Question

Which of the following are true

Select one or more:

a. If you throw away a large number the initial samples (the burn in) from a Gibbs sampler what remains will approximate independent random samples from the stationary distribution.

b. Gibbs sampling can not be used to sample from a Bayesian network if we wish to condition on one of the variables taking a particular value.

c. Gibbs sampling is used when we wish to sample from a joint distribution when we only know the conditional distribution.

d. One of the advantages of using Gibbs sampling is that the samples it generates are independent of each other.

Answer #1

- The statement is
**not true**, because, the main idea of Gibbs sampling is to break the problem of sampling from the high-dimensional joint distribution into a series of samples from low-dimensional conditional distributions. Because these are done in a loop, samples are not independent and these dependence of the samples follow a Markov distribution. - This statement is
**true**because the Bayesian approach to inference involves simply summarizing the posterior density using basic sample statistics. - This statement is
**true**, because Gibbs sampling is applicable when the joint distribution is not known explicitly or is difficult to sample from directly, but the conditional distribution of each variable is known and is easy (or at least, easier) to sample from. - This statement is
**not true**, as the samples are auto correlated.

Which of the following statements are TRUE?
Note that there may be more than one correct answer; select all
that are true.
1. a) All else being equal, the standard deviation of the
sampling distribution of the sample mean will be smaller for n = 10
than for n = 40.
b) The value of a statistic does not vary from sample to
sample.
c) Statistics have sampling distributions.
d) The value of a parameter does not vary from sample...

A statistic is unbiased if...
you can choose more than one answers
a.
b. The mean of its sampling distribution is equal to the true
value of the parameter it estimates.
c. The value of the statistic is equal to the true value of the
parameter it estimates.
d. If samples of n random and independent observations are
repeatedly and independently drawn from a population, then as the
number of samples becomes very large, the mean of the sample means...

Which one of the following is a true statement about the
correlation coefficient r?
The unit of measure for r is the same as the unit of measure for
the response variable y. Values of r range from -∞ to +∞.
If the sign of r is negative, then increases in one variable
tend to be associated with decreases in the other variable.
The designations of which is the explanatory variable and which
is the response variable cannot be interchanged...

1. Which of the following statements are true of One-way
ANOVA test?
a. It is a robust test (with sufficiently large samples and
relatively equal groups) even when the sample data are
statistically significantly different from normal distribution.
b. All of the other statements are correct.
c. It involves a dependent variable measured on a continuous
scale.
d. It involves an independent variable measured on a categorical
scale with 2+ groups/categories.
e.It compares the mean/average scores of the 2+ groups...

Which of the following statements are true concerning the mean
of the differences between two dependent samples? (matched pairs)?
Select all that apply. A. The methods used to evaluate the mean of
the differences between two dependent variables apply if one has 60
weights of men from Ohio and 60 weights of men from New York. B. If
one has more than 5 matched pairs of sample? data, one can consider
the sample to be large and there is no...

(1) A Chi-squared test is typically used to test for any of the
following except which of the following?
(A) If a mathematical model accurately predicts our observed
frequencies of data values.
(B) If a mathematical model accurately predicts the total number
of observed data values.
(C) If a mathematical model accurately predicts the pattern of
our observed data values.
(D) Whether two factors present in a population are independent
of one another.
(E) Whether a series of populations experience...

T F 1. A p-value of .008 in hypothesis testing means there is
only a .8% chance we could get such sample statistics from the
population if the null hypothesis is as stated. Such an event is
considered unlikely and we would reject the null hypothesis.
T F 2. As a general rule in hypothesis testing, it is always
safer to set up your alternate hypothesis with a greater-than or
less-than orientation.
_____3. If the level of significance is .02...

Problem 1: Relations among Useful Discrete Probability
Distributions. A Bernoulli experiment consists of
only one trial with two outcomes (success/failure) with probability
of success p. The Bernoulli distribution
is
P (X = k) =
pkq1-k,
k=0,1
The sum of n independent Bernoulli trials forms a binomial
experiment with parameters n and p. The binomial probability
distribution provides a simple, easy-to-compute approximation with
reasonable accuracy to hypergeometric distribution with parameters
N, M and n when n/N is less than or equal...

True or false? A larger sample size produces a longer confidence
interval for μ.
False. As the sample size increases, the maximal error
decreases, resulting in a shorter confidence interval.True. As the
sample size increases, the maximal error decreases, resulting in a
longer confidence interval. True. As the
sample size increases, the maximal error increases, resulting in a
longer confidence interval.False. As the sample size increases, the
maximal error increases, resulting in a shorter confidence
interval.
True or false? If the...

R Code
Directions: All work has to be your own, you may not work in
groups. Show all work. Submit your solutions in a pdf document on
Moodle. Include your R code (which must be
commented and properly indented) in the pdf file. Name this pdf
file ‘your last name’-HW5.pdf. Also submit one text file with your
R code, which must be commented and properly indented. You may only
use ‘runif’ to generate random numbers; other random number
generating functions...

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