Tagged Questions

12 views

Folded normal distribution

I am using bayesian stats for image classification and I have a variety of input variables. These inputs are normally distributed except for two. One has a truncated normal distribution and the other ...
25 views

Finding the joint posterior distribution of AR(2) process

Suppose we have AR(2) process for $\{y_t, t=3,4,..\}$ and let $a_1,a_2,\sigma^2$ be the parameters of the time series. We assume that $y_1$ and $y_2$ er independent normally distributed with mean zero ...
77 views

Maximum Posterior: $p(\bf{w}\mid\bf{x},\bf{t},\alpha,\beta) \propto p(\bf{t}\mid\bf{x},\bf{w},\beta)p(\bf{w}\mid\alpha)$ for Gaussian Distribution

At the moment I take a look at the book Pattern Recognition and Machine Learning from Christopher Bishop and as I try to understand the basics of the probability theory I get stuck trying to ...
258 views

Bayesian posterior with truncated normal prior

Suppose we observe one draw from the random variable $X$, which is distributed with normal distribution $\mathcal{N}(\mu,\sigma^2)$. The variance $\sigma^2$ is known, $\mu$ isn't. We want to estimate ...
118 views

Bayesian Updating with Gaussian Signals

My question relates to a standard bayesian result. Let $A$ be some unknown parameter normally distributed with mean $\mu$ and variance $\sigma^2$. Is we observe $X = A + \epsilon$ where $\epsilon$ ...
181 views

Bayesian posterior with integrals over normal densities

Realizations from normal distributions with known precision are used to estimate the mean, but the realizations are not always precisely observed. Instead, only a range of the realization is observed. ...
Consider this normal distribution: $N(b,\Sigma)$ How can I prove that the Posterior distribution of the mean ($b$) 1. When the covariance matrix (i.e. $\Sigma$ is known) is known and 2. The prior is a ...
Gaussian Bayesian filtering with bound observation ($b_1<x<b_2$)
Suppose we have a Normal r.v $$x \sim \mathcal{N}(\mu, \sigma^2)$$ and a Normal prior of $\mu$ $$\mu \sim \mathcal{N}(\theta, \delta^2)$$ I know how to do the Bayesian update with a ...