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Bayesian inference is a method of statistical inference that relies on treating the model parameters as random variables and applying Bayes' theorem to deduce subjective probability statements about the parameters or hypotheses, conditional on the observed dataset.

14 votes

Is the mean of samples still a valid sample?

No, it is only valid in cases as the Cauchy distribution, the means of samples of the Cauchy follow the same Cauchy dstribution.
javierazcoiti's user avatar
1 vote

How is MCMC relevant for Bayesian inference?

At each step of a Bayesian procedure you may need to normalize the product of the likelihood times the prior by computing an integral. Example of a basic integration of x^2 in the interval [5,12]. …
javierazcoiti's user avatar
1 vote

Bayes' theorem applied to a binomial variable

You start using an Uniform prior, equivalent to a $Be(1,1)$. This two 1's can be understood as pseudo observations of "previous" experiments, let's say, having obtained 1 Yes, 1 No previously. Now let …
javierazcoiti's user avatar
1 vote

In Bayesian statistics does posterior probability become prior probability when new observat...

Just one thing, prior is a probability distribution, not a value like 50% (prior may be also improper.) As an example with the Binomial and Beta prior: Starting with a prior distribution $Be(1,1)$ …
javierazcoiti's user avatar
0 votes

Sequential Bayesian estimation of binary outcome

That is not a bayesian approach. … If you want to know the parameter p of a Bernouilli distribution, in the Bayesian approach, you start with a distribution of this parameter p, called the prior distribution. …
javierazcoiti's user avatar