- Bayesian inference (English: Bayesian Inference) is inferential statistics one method. This method uses Bayes theorem , the more evidence and information , the update specific assumptions of probability . p (θ | y) or p (y | y)
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How to understand the 95% confidence interval?
Among a lot of answers about the true value with probability description to explain the confidence interval is not accurate. Frequency school (frequentist) we normally use 95% confidence interval of the mean probability that the true value is not within this interval is 95%. Either the true value or not. Since the frequency among the school, the true value is a constant, rather than a random variable (which is the Bayesian), so we do not really value probabilistic description. For this problem, the key is that we do understand the probability of this method to construct confidence intervals described, rather than the true value, nor we calculated this interval itself.
In other words, we can say that if we repeat the sampling after each sample are using this method to construct confidence interval, 95% confidence interval will contain the true value . However (in frequency among school) we can not be certain where the probability of a confidence interval contains the true value of the discussion.
Bayesian probability would only say that a particular interval contains the true value is how much, but we need to assume that the true value of an a priori probability distribution (prior distribution). This does not apply to the confidence interval construction method based on the frequency of school we normally use.
Comments in the supplementary explanation:
In other ways, let's say we have not sampled, but has developed method to construct 95% confidence interval after a good sampling. We can say that after the first sampling, the probability that the confidence interval obtained (do not know) contains the true value was 95%. However, after sampling and get a specific interval, at a frequency of school framework we could not discuss the probability that the interval contains the true value.Before sampling can be discussed, but not after sampling the discussion, which could make a lot of people feel very natural. By extension, the traditional school of frequencies has happened, but we do not know the difficulties discussed the results of the event. Although this problem is usually harmless in the application, but there are indeed many scholars therefore seek different interpretations of probability.
The core idea is to use classical statistical sample to estimate population; population parameters are unknown, unfathomable or difficult to measure, note that it is a fixed value;
- conjugate prior: the prior and posterior have the same form.
- In Bayesian statistics, a credible interval is an interval within which an unobserved parameter value falls with a particular probability. It is an interval in the domain of a posterior probability distribution or a predictive distribution.[1] The generalisation to multivariate problems is the credible region. Credible intervals are analogous to confidence intervals in frequentist statistics,[2] although they differ on a philosophical basis:[3] Bayesian intervals treat their bounds as fixed and the estimated parameter as a random variable, whereas frequentist confidence intervals treat their bounds as random variables and the parameter as a fixed value. Also, Bayesian credible intervals use (and indeed, require) knowledge of the situation-specific prior distribution, while the frequentist confidence intervals do not.
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