# 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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### Best estimate of underdetermined system using prior

I have measured two variables which depend on the same set of four parameters. I want to know the parameters which best explain my measurements. Of course, I cannot solve for four unknowns from just ...
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### Posterior density for a linear regression model

Given a classical linear regression model $$y = X\beta + \varepsilon,$$ $$\varepsilon\sim N(0,\sigma^2I_n),$$ the posterior density is proportional to the product of the likelihood and the selected ...
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### What would be an ignorance prior of AB, given the probabilities of A and B?

Let us have two events, $A$ and $B$ whose probabilities are $P(A)$ and $P(B)$. In the absence of any other information, what would be a reasonable probability to assign to $AB$, that is, $A$ and $B$ ...
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### What are the limitations on the flat prior in the BAT framework?

By default, the BAT framework sets the flat priors on the parameter. My question is: how in this case allowed range for a parameter of the flat function is estimated?
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### How to Change prior probabilities for predicted variable in neural networks and other methods in SPSS Statistics

i am trying to find right model for predicting categorical variable with two values. Problem is that ratio of cases in group 1 and group 2 is not equal but rather in ratio of 2:1. When i try to find a ...
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### Prior/degree of belief/degree of lack-of-information/algorithms/complexity

For a long time I had a bit of difficulty understanding what "degree of belief" means. Recently I had some thoughts about it and I wonder if they make any sense, or is there some literature about ...
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### Is a mean of 0 and sd of 0.5 acceptable scaling for a normal prior?

I have thus far been fitting a Cauchy prior (centred at 0; scale of 2.5) on my parameters, as recommended by Gelman et al. (2008). They recommend scaling variables (predictors, and in the case of a ...
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### Correcting an unnormalized posterior for the weighting of the prior

Bayes' rule tells us that, $P(h|d) = \frac{ P(d|h) P(h) }{ \sum_i P(d|h_i) P(h_i) }$. Let's say we have four hypotheses: $h_1$, $h_2$, $h_3$, and $h_4$. The likelihood over hypotheses looks like ...
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### Basic Bayesian updating priors

I have a question about simple Bayesian reasoning. Suppose there are N datasets, two mutually exclusive models, priors for models can be chosen as 0.5 to 0.5. The datasets have different ...
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### Combining two estimates of p in a binomial estimation

I have an estimation problem for a binomial data. I got a sample and from that I can get an estimation. But I also have a kind of prior information about the p. But mind it, this prior is just a ...
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### learning hyper parameters: are we allowed to touch the prior parameters after observing the data?

There are many algorithms/applications that aim to learn the hyper parameters i.e. the parameters of a prior distribution from the observed data. A typical algorithm works in an iterative function ...
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### Weighted Distributions in Predictive Model

I'm not a statistician but do work with large datasets and have a problem I'd like to use a predictive model for. I have two datasets that I'd like to use together to build predictions. The first ...
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### What Bayesian prior for normally distributed data with knowledge observations are too high

I'm just learning Bayesian statistics with stan, so bear with me. Let's say we have one observed data points: ...
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### How are these priors generated? [closed]

I am trying going through an exercise, I don't understand how the information provided in the text below transitions into the parameters displayed in the beta priors. How are these informative priors ...
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### Bayesian estimation Prior adaptation [closed]

I have a dataset of 1 dimensional 20points as prior information, so assuming prior distribution to be Gaussian distribution we can easily find its variance and mean. Now we will use this prior finding ...