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# Questions tagged [inverse-gamma-distribution]

The inverse gamma distribution is a right-skew, continuous distribution for a random variables taking positive values.

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### bayesian problem using inverse gamma: negative initial values

My study involves a dependent variable measuring reading times (minimum value = 0.3) and two categorical variables (y = "quick" or "slow"; t = "cute" or "ugly") ...
80 views

### 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 ...
41 views

### Proof of an approximation of Welch

Let $S^2 = X/\nu$ where $X \sim \chi^2(\nu)$ and define $W = \frac{1}{S^2}$. In Welch's paper, "On the comparison of several mean values: an alternative approach" (1951), he gives the ...
42 views

### Bayesian experiment analysis of multi-cell experiment

I have an experiment running with four cells divided by two axes; the axes are (1) experiment group (test, control) and demand period (high, low). There are four total combinations therein, test-high, ...
169 views

### How to write the derivative of the inverse gamma function?

I have recently been writing an R program on the inverse of the gamma function and the derivative of the inverse function. Now there is some confusion I would like to ask for advice. I have written ...
2k views

### inverse gamma (0.001,0.001) prior on the variance in the Bayesian hierarchical model

This 8 schools data is from Gelman 2006 paper: http://www.stat.columbia.edu/~gelman/research/published/taumain.pdf. In Figure 1 (c), the prior density of inverse gamma (0.001,0.001) was overlain on ...
181 views

### Moments of the natural statistics of the normal gamma

I am trying to find the Moments of the natural statistics of the normal-gamma distribution. $$(X,T) - NormalGamma(\mu, \lambda,\alpha,\beta)$$ I found on its Wikipedia page that the moments of the ...
1 vote
73 views

### Rejection sampling with inverse-gamma-like density [closed]

I would like use rejection sampling to sample from a density, $f_y$ on $(0, \infty)$ satisfying $$f_y(y) \propto \frac{y^{-1}}{1 + y^{-1}}e^{-by^{-1}}$$ I made a first observation that \begin{align*} ...
325 views

1 vote
51 views

### Posterior varince for multiple normal variables with identical variance

Suppose one is given $n$ random normal variables, all with the same variance but with different means: $$X_i\sim N(\mu_i, \sigma^2)$$ Now suppose we observe $m_i$ observations $\{x_{ij}\}_{j=1}^{m_i}$ ...
830 views

### What kind of distribution does this have?

Currently I'm trying to figure out the distribution of the following: $X \sim \frac{\sqrt{n}}{\sqrt{Gamma(n,\beta)}}$ where the denominator follows a $Gamma(n,\beta)$ distribution. I've checked out ...
1 vote
356 views

### What exactly is a inverse $\chi^2$ distribution?

What exactly is a inverse-chi square distribution? 1 vote
45 views

### Interpretation of interactions in inverse gamma glmm

i want to calculate the effects that the interaction between zone (4 levels), species (2 levels) and distance from contact zone (continuous) has on the pulse repetition period - song rate of the two ...
33 views

### How to evaluate the ratio of (large) gamma functions in the normal inverse gamma marginal likelihood?

I am doing some Bayesian modeling where I am using Normal-Inverse-Gamma as prior for the unknown mean and variance, and Normal for likelihood. In my application, I need the marginal likelihood, where ...
72 views

### how to determine a priori probability distribution of sigama2 in montecarlo simulation?

1、the monte carlo simulation code in SAS： Example1: https://support.sas.com/rnd/app/stat/examples/BayesStd/new_example/index.html ...
192 views

### mismatch in sampling between t distribution and normal-inverse-gamma distribution

I am looking at equivalence of sampling between t distribution and normal-inverse-gamma (NIG) distribution in python. The results don't match, and I want to see if there's a mistake in how I am ...
659 views

### Posterior distribution for Weibull scale parameter with censored data

I am modeling a survival problem using a Weibull distribution with known shape parameter $k$ and unknown scale parameter $\theta$. The PDF and CDF are given by, \begin{align} f(t|k,\theta)=\frac{k}{\...
1 vote
316 views

### Closed form posterior for product of inverse Gamma and Normal distribution

I am currently reading a book about mixture analysis, and in the textbook a posterior for the parameters $\mu1,\mu2,\sigma_1^2,\sigma_2^2$ of a two-component gaussian mixture is derived as follows (S ...
1 vote
3k views

### Interpretation of the rate parameter of a Gamma distribution

I am toying with mixture models, especially in a bayesian context and the Gamma (or the inverse Gamma) distribution appears quite often. For example, inverse Gamma is used as a conjugate prior for the ...
551 views

### hypothesis testing - gamma distribution

Let W = Y/B0 be a Random variable that has a gamma(2n,1) distribution. [Y has a gamma(2n,B) distribution and W = Y/B]. i) Suppose you want to test H0 : B ≤ B0 against H1 : B > B0 for some B0 > 0. How ...
559 views

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### Effect of sample reduction in normal-inverse gamma

I am trying to interpret/explain a result that I obtained while generating a posterior distribution, and maybe add some informations to what I had so far. The environment that I am using is the ...
1k views

### Variation on inverse gamma: $1/X^r \sim \textrm{InvGamma}({}~~,{}~~)$ if $X \sim \textrm{Gamma}(a, b).$

If $X \sim \textrm{Gamma}(a, b),$ then $1/X \sim \textrm{InvGamma}(a, b).$ Therefore if $X \sim \textrm{Gamma}(a, b),$ then $1/X^r \sim \textrm{InvGamma}({}~~,{}~~)?$ My brain is exploding I don't ...
1 vote
138 views

### Gamma likelihood with InverseGamma prior

I've got a gamma likelihood $\Gamma(\tau_c | \alpha_k, \frac{\alpha_k} {\tau_k})$ (parameterized with shape and rate) with an InverseGamma prior $IG(\tau_k|a_0, b_0)$. I know that the resulting ...
1k views

### inv-gamma distribution as prior for multivariate normal distribution

it's known the conjugate priors for multivariate normal distribution are the normal & inverse-whishart distributions. but i'm interest in very specific case where the correlation matrix is $R$ ...
1k views

### What is the correct to model inverse gamma distribution [closed]

I tried to use below R code to model inverse gamma distribution (alpha=1,beta=1). However, the resulting histogram is not alike the one plotted in the wiki. Could anyone provide any hint about this? ...
2k views

### Calculating the parameters of a Normal distribution using alpha and beta from Inverse-gamma (conjugate prior)

How is it possible to calculate the variance $\sigma^2$ for the Normal distribution if only $\alpha$ and $\beta$ (based on data) from the Inverse-gamma distribution are available? I followed the ...
1k views

### Why is Inverted Gamma (3,0.0005) a diffuse prior when variance of this random variable is small?

A few times I came across the statement that an Inverted Gamma (3, 0.0005) prior for the variance is quite diffuse but proper. Hence, my understanding is that the prior variance of this random ...