Prior probability distributions

In summary, a prior probability distribution is a probability distribution that represents our initial beliefs or assumptions before any new data is observed. It is important to consider prior probability distributions because they allow us to incorporate existing knowledge or beliefs into our analysis and reduce bias. Choosing a prior probability distribution can be subjective and depends on the specific problem, but non-informative or uniform priors can be used when there is little prior knowledge available. A prior probability distribution can significantly affect the results of a statistical analysis, including estimated probabilities or outcomes, uncertainty or confidence intervals, and conclusions drawn. It can be updated with new data using Bayes' theorem, resulting in a posterior probability distribution.
  • #1
lotharson
2
0
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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  • #2
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?
 

FAQ: Prior probability distributions

What is a prior probability distribution?

A prior probability distribution is a probability distribution that represents our initial beliefs or assumptions about the likelihood of various outcomes before any new data is observed. It serves as a starting point for statistical inference.

Why is it important to consider prior probability distributions?

Prior probability distributions allow us to incorporate existing knowledge or beliefs into our statistical analysis, providing a more informed and accurate estimation of probabilities or outcomes. They also help to reduce bias in our analysis.

How do you choose a prior probability distribution?

Choosing a prior probability distribution can be subjective and depends on the specific problem at hand. It can be based on expert knowledge, previous studies, or a general understanding of the problem. Alternatively, non-informative or uniform priors can be used when there is little or no prior knowledge available.

How does a prior probability distribution affect the results of a statistical analysis?

A prior probability distribution can significantly affect the results of a statistical analysis. It can influence the estimated probabilities or outcomes, as well as the uncertainty or confidence intervals. It can also impact the conclusions drawn from the analysis.

Can a prior probability distribution be updated?

Yes, a prior probability distribution can be updated with new data using Bayes' theorem. This allows us to incorporate new evidence and adjust our initial beliefs or assumptions based on the observed data, resulting in a posterior probability distribution.

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