Data Science

Likelihood

Question 1
Marks : +2 | -2
Pass Ratio : 50%
The _________ of a collection of data is the joint density evaluated as a function of the parameters with the data fixed.
probability
likelihood
poisson distribution
all of the mentioned
Explanation:
Likelihood analysis of data uses the likelihood to perform inference regarding the unknown parameter.
Question 2
Marks : +2 | -2
Pass Ratio : 50%
Point out the correct statement.
Asymptotics are incredibly useful for simple statistical inference and approximations
Asymptotics often lead to nice understanding of procedures
An estimator is consistent if it converges to what you want to estimate
All of the mentioned
Explanation:
Consistency is neither necessary nor sufficient for one estimator to be better than another.
Question 3
Marks : +2 | -2
Pass Ratio : 50%
The beta distribution is the default prior for parameters between ____________
0 and 10
1 and 2
0 and 1
None of the mentioned
Explanation:
Bayesian statistics posits a prior on the parameter of interest.
Question 4
Marks : +2 | -2
Pass Ratio : 50%
Which of the following is a property of likelihood?
Ratios of likelihood values measure the relative evidence of one value of the unknown parameter to another
Given a statistical model and observed data, all of the relevant information contained in the data regarding the unknown parameter is contained in the likelihood
The Resultant likelihood is multiplication of individual likelihood
All of the mentioned
Explanation:
Likelihood is the hypothetical probability that an event that has already occurred would yield a specific outcome.
Question 5
Marks : +2 | -2
Pass Ratio : 50%
Which of the following mean is a mixture of the MLE and the prior mean?
interior
exterior
posterior
all of the mentioned
Explanation:
MLE stands for maximum likelihood.
Question 6
Marks : +2 | -2
Pass Ratio : 50%
Usually replacing the standard error by its estimated value does change the CLT.
True
False
Explanation:
Usually replacing the standard error by its estimated value doesn’t change the CLT.
Question 7
Marks : +2 | -2
Pass Ratio : 50%
CLT is mostly useful as an approximation.
True
False
Explanation:
The CLT applies in an endless variety of settings.
Question 8
Marks : +2 | -2
Pass Ratio : 50%
Gosset’s distribution is invented by which of the following scientist?
William Gosset
William Gosling
Gosling Gosset
All of the mentioned
Explanation:
Gosset’s distribution is indexed by a degrees of freedom.
Question 9
Marks : +2 | -2
Pass Ratio : 50%
Point out the wrong statement.
Asymptotics generally give assurances about finite sample performance
The sample variance and the sample standard deviation are consistent as well
The sample mean and the sample variance are unbiased as well
None of the mentioned
Explanation:
The kinds of asymptotics that do are orders of magnitude more difficult to work with.
Question 10
Marks : +2 | -2
Pass Ratio : 50%
The _________ of the Chi-squared distribution is twice the degrees of freedom.
variance
standard deviation
mode
none of the mentioned
Explanation:
The mean of the Chi-squared is its degrees of freedom.