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### What is an “uninformative prior”? Can we ever have one with truly no information?

Inspired by a comment from this question: What do we consider "uninformative" in a prior - and what information is still contained in a supposedly uninformative prior? I generally see the prior in ...
25k views

### Bayes regression: how is it done in comparison to standard regression?

I got some questions about the Bayesian regression: Given a standard regression as $y = \beta_0 + \beta_1 x + \varepsilon$. If I want to change this into a Bayesian regression, do I need prior ...
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### What are posterior predictive checks and what makes them useful?

I understand what the posterior predictive distribution is, and I have been reading about posterior predictive checks, although it isn't clear to me what it does yet. What exactly is the posterior ...
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### Bayesian updating with new data

How do we go about calculating a posterior with a prior N~(a, b) after observing n data points? I assume that we have to calculate the sample mean and variance of the data points and do some sort of ...
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### Choosing between uninformative beta priors

I am looking for uninformative priors for beta distribution to work with a binomial process (Hit/Miss). At first I thought about using $\alpha=1, \beta=1$ that generate an uniform PDF, or Jeffrey ...
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### Why I should use Bayesian inference with uninformative prior? [duplicate]

I am a Ph.D. student and currently I am studying Bayesian inference concerning vector autoregressive models. A lot of researchers when talking about uninformative prior, conclude that the results of ...
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### If I can make up priors, why can't I make up posteriors?

My question is not meant to be a criticism of Bayesian methods; I am simply trying to understand the Bayesian view. Why is it reasonable to believe we know the distribution of our parameters, but not ...
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### Does a Bayes estimator require that the true parameter is a possible variate of the prior?

This might be a bit of a philosophical question, but here we go: In decision theory, the risk of a Bayes estimator $\hat\theta(x)$ for $\theta\in\Theta$ is defined with respect to a prior distribution ...
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### How is prior knowledge possible under a purely Bayesian framework?

This is more of a philosophical question, but from a purely Bayesian standpoint how does one actually form prior knowledge? If we need prior information to carry out valid inferences then there seems ...
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### When a prior distribution would not be overwhelmed by data, regardless of the sample size?

I came across a question 8 at the end of chapter 3 of the book: "Give two simple examples showing a case in which a prior distribution would not be overwhelmed by data, regardless of the sample size"...
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### Why does MAP converge to MLE?

In Kevin Murphy's "Machine learning: A probabilistic perspective", chapter 3.2, the author demonstrates Bayesian concept learning on an example called "number game": After observing $N$ samples from \$...
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### Weighted arithmetic mean weight choice in a simplified Bayes estimator

A Bayesian estimator as defined in the Wikipedia article Practical example of Bayes estimators balances the prior knowledge of the entire data set with the knowledge of the subset. This is usually ...
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### Does prior distribution affect classification results SVM?

I trained an SVM (RBF kernel, optimized C and G) on a dataset with a balanced class distribution (i.e., 50% positive, 50% negative class samples). Testing the model on a corpus with an unbalanced ...