Linked Questions
32 questions linked to/from Do Bayesian priors become irrelevant with large sample size?
100
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4
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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 ...
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85
votes
2
answers
46k
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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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56
votes
1
answer
27k
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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 ...
26
votes
3
answers
36k
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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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21
votes
1
answer
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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 ...
- 211
16
votes
4
answers
1k
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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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12
votes
4
answers
4k
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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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10
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5
answers
2k
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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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6
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2
answers
3k
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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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9
votes
3
answers
642
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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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9
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2
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940
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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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4
votes
2
answers
2k
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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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4
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4
answers
1k
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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 ...
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11
votes
1
answer
4k
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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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5
votes
2
answers
451
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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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