--%>

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 : Probability of signaling Quality

    Quality control: when the output of a production process is stable at an acceptable standard, it is said to be "in control?. Suppose that a production process has been in control for some time and that the proportion of defectives has been 0.5. as a means of monitorin

  • Q : Variation what are the advantages and

    what are the advantages and disadvantages of seasonal variation

  • Q : Grouped Frequency Distributions Grouped

    Grouped Frequency Distributions: Guidelines for classes: A) There must be between 5 to 20 classes. B) The class width must be an odd number. This will assure that the class mid-points are integers rather than decimals. C) The classes should be mutually exclusive. This signifies that no data valu

  • Q : Problem on Chebyshevs theorem 1. Prove

    1. Prove that the law of iterated expectations for continuous random variables.2. Prove that the bounds in Chebyshev's theorem cannot be improved upon. I.e., provide a distribution which satisfies the bounds exactly for k ≥1, show that it satisfies the

  • 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 : Probability problem A) What is the

    A) What is the probability of getting the following sequence with a fair die (as in dice):B) What is the probability of getting the same sequence with a die that is biased in the following way: p(1)=p(2)=p(3)=p(4)=15%;

  • Q : Discrete and continuous data

    Distinguish between discrete and continuous data in brief.

  • Q : What is your statistical decision

    Question 1 Do parents with more children travel more than parents of small families? To find out, a survey was done of a large number of adults. Respondents were asked how many children they had and how many times

  • Q : Statistics Homework with SAS File is

    File is attached, need it by 8:30 AM Pacific (Seattle, WA) time. No delay acceptable. Need it March 25, 2014 on 8:30 AM Pacific time.

  • Q : Problem on income probability Kramer

    Kramer spends all of his income  $270  on two products, soup (S) and on golf balls (G). He always bought 2 golf balls for every 1 cup of soup he consumes. He acquires no additional utility from the other cup of soup unless he as well gets 2 more golf balls a