All Questions
Tagged with prior normal-distribution
52
questions
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17
views
Strange Variance Term for Normal Prior $w^2\sigma^2$
I've attached two screenshots, one with the question and one with the answer. It seems to me that the prior is wrong and it should include $w^2$ not $w^2\sigma^2$
I apologise for, including such a ...
- 161
0
votes
1
answer
32
views
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
0
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0
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103
views
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
3
votes
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answers
39
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prior distribution for iid gaussian, with a known variance
I have been reading Pattern Recognition and Machine Learning by Bishop, and I have a question regarding the prior distribution of an iid Gaussian with known variance.
The relationship $\dfrac{n}{\...
- 9,217
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191
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Bayesian Gaussian mixture - is my prior correct?
I'd like to sample from the Bayesian Posterior of a Gaussian mixture model, but I am not sure about the correct Bayesian formulation of the latter. Is the following correct?
I consider the 1-...
- 1
3
votes
1
answer
115
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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 ...
- 943
2
votes
1
answer
164
views
Joint posterior distribution of differences
I have data $x_1,...,x_n$, $y_1,...,y_m$ and $z_1,...,z_p$ where
$$x_1,...,x_n\sim N(\mu_x,\sigma^2_x)$$
and
$$y_1,...,y_m\sim N(\mu_y,\sigma^2_y)$$
and
$$z_1,...,z_p\sim N(\mu_z,\sigma^2_z)$$
Now let'...
- 69
2
votes
1
answer
209
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For multivariate normal posterior with improper prior, why posterior is proper only if $n\geq d$
This is related to Gelman's BDA chapter 3 section 5's noninformative prior density for $\mu$.
Let $\Sigma$ be fixed positive definite symmetric matrix of size $d$ by $d$. Let $y_1,\dots, y_n$ be iid ...
- 1,445
0
votes
1
answer
67
views
Prior selection in Gaussian - an application to height measurement
Say I have just purchased ACME's Tree Height Measuring Device (THMD). ACME states that the error $\epsilon$ in tree height measurement from this device can be modelled as a normal distribution with ...
- 53
3
votes
2
answers
238
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The PDF of the Data Given (Marginal Likelihood) the Likelihood and the Prior of a Normal Distribution with Prior on the Mean
Given a model where $ x_i | \mu \sim \mathcal{N} ( \mu, \sigma^2 ) $ where $ \mu \sim \mathcal{N} ( \mu_0, \sigma_0^2 ) $, is there a closed form formula for the PDF of $ x_i $? Namely, what's $ p (...
- 145
1
vote
1
answer
399
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Kl Divergence between factorized Gaussian and standard normal
Given two distributions, one a parameterized gaussian and the other a standard normal gaussian:
$q(x) \sim \mathcal{N}(\mu,\sigma)$
$p(x) \sim \mathcal{N}(0,I)$
We want to compute the KL Divergence $...
0
votes
1
answer
42
views
Bayesian statistics
Assuming I have that $Y_i\mid \mu$ is an iid ~ $N(\mu,\sigma^2)$, for $i \in (1,\dotsc,n)$ with $\sigma_i$ known and improper prior $\pi(\mu)=1$ for all $\mu$.
i. How can I derive a formula for the ...
4
votes
2
answers
1k
views
Informative priors for standard deviation (or variance)
Suppose I want to perform Bayesian estimation of the mean $\mu$ and standard deviation $\sigma$ of a Gaussian distribution. Is there a standard way to specify an informative prior over $\sigma$, ...
- 350
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148
views
Ridge regression, argmax of the MAP
How can i prove it? I only proved that it is equivalent to $$arg\min_w \sum_{i=1}^N(y_i-w_0-\textbf{w}^T\textbf{x}_i)^2+\lambda||\textbf{w}||^2_2$$
- 11
1
vote
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answers
70
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Prior probability of Normal distribution [closed]
I was solving one problem and got to the point where I needed to find the prior probability of the normally distributed variable, with the known mean and variance. I'm a little confused because I've ...
- 247