--%>

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 : Components of time series Name and

    Name and elaborate the four components of time series in brief.

  • 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 : MANOVA and Reflection Activity 10:

    Activity 10: MANOVA and Reflection 4Comparison of Multiple Outcome Variables This activity introduces you to a very common technique - MANOVA. MANOVA is simply an extension of an ANOVA and allows for the comparison of multiple outcome variables (again, a very common situation in research a

  • 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 : Frequency Distributions Define the term

    Define the term Frequency Distributions?

  • Q : Conclusion using p-value and critical

    A sample of 9 days over the past six months showed that a clinic treated the following numbers of patients: 24, 26, 21, 17, 16, 23, 27, 18, and 25. If the number of patients seen per day is normally distributed, would an analysis of these sample data provide evid

  • 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 : Random variables Random variables with

    Random variables with zero correlation are not necessarily independent. Give a simple example.    

  • Q : Analyse the statistics of the data

    Assigment Question Select any two manufacturing companies and formulate the cost and revenue functions of the companies. analyse the statistics of the data and then sketch the functions and determine their breakeven points. (Note: You are required to interview the production and sales manag

  • Q : Binomial distribution 1) A Discrete

    1) A Discrete random variable can be described as Binomial distribution if is satisfies four conditions, Briefly discuss each of these conditions2) A student does not study for a multiple choice examination and decides to guess the correct answers, If the