All Questions
Tagged with prior gamma-distribution
29
questions
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32
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How to choose between gamma and Gaussian given a choice of gauges?
I'm trying to make the choice between the gamma and Gaussian distributions as a prior distribution for some data. When I learned statistics a while ago, I was given the rule of thumb: if your data ...
- 111
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103
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posterior predictive of a normal distribution with normal prior over mean and Gamma prior over precision
What is the posterior predictive of a normal distribution with normal prior over mean and Gamma prior over precision. Thus, what is the distribution of x given:
\begin{equation}
x \sim \mathcal{N}(x; \...
- 331
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1
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57
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Eliciting a Gamma informative prior in a Gamma–Poisson Bayesian problem
I employ the Gamma–Poisson conjugate family for my statistical model.
I want to use an informative prior.
From theory, I know that the values of the Gamma-distributed random variable lie within the ...
- 37
1
vote
1
answer
336
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How can I find the posterior distribution for gammadistributed data and prior?
I am working on a project where I believe Bayesian statistics should be useful. However, my knowledge about Bayesian statistics are very scarce. Suppose I got data following a Gamma distribution with ...
- 31
1
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1
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206
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The PDF of the Data (Marginal Likelihood) Given the Prior of a Gamma Distribution with Prior on the $ \beta $ Paraneter
Given a model where $ x_i | \beta \sim \mathcal{Gamma} ( \alpha, \beta ) $ where $ \beta \sim \mathcal{Gamma} ( \alpha0, \beta0 ) $, is there a closed form formula for the PDF of $ x_i $?
Namely, what'...
- 145
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1k
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Choosing priors for the parameters of Gamma distribution
Suppose that $X_1, X_2, \cdots, X_n$ is a sample drawn from a Gamma distribution with parameter $\alpha$ and $\beta$. Then, the likelihood function can be written as follows:
\begin{equation}
L(\...
- 153
4
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1
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451
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Showing $X\sim \operatorname{Poi}(\lambda)$ is minimax
Assume that $X$ has $\operatorname{Poisson} (\lambda)$ distribution and the loss function is $\ell(\lambda,a)=\frac{(\lambda-a)^2}{\lambda}$. Now, I want to show that $X$ is minimax. A hint that is ...
- 703
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3k
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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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3
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1
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107
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How to calculate the posterior distribution from the density
I'm stuck on a answer from an old exam.
The task is to use a Poisson distribution and a Gamma distribution as prior to calculate the posterior density:
$$
p(\lambda|x) \propto L(\lambda)p(\lambda)\...
- 113
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22
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What is the distribution of a r.v. if the reciprocal is distributed gamma?
I want to find the posterior distribution of σ^2 when (X1, X2, ..., Xn) ~ N(μ,σ^2), μ is known, and 1/(σ^2) ~ Gamma(α,β), but I'm not sure how to find the prior of σ^2 given the prior of 1/(σ^2). ...
- 11
3
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317
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How do I choose a prior for this hierarchical model? (Kruschke book)
I am working through Kruschke's "Doing Bayesian Data Analysis",
currently working on the Hierarchical models chapter. The book uses
JAGS for MCMC.
One of the exercises asks the reader to compare two ...
- 31
1
vote
1
answer
460
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Deriving Marginal Distribution of Poisson [duplicate]
How do you find the marginal distribution of a Poisson distribution given a gamma(a,b) prior?
- 11
3
votes
1
answer
5k
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Show posterior mean can be written as a weighted average of the prior mean and MLE
Suppose $Y_1, \dots Y_n$ are exponentially distributed: $Y_i | \lambda \sim Exp(\lambda)$.
Find the conjugate prior for $\lambda$, and the corresponding posterior distribution.
Show that the posterior ...
- 53
2
votes
1
answer
261
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Strange behavior of Gamma prior in a setting with binomial likelihood
I am trying to use Bayes theorem to estimate the probability of a binary event. To give a (simplified) example:
Let's say our a priori guess of the probability of the event per trial is 0.3 (and the ...
- 1,900
1
vote
0
answers
397
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Gamma-2 Distribution in Bayesian
According to the material I have in hand for Bayesian Econometrics, we define the pdf of a Gamma-2 distributed random variable $Z$ with parameter $\mu > 0$ and degrees of freedom $\nu > 0 $, ...
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