- 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).
In hypothesis testing, a region in the sample space of the test statistic such that if the test statistic falls within it, the null hypothesis cannot be rejected. This terminology is used because rejection of H0 is always a strong conclusion and acceptance of H0 is generally a weak conclusion
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
In statistical hypothesis testing, this is a hypothesis other than the one that is being tested. The alternative hypothesis contains feasible conditions, whereas the null hypothesis speciies conditions that are under test
See Arithmetic mean.
Sequences of independent trials with only two outcomes, generally called “success” and “failure,” in which the probability of success remains constant.
Data consisting of counts or observations that can be classiied into categories. The categories may be descriptive.
Components of variance
The individual components of the total variance that are attributable to speciic sources. This usually refers to the individual variance components arising from a random or mixed model analysis of variance.
The mean of the conditional probability distribution of a random variable.
A graphical display used to monitor a process. It usually consists of a horizontal center line corresponding to the in-control value of the parameter that is being monitored and lower and upper control limits. The control limits are determined by statistical criteria and are not arbitrary, nor are they related to speciication limits. If sample points fall within the control limits, the process is said to be in-control, or free from assignable causes. Points beyond the control limits indicate an out-of-control process; that is, assignable causes are likely present. This signals the need to ind and remove the assignable causes.
Another name for factors that are arranged in a factorial experiment.
A probability distribution for a discrete random variable
Discrete random variable
A random variable with a inite (or countably ininite) range.
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.
A study in which a sample from a population is used to make inference to the population. See Analytic study
An analysis of how the variance of the random variable that represents that output of a system depends on the variances of the inputs. A formula exists when the output is a linear function of the inputs and the formula is simpliied if the inputs are assumed to be independent.
The variance of an error term or component in a model.
Estimate (or point estimate)
The numerical value of a point estimator.
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.
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 .