Prior probability distributions

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SUMMARY

This discussion focuses on the use of Jeffreys prior and Bernardo's prior in Bayesian statistics for estimating a parameter k within a finite interval (a;b). The participants explore whether these priors can effectively mimic the shape of the likelihood function, ensuring that the resulting posterior distribution approximates the Maximum Likelihood Estimate (MLE). The conversation highlights the importance of understanding the relationship between prior distributions and likelihoods in achieving accurate parameter estimation.

PREREQUISITES
  • Understanding of Bayesian statistics and prior distributions
  • Familiarity with Jeffreys prior and Bernardo's prior
  • Knowledge of Maximum Likelihood Estimation (MLE)
  • Basic concepts of likelihood functions and posterior distributions
NEXT STEPS
  • Research the mathematical foundations of Jeffreys prior and its applications
  • Study Bernardo's prior and its advantages in Bayesian analysis
  • Explore the relationship between prior distributions and likelihood functions
  • Learn about the implications of using different priors on posterior estimates
USEFUL FOR

Statisticians, data scientists, and researchers involved in Bayesian analysis and parameter estimation, particularly those interested in the implications of prior distributions on model outcomes.

lotharson
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Hi folks.

I've a question.

Let k be a parameter which must be estimated. It lies within the interval (a;b), a and b being finite real numbers.

Let us further assume we dispose of a series of measurements X of known standard deviations.
X is a complex function of k.

What are Jeffreys prior Bernardo's prior?

Many thanks for your answer :-)
 
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Do we dispose of some type of guarantee that these priors imitate the shape of the likelihood in such a way that the posterior distribution delivers us a result close enough to the Maximum Likelihood Estimate?
 

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