42k views

### 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 ...
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### 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 ...
36k views

### 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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1k views

### Priors that do not become irrelevant with large sample sizes

This may be a weird question. My colleagues and I are working on a medical estimation problem, where relevant prior knowledge regarding plausible values of some physiological parameters exists. In ...
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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 ...
3k views

### Shrinkage priors

I am building a Bayesian model where I to put shrinkage priors such as spike and slab, horseshoe prior, etc on some parameters for feature selection, but I am not able to decide which one is the best. ...
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642 views

### 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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940 views

### 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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### Are there good methods to increase the weight of prior distribution in parameter estimation using Bayesian method

say, I have a prior distribution of parameter $\pi(\theta)$ Then, given observation $x_1,x_2,...x_n=x$, we have $\pi(\theta \mid x) \propto f(x \mid \theta) \pi(\theta)$, which is then used for ...
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1k views

### When Bayesian and frequentist statistics give different answers, is there a way to empirically test which one corresponds more closely to reality?

For example for this problem: You have a coin that when flipped ends up head with probability p and ends up tail with probability 1−p. (The value of p is unknown.) Trying to estimate p, you flip the ...
4k views

### 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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