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1answer
22 views

Probability Distribution of z/x given x

It may seem a simple question for you, but it's driving me crazy. Given the regression model $z = wx + \epsilon$, where $ \epsilon \sim \mathcal{N} (0, (\sigma x)^{2} $, $ z \sim \mathcal{N}(wx, ...
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0answers
38 views

Efficient approximation of derivatives of an integral

Suppose $ \phi(z) $ is the probit function (http://en.wikipedia.org/wiki/Probit). And $$ Z = \int \phi(\mathbf{w}^\top \mathbf{x}) \mathcal{N}(\mathbf{w}; \mathbf{\mu}, \mathbf{\Sigma}) d\mathbf{w} ...
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1answer
87 views

Is there a way to directly compute maximum of a sum of several Gaussian functions?

I have a problem which goes as follows. I am trying to predict the value of a variable $x$. I also have a set of measurements (the actual context is an image) $x^i$. I know from some training ...
1
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1answer
463 views

Conditional probability distribution with Gaussian noise

If I have a relationship as follows: $$Y = a X + G(0,\sigma^2),\text{ so }y = a X + \text{some Gaussian noise}.$$ The conditional probability distribution of $y$ given $x$, i.e. $P(y|x)$, is equal ...