Questions tagged [prior]

In Bayesian statistics a prior distribution formalizes information or knowledge (often subjective), available before a sample is seen, in the form of a probability distribution. A distribution with large spread is used when little is known about the parameter(s), while a more narrow prior distribution represents a greater degree of information.

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4k views

What is a “Unit Information Prior”?

I've been reading Wagenmakers (2007) A practical solution to the pervasive problem of p values. I'm intrigued by the conversion of BIC values into Bayes factors and probabilities. However, so far I ...
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429 views

Marginal prior distribution with restricted parameters

I'm analysing one paper on bayesian inference for network reliability and got stuck at trying to validate some (quite simple at first sight) formulas. Suppose the probabilities of failure has ...
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Deriving posterior of Beta distribution

You test a classifier on a test set consisting of 10 iid items. The classifier makes 2 mistakes. Assume the true error rate is $x$. Let the prior be $ x \sim Beta(\alpha, \beta)$. Derive the ...
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What prior distributions are used in mcmcsamp() from lme4?

The mcmcsamp() function generates simulations from the posterior distributions of a Bayesian mixed model fitted with the lmer() ...
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Softmax regression bias and prior probabilities for unequal classes

I'm using Softmax regression for a multi-class classification problem. I don't have equal prior probabilities for each of the classes. I know from Logistic Regression (softmax regression with 2 ...
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4answers
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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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1answer
527 views

Prior of multivariate Polya distribution?

Anyone knows a prior (preferably conjugate) to the multivariate Polya distribution? I need it for Gibbs sampling. So if anyone has another idea, I am interested.
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1answer
186 views

How can the F distribution be used, other than for hypothesis testing and confidence interval estimation?

I am trying to fit informed prior distributions to data using MLE, and F occasionally provides a best fit (lowest AIC value). I am starting with only very basic knowledge of probability theory, so I ...
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1answer
484 views

What are the modeling approaches in this cartoon?

What are the modeling approaches depicted here? Can you name them and their prominent proponents or a landmark model? Is there an accepted superior approach? Who prefers which approach? (From: http://...
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Computing ridge regression with prior different from 0

I compute ridge regression results with Matlab, not using their implementation but simply computing (trans(X)X)+kI)^-1+trans(X)y as seen here. The given formula ...
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2answers
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Allow data to dictate the priors and then run the model using these priors? (e.g., data-driven priors from same data set)

It is my understanding that we should not be allowing the same data set we are analyzing to drive/define what the prior distributions look like in a Bayesian analysis. Specifically, it is ...
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Selection of priors for a BYM spatial regression model

I am using a BYM model in WinBugs to describe the distribution of a non-infectious disease. The model at present is a standard enough BYM model without much modification, (a Poisson-gamma hierarchical ...
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How is the bayesian framework better in interpretation when we usually use uninformative or subjective priors?

It is often argued that the bayesian framework has a big advantage in interpretation (over frequentist), because it computes the probability of a parameter given the data - $p(\theta|x)$ instead of $p(...
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When using the beta distribution as a prior distribution for binomial, why won't the distribution results match with the calculated probability?

Let's say I have 1 success in 4 bernoulli trials, and I wish to plot the distribution of the parameter $p$ of the corresponding binomial distribution. I'm using R. The probability of seeing 1 sucess ...
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Algorithm to create Bayesian priors from measurements

I am trying to devise a simple algorithm to create a Bayesian prior from measurements obtained from time series data. Firstly, I presuppose that the data can take on one of five possible "shapes" or ...
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What does $d$ mean in this notation of the “usual noninformative prior of $\mu_i$ and $\sigma_i$?”

Samiuddin, (1976) states: or, typset with $\LaTeX$ as originally posted We start with the usual noninformative prior distribution of $\mu_i$ and $\sigma_i (i = 1,2,\ldots, k)$ $$\pi(\mu_1,...
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1answer
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Jeffreys prior for geometric distribution?

What is the Jeffreys prior for the geometric distribution?
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Why is a $p(\sigma^2)\sim\text{IG(0.001, 0.001)}$ prior on variance considered weak?

Background One of the most commonly used weak prior on variance is the inverse-gamma with parameters $\alpha =0.001, \beta=0.001$ (Gelman 2006). However, this distribution has a 90%CI of ...
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Why are Jeffreys priors considered noninformative?

Consider a Jeffreys prior where $p(\theta) \propto \sqrt{|i(\theta)|}$, where $i$ is the Fisher information. I keep seeing this prior being mentioned as a uninformative prior, but I never saw an ...
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Is a vague prior the same as a non-informative prior?

This is a question about terminology. Is a "vague prior" the same as a non-informative prior, or is there some difference between the two? My impression is that they are same (from looking up vague ...
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Creating a uniform prior on the logarithmic scale

A uniform prior for a scale parameter (like the variance) is uniform on the logarithmic scale. What functional form does this prior have on the linear scale? And why so?
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346 views

Rotation matrices and prior invariance for arbitrary dimensions

I have a question about a rotation matrix, which can be represented in 2 dimensions as: $$R_{2}(\theta)=\begin{bmatrix} \cos\theta & \sin\theta \\ -\sin\theta & \cos\theta \end{bmatrix}$$ For ...
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1answer
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Bayesian inference for multinomial distribution with asymmetric prior knowledge?

Suppose I will be getting some samples from a binomial distribution. One way to model my prior knowledge is with a Beta distribution with parameters $\alpha$ and $\beta$. As I understand it, this is ...
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Weakly informative prior distributions for scale parameters

I have been using log normal distributions as prior distributions for scale parameters (for normal distributions, t distributions etc.) when I have a rough idea about what the scale should be, but ...
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What's a good prior distribution for degrees of freedom in a t distribution?

I want to use a t distribution to model short interval asset returns in a bayesian model. I'd like to estimate both the degrees of freedom (along with other parameters in my model) for the ...
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1answer
471 views

Non-informative priors for the AR(1) model

I have a question about the AR(1) model. Expressed mathematically as: $$ Z_{t} = \rho Z_{t-1} + \epsilon_{t}, t=1,..,T$$ $$ \epsilon_{t} \sim iid \ N(0,1) $$ My question is about the "...
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618 views

What methods can be used to specify priors from data?

Background I am generally interested in learning appropriate methods of using data to specify priors. A previous question asks how to elicit priors from experts and received some good recommendations....
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Specifying conditional probabilities in hybrid Bayesian networks

I am trying to get a deeper understanding of the various types of Bayesian networks. Most of the literature/lectures I've come across use discrete random variables exclusively and only mention ...
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2answers
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Updating a beta-binomial

Suppose I'm modeling a set of processes using a beta-binomial prior. I can build parameterized beta-binomial models that average over large groups of the processes to give reasonable, although coarse, ...
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Eliciting priors from experts

How should I elicit prior distributions from experts when fitting a Bayesian model?

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