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(Smith and Gelfand, 1992) Show that when evaluating an integral based on a posterior distribution
π(θ|x) ∝ π(θ)l(θ|x)
where π is the prior distribution and the likelihood function, the prior distribution can always be used as an instrumental distribution.
a. Show that the variance of the weight is finite when the likelihood is bounded.
b. Compare the previous choice with choosing (θ|x) as the instrumental distribution when the likelihood is proportional to a density. (Hint: Consider the case of exponential families.)
c. Discuss the drawbacks of this (these) choice(s) in specific settings.
d. Show that a mixture between both instrumental distributions can ease some of the drawbacks.
Let be the random variable that represents the number of cards that are drawn before the second appearance of an ace.- Find the probability mass function.-
Medical Mutual Insurance is investigating the cost of a routine office visit to family-practice physicians in the Rochester, New York, area. The following is a list of family-practice physicians in the region.
An experiment is set to test the hypothesis that a given coin is unbiased. The decision rule is the following: Accept the hypothesis if the number of heads in a sample of 200 tosses is between 90 and 110 inclusive, otherwise reject the hypothesis.
Independently of all the others. The system is operational if no two adjacent lamps fail. Obtain an expression for system reliability.
Use the binomial distribution with n = 20, π = .5 to compare accuracy of the normal approximation to the binomial. Compute the exact probabilities and corresponding normal approximations for y = 5.
let x denote the number of heads obtained when a fair coin is tossed 4 times.a what is ex and varx?b repeat 10 times
In order for the blood glucose level of a diabetic to be in the lower 20 percent of all diabetics, that person's blood level must be less than what value?
Form a Markov chain with states the number of sites occupied. Modify the program FixedVector to compute the fixed vector. Use this to check your conjecture by simulation.
When using the distribution of sample means to estimate the population mean, what is the benefit of using larger sample sizes?
Can you tell me why is a data analysis plan important for good business research? What are descriptions of some of a plan's major components and what data analysis tools can be included.
q1. in a city in italy 30 of the families have a mastercard 20 have an american express card and 25 have a visa card.
The San Luis Obispo Telegram-Tribune (November 29, 1995) reported the values of the mean and median salary for major league baseball players for 1995. The values reported were $1,110,766 and $275,000. Which of the two given values do you think ..
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