Deck 20: Likelihood

Question 1

Likelihood measures which of the following?

A) How probable it is that the null hypothesis is false
B) How probable it is that the parameter equals a certain value
C) The probability of obtaining the sample values if the alternative hypothesis is true
D) The probability of obtaining the sample values if the parameter equals a certain value

Answer 1

D

Question 2

Which of the following best describes the maximum likelihood estimate?

A) The likelihood value with the highest probability
B) The likelihood value with the highest value
C) The parameter closest to the sample likelihood
D) The parameter that results in the highest likelihood

Answer 2

D

Question 3

When comparing alternative phylogenies to decide on the most probable one, which best describes the process?

A) The likelihood of each phylogeny, based on the gene sequence data, is calculated and the one with the highest likelihood is deemed most likely.
B) The likelihood of each phylogeny, based on the gene sequence data, is calculated and the one with the lowest likelihood is deemed most likely.
C) The likelihood of each phylogeny, based on the gene sequence data, is calculated and the one with P < 0.05 is deemed most likely.
D) The likelihood of each phylogeny, based on the gene sequence data, is calculated and the one with P > 0.05 is deemed most likely.

Answer 3

A

Question 4

When using likelihood to find the locations of genes that cause disease, which best describes the process?

A) The likelihood that a gene located at each marker site causes the disease was compared to 0.05
B) The likelihood that a gene located at each marker site causes the disease was compared to the null hypothesis.
C) The likelihood that a gene located at each marker site causes the disease was compared to the likelihood that a gene located at each marker site is unrelated to the disease.
D) The likelihood that a gene located at each marker site causes the disease was compared to the likelihood that a gene located at each marker site prevents the disease.

Question 5

The maximum likelihood estimate (MLE) can be determined by doing which of the following?

A) Across the whole range of possible parameter values, we calculate the likelihood and the MLE is the largest probability value.
B) Across the whole range of possible parameter values, we calculate the likelihood and the MLE is the smallest probability value.
C) Across the whole range of possible parameter values, we calculate the log-likelihood and the MLE is the parameter that gives the largest value.
D) Across the whole range of possible parameter values, we calculate the log-likelihood and the MLE is the parameter that gives the smallest value.

Question 6

Which of the following equations correctly shows the relationship between likelihoods and probabilities?

A) pr [ data | parameter = value ] = L [ data | value ]
B) pr [ data | parameter = value ] = L [ value | data ]
C) pr [ parameter = value | data ] = L [ data | value ]
D) pr [ parameter = value | data ] = L [ value | data ]

Question 7

To find the 95% confidence interval for the maximum likelihood estimate (MLE), we can do which of the following?

A) Finding the range of parameter values with log-likelihood estimates within 0.05 of the MLE
B) Finding the range of parameter values with log-likelihood estimates within 0.95 of the MLE
C) Finding the range of parameter values with log-likelihood estimates within 1.92 of the of the MLE
D) Finding the range of parameter values with log-likelihood estimates within 1.96 of the log of the MLE

Question 8

In the log-likelihood figure shown, which of the following ranges best matches the 95% confidence interval for the values on the X-axis?
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A) 25 to 70
B) 30 to 65
C) 35 to 60
D) 40 to 55

Question 9

In the log-likelihood figure shown, which of the following ranges best matches the 95% confidence interval for the values on the X-axis?
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A) 58 to 78
B) 60 to 76
C) 62 to 74
D) 64 to 72

Question 10

Which of the following is the correct test statistic for a likelihood ratio test?

A) $G=\ln \left(\frac{L\left[\text { parameter value for } H_{0} \mid \text { data }\right]}{L[\text { max. likelihood value for parameter } \mid \text { data }]}\right)$
B) $G=\ln \left(\frac{L[\text { max. likelihood value for parameter|data }]}{L\left[\text { parameter value for } H_{0} \mid \text { data }\right]}\right)$
C) $G=2 \ln \left(\frac{L\left[\text { parameter value for } H_{0} \mid \text { data }\right]}{L[\text { max, tikel thood value for parameteridata }]}\right)$
D) $G=2 \ln \left(\frac{L[\text { max. likelihood value for parameter } \mid \text { data }]}{L\left[\text { parameter value for } H_{0} \mid \text { data }\right]}\right)$

Question 11

Which of the following is the correct test statistic for a likelihood ratio test?

A) $G=\ln \left(L\left[\text { parameter value for } H_{0} \mid \text { data }\right]\right)-\ln (L[\text { max.likelihood value for parameter } \mid \text { data }])$
B) $G=2 \ln \left(L\left[\text { parameter value for } H_{0} \mid \text { data }\right]\right)-2 \ln (L[\text { max.likelihood value for parameter } \mid \text { data }])$
C) $G=\ln (L[\text { max.likelihood value for parameter } \mid \text { data }])-\ln \left(L\left[\text { parameter value for } H_{0} \mid \text { data }\right]\right)$
D) $G=2 \ln (L[\text { max.likelihood value for parameter } \mid \text { data }])-2 \ln \left(L\left[\text { parameter value for } H_{0} \mid \text { data }\right]\right)$

Question 12

For a likelihood ratio test in which the null hypothesis requires the estimation of four parameters and the alternative requires the estimation of one parameter, the degrees of freedom will be which of the following?

A) 1
B) 2
C) 3
D) 4

Question 13

Likelihood measures the probability we would get the data we did if a hypothesis is true.

Question 14

Likelihood measures the probability that the null hypothesis is true.

Question 15

The maximum likelihood estimate is the parameter value that results in the highest likelihood value.

Question 16

The maximum likelihood estimate is the highest probability value we calculate when calculating probabilities of occurrence in our data set.

Question 17

When using maximum likelihood to choose the most probably phylogeny, the probabilities of getting the data if each phylogeny is true were compared.

Question 18

When using maximum likelihood to determine the locations of genes that influence traits, the ratio of two different probabilities was calculated for each marker location.

Question 19

The maximum likelihood estimate of a parameter is the value that results in the highest log-likelihood, given the data.

Question 20

The maximum likelihood estimate will always give the highest log-likelihood value.

Question 21

To determine the maximum likelihood estimate, we can calculate the likelihood for a range of parameter values and choose the parameter that gives the smallest value.

Question 22

When we use the maximum likelihood method in complicated scenarios, the likelihood value corresponding to the maximum likelihood estimate is often quite small.

Question 23

A good rule of thumb for the 95% confidence interval for the maximum likelihood estimate is the range of values that lie within 1.92 log-likelihood values of the maximum likelihood estimate.

Question 24

The maximum likelihood approach is very powerful for small and moderate data sets, but it is very limited in the types of scenario it can be used for.

Question 25

Larger sample sizes reduce the bias often seen in maximum likelihood estimation.

Question 26

The bias in maximum likelihood estimation is usually small compared to the magnitude of the confidence interval.

Question 27

If the null hypothesis is true, then log-likelihood ratio values based on large sample sizes will be chi-squared distributed.

Question 28

When doing a log-likelihood ratio test, the degrees of freedom for the test statistic is the sum of the number of parameters estimated in each hypothesis minus two.

Question 29

In your own words describe what likelihood is and what a maximum likelihood estimate is for a data set.

Question 30

Consider a situation in which we plot the log-likelihood values for a range of parameter values as shown in the figure. What is the MLE and 95% confidence interval of the MLE based on this figure?
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Question 31

Consider a situation in which we plot the log-likelihood values for a range of parameter values as shown in the figure. What is the MLE and 95% confidence interval of the MLE based on this figure?
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Question 32

Describe how and why we can use likelihood to conclude that an extremely unlikely situation is probably true.

Question 33

Describe the logic of the log-likelihood ratio test. What does it compare and what conclusions does it make?