--%>

Bayesian Point Estimation

What are the Bayesian Point of estimation and what are the process of inference in Bayesian statistics?

E

Expert

Verified

Bayesian Point Estimation:

A) Bayesian Statistics is one way of incorporating prior information about a parameter into the estimation process.

B) Adherents claim that this helps to make the estimation more relevant to the scienti c problem at hand.

C) Opponents counter that it makes statistical inference subjective.

D) The underlying principle of Bayesian statistics also di ers from the more common Frequentist inference that we have covered to date.

E) In Bayesian statistics, all unknown quantities are considered random variables.

F) Thus the parameters of a distribution are now considered random.

G) The usual model is then considered to be a conditional distribution of the data given the parameters.

H) Since the parameter vector θ is considered random it also has a distribution.

I) The marginal distribution of θ is called the Prior Distribution.

J) The prior distribution is supposed to capture our beliefs about θ before the collection of data.

The process of inference in Bayesian statistics is as follows.

1. Specify a conditional distribution of the data given the parameters. This is identical to the usual model speci cation in frequentist statistics.

2. Specify the prior distribution of the model parameters Π(θ).

3. Collect the data, X = x.

4. Update the prior distribution based on the data observed to give a Posterior Distribution of the parameters given the observed data x, Π(θ|x).

5. All inference is then based on this posterior distribution.

   Related Questions in Advanced Statistics

  • Q : Analytical Report Hi I WOULD LIKE TO

    Hi I WOULD LIKE TO KNOW IF YOU CAN HELP ME TO DO THE ASSIGNMENT IN HEALTH STATISTICS THANKS

  • Q : Use the law of iterated expectation to

    Suppose we have a stick of length L. We break it once at some point X _

    Q : Statistics A nurse practitioner working

    A nurse practitioner working in a dermatology clinic is studying the efficacy of tretinoin in treating women’s post partum abdominal stretch marks. From a sample of 15 women, the mean reduction of stretch mark score is -0.33 with a sample standard deviation of 2.46. Describe what happens to the c

  • Q : Problem on consumers marginal utility

    Consider a consumer with probability p of becoming sick.  Let Is be the consumer’s income if he becomes sick, and let Ins be his income if he does not become sick, with Is < Ins. Suppo

  • Q : Probability of winning game Monte Carlo

    Monte Carlo Simulation for Determining Probabilities 1. Determining the probability of winning at the game of craps is difficult to solve analytically. We will assume you are playing the `Pass Line.'  So here is how the game is played: The shooter rolls a pair of

  • Q : Frequency Distributions Define the term

    Define the term Frequency Distributions?

  • Q : Probability Distributions and Data

    1. A popular resort hotel has 300 rooms and is usually fully booked. About 4% of the time a reservation is canceled before 6:00 p.m. deadline with no penalty. What is the probability that at least 280 rooms will be occupied? Use binomial distribution to find the exact value and the normal approxi

  • Q : Calculate corresponding t value or s

    1)    Construct a 99% confidence interval for the population mean µ.   2)    At what significance level do the data provide good evidence that the average body temperature is

  • Q : Problem on utility funtion probability

    Suppose that your utility, U, is a function only of wealth, Y, and that U(Y) is as drawn below. In this graph, note that U(Y) increases linearly between points a and b.  Suppose further that you do not know whether or not you

  • Q : Problem on Poisson distribution The

    The number of trucks coming to a certain warehouse each day follows the Poisson distribution with λ= 8. The warehouse can handle a maximum of 12 trucks a day. What is the probability that on a given day one or more trucks have to be sent away? Round the answer