- 16.16.13: Applet Exercise Activate the applet Binomial Revision and scroll do...
- 16.16.14: Applet Exercise Refer to Exercise 16.13. Select a value for the tru...
- 16.16.15: Applet Exercise In Exercise 16.7, we reconsidered our introductory ...
- 16.16.16: Applet Exercise Repeat the instructions for Exercise 16.15, assumin...
- 16.16.17: Applet Exercise In Exercise 16.9, we used a beta prior with paramet...
- 16.16.18: Applet Exercise In Exercise 16.10, we found the posterior density f...
- 16.16.19: Applet Exercise In Exercise 16.11, we found the posterior density f...
- 16.16.21: Applet Exercise In Exercise 16.15, we determined that the posterior...
- 16.16.22: Applet Exercise Exercise 16.16 used different prior parameters but ...
- 16.16.23: Applet Exercise In Exercise 16.17, we obtained a beta posterior wit...
- 16.16.24: Applet Exercise In Exercise 16.18, we found the posterior density f...
- 16.16.25: Applet Exercise In Exercise 16.19, we found the posterior density f...
- 16.16.26: Applet Exercise In Exercise 16.20, we determined the posterior of v...
Solutions for Chapter 16: Introduction to Bayesian Methods for Inference
Full solutions for Mathematical Statistics with Applications | 7th Edition
`-error (or `-risk)
In hypothesis testing, an error incurred by rejecting a null hypothesis when it is actually true (also called a type I error).
a-error (or a-risk)
In hypothesis testing, an error incurred by failing to reject a null hypothesis when it is actually false (also called a type II error).
A formula used to determine the probability of the union of two (or more) events from the probabilities of the events and their intersection(s).
All possible (subsets) regressions
A method of variable selection in regression that examines all possible subsets of the candidate regressor variables. Eficient computer algorithms have been developed for implementing all possible regressions
Asymptotic relative eficiency (ARE)
Used to compare hypothesis tests. The ARE of one test relative to another is the limiting ratio of the sample sizes necessary to obtain identical error probabilities for the two procedures.
Binomial random variable
A discrete random variable that equals the number of successes in a ixed number of Bernoulli trials.
Box plot (or box and whisker plot)
A graphical display of data in which the box contains the middle 50% of the data (the interquartile range) with the median dividing it, and the whiskers extend to the smallest and largest values (or some deined lower and upper limits).
Central limit theorem
The simplest form of the central limit theorem states that the sum of n independently distributed random variables will tend to be normally distributed as n becomes large. It is a necessary and suficient condition that none of the variances of the individual random variables are large in comparison to their sum. There are more general forms of the central theorem that allow ininite variances and correlated random variables, and there is a multivariate version of the theorem.
The probability of an event given that the random experiment produces an outcome in another event.
A linear function of treatment means with coeficients that total zero. A contrast is a summary of treatment means that is of interest in an experiment.
In hypothesis testing, this is the portion of the sample space of a test statistic that will lead to rejection of the null hypothesis.
Cumulative sum control chart (CUSUM)
A control chart in which the point plotted at time t is the sum of the measured deviations from target for all statistics up to time t
A probability distribution for a discrete random variable
A concept in parameter estimation that uses the variances of different estimators; essentially, an estimator is more eficient than another estimator if it has smaller variance. When estimators are biased, the concept requires modiication.
Exponential random variable
A series of tests in which changes are made to the system under study
Extra sum of squares method
A method used in regression analysis to conduct a hypothesis test for the additional contribution of one or more variables to a model.
A method of variable selection in regression, where variables are inserted one at a time into the model until no other variables that contribute signiicantly to the model can be found.
Fractional factorial experiment
A type of factorial experiment in which not all possible treatment combinations are run. This is usually done to reduce the size of an experiment with several factors.
The geometric mean of a set of n positive data values is the nth root of the product of the data values; that is, g x i n i n = ( ) = / w 1 1 .
The harmonic mean of a set of data values is the reciprocal of the arithmetic mean of the reciprocals of the data values; that is, h n x i n i = ? ? ? ? ? = ? ? 1 1 1 1 g .