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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Bounded uniform prior in R
I have been fitting a bayesian GLM using brms. The code works well but when I loop this over several data and make it a bit more complex, R encounters a fatal error and crashes. This seems to be ...
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Parameter distribution of $\theta$ from a rectangular matrix multiplication $C\theta$
I am struggeling to see where this problem fits - i.e. what topics this problem relates to, so I am not able to find the right literature. I want to use some particular information as a prior to a ...
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Importance sampling for a parameterized family of distributions using a wide distribution from the same family
I'm motivated here by a problem for robust Bayesian analysis. Let $l(Y|X)$ be the likelihood and let $\{p_\xi(X)\}$ be a parameterized family of prior distributions where $\xi$ denotes the ...
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Laplace approximation from a log-posterior in R
I would like to perform a Laplace approximation of a log-posterior.
The evolution of a cancer cell at given time $t_j$, $j = 1,\cdots,n$ for an experiment $i$ follows the following Poisson ...
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Computing log-posterior for large variance priors
Let's say that some quantity is modelled by a time-dependent Poisson distribution,
$$
y(t) \sim \text{Pois}(\mu(t))
$$
where
$$
\mu(t) = \alpha_0 \exp(-\alpha_1 e^{-\alpha_2 t})
$$
and $\alpha_k > ...
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Light tailed symmetric distribution
Is there a family of distributions that resemble the normal distribution (symmetric, spanning all real numbers, and approximately bell-shaped) but have lighter tails than normal distribution?
I'm ...
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Some questions about the posterior distribution when the marginal distribution is zero
Let $\{f(\cdot|\theta): \theta \in \Theta \}$ be a family of pdfs and let $\pi: \Theta \to \mathbb{R}$ be a prior. According to Bayes' theorem (as stated in, e.g., Casella and Berger), the posterior ...
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Distribution families whose likelihoods integrate to $+\infty$ for some sample values
I've recently started learning about Bayesian statistics, and I came across this very nice answer by Xi'an https://stats.stackexchange.com/a/129908/268693, which [in my slight paraphrasing] says the ...
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Using Jeffreys prior for Bernoulli distribution to find the prior of a transformation on p
The question goes like this: Use Jeffreys prior for Bernoulli distribution and find the prior for $\eta$ where: $$\eta(p) = \left(\frac{p}{1-p}\right) $$
So $\eta$ here is some kind of a ...
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How does an ideal prior distribution needs a probability mass on zero to reduce variance, and have fat tails to reduce bias?
I am reading this article about the horseshoe prior and how it is better than lasso and ridge priors. The author makes several points that I don't understand. One of them is "The ideal prior ...
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Power of Bernoulli likelihood in Jags (R2jags) [closed]
In a fixed power prior model, the model is set up as:
$$ \pi(p_i \mid \alpha,\mathcal{D}_0) \propto L(p_i\mid \mathcal{D}_0)^{w} \pi(p_i) $$
Suppose that the event follows a Bernoulli distribution ...
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What is the best way to encode the prior of a Gaussian Process model in this application?
I'm using Gaussian Process regression for the first time to model the unknown energy efficiency of a compressor which I know is a smooth, non-linear relationship that looks something like the line in ...
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Bayesian statistics -- interpreting the mean and standard deviation of priors
I have just started reading about Bayesian statistics and have a question regarding the general interpretations of priors. Let’s say I have recorded the reaction times (RT, in ms) every time a single ...
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Parameterization of inverse gamma prior in Bayesian methods
For a prior of $\sigma^2 \sim IG(0.01, 0.01)$, often recommended as an uninformative prior for the variance parameter in MCMC approaches and other Bayesian methods, which parameterization does this ...
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How to choose priors for bounds on circular truncated distributions?
I am considering choices of priors for truncated distributions on a circle. Let's take the truncated normal distribution on the unit circle as an example. It has parameters $\mu \in [-\pi, \pi]$ and $\...
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