# 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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### Information of priors? [closed]

In an assigment I am working on, I am asked to rate the information given by different priors from the most uninformative to the most informative. I am not quite sure how to judge this criterion. Can ...
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### What are the bayesian prior distributions to use for a binomial model with unknown $n$ and $p$

I a experimenting with a new MCMC software and before I delve into more complicated models I wanted to run some simple simulations. This is a very very simple simulation, so not meant to be very ...
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### bayesian question: why prior = mu * sigma?

I'm doing a course of Fundamental of Bayesian Analysis in Datacamp and these codes were presented. What is the rationale of prior being mu * sigma ? code: ...
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### Metrics for assessing the quality of prior distributions

Clarification: My purpose is to compare different methods for selecting/creating priors (or perhaps I should refer to them as predictive distributions for a quantity of interest/parameter). I do not ...
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### What are Large Scale and Complicated Priors?

We use priors in Bayesian networks to include prior knowledge in our models. In this context, what are these two terms: -complicated prior -large scale prior I have seen priors like Laplace, zero-mean ...
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### How to get prior distribution based on confidence interval [closed]

If we have mean value and 95% confidence interval of a parameter. For example, sensitivity = 0.5, CI = [0.2,0.78](as you can see, it is asymmetric) How to decide the prior distribution? How to ...
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### Decision Theory: Why is it called a “least favorable prior”?

I'm currently reading the chapter on Statistical Decision Theory in Larry Wasserman's "All of Statistics". Reading the section 13.4 about Minimax Rules he introduces the so called Least ...
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### Postetior from Jeffrey prior of Normal distribtion

Context I am given a sample from normal distribution $v_i \sim N(\gamma \cdot u_i, \sigma^2)$, $i =1,..., n$. I need to obtain the posterior distribution using Jeffreys prior for $\gamma$. My solution ...
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### Confusion about prior used in Recursive Bayes Filter

I'm currently using this thesis to understand key concepts about probabilistic inference in computer vision which is being a great source. The frame of the question is the following: Let us assume we ...
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### How does one place an uninformative prior on a Gamma Distribution?

I'd like to choose an uninformative prior for the scale and shape parameters of the Gamma distribution. Any help and suggestions will be appreciated.
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### Choosing the Dirichlet prior in a mixture model

Consider the following mixture model with $K < \infty$ components,  f\left(x \mid \theta_{1}, \ldots, \theta_{K}, \pi_{1}, \ldots, \pi_{K}\right)=\sum_{k=1}^K \pi_{k} \varphi\left(x \mid \theta_{...
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### What is the “prior standard deviation of the modelled predictive means” and how do you calculate this?

In the book Regression and Other Stories (Gelman et al., 2021, p. 208), there is an example where a multi-linear regression model has: $26$ coefficients; standardised predictors with mean $0$ and ...
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### Bayesian Statistics: Properly updating the Prior for new analysis

I have three tables of information about $A$ and $B$ (gray cells, black font), their row and column marginal totals (black cells white font), and the grand total (white cell black font). The first two ...
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### How to choose priors for experimental data

My question results from the subjectivity of priors, and if there are bodies of work that help to create a more objective approach towards prior choices. My question specifically is to do in the realm ...
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### Expression for the prior predictive density for a multivariate normal distribution with unknown mean and unknown variance?

I am trying to find the expression for the prior predictive density for a multivariate normal distribution with unknown mean and unknown variance. In the short document Bayesian Inference for the ...
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### Does incorporation of prior expert opinions with Bayesian analysis actually work in practise or is it too much to ask of non-statisticians?

Suppose we have a sample from some population of people and we want to perform Bayesian regression of height vs weight using this sample. Suppose the true relationship between height $y$ and weight $x$...
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### Hierarchical clustering with a prior

I would like to perform a clustering (in the best case scenario a hierarchical clustering) of N entities and the distance among those entities is a known input. I also have an a priori on the ...
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### Noninformative prior distribution: uniform or normal? [closed]

The uniform distribution, with the support that has a finite measure, guarantees that the entropy is maximum(as stated in this answer), but in our daily life, normal distribution seems more ...
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### Can a range of priors being used for a linear regression be applied to a logistic regression?

I have trial level data from a study in which participants responded to a series of stimuli. I have a predictor of interest. For the sake of this example, let's call it the size of the stimulus. There ...
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### Theoretical Justification for Zellner's g Prior

What is the theoretical justification for Zellner's g prior for linear regression? I cannot see how it is possible to justify from a purely Bayesian perspective, in which probabilities are epistemic, ...
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### Prior and posterior distributions involving a prior Beta distribution [duplicate]

Question: A poll is conducted to help ascertain whether the Labour party candidate or Tory candidate will win in a forthcoming election for Coventry Mayor ( there are no other candidates, and the ...
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### What does it mean to say that “the prior over $f$ induces a prior over probabilistic classifications $\pi$”?

I am currently studying the textbook Gaussian Processes for Machine Learning by Carl Edward Rasmussen and Christopher K. I. Williams. Chapter 1 Introduction says the following: We now turn to the ...
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### Gaussian processes: The uncertainty is reduced close to the observations?

I am currently studying the textbook Gaussian Processes for Machine Learning by Carl Edward Rasmussen and Christopher K. I. Williams. Chapter 1 Introduction says the following: In this section we ...
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### Why does a function being smoother make it more likely?

I am currently studying the textbook Gaussian Processes for Machine Learning by Carl Edward Rasmussen and Christopher K. I. Williams. Chapter 1 Introduction says the following: Given this training ...
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### Numbers of draws on a modified Bernouilli process

Here is the setup: Bob runs an experiment: he flips a coin N times (between 0 and +$\infty$). The coin has a probability p of landing on heads. Bob starts with zero points. For each head, Bob scores a ...