Computation about Gaussian and Dirac Delta Function

1. Apr 20, 2014

keliu

I have a Gaussian distribution about t, say, N(t; μ, σ), and a a Dirac Delta Function δ(t).

Then how can I compute: N(t; μ, σ) * δ(t > 0)

Any clues? Or recommender some materials for me to read?

Thanks!

2. Apr 20, 2014

Matterwave

I've never seen the notation δ(t > 0) for a Dirac delta function, what do you mean by this? Also, Dirac delta functions are not really functions (they are "distributions") and should not really appear outside of an integral, so I'm not sure what you're trying to compute...maybe you could specify what your motivations are for looking at this quantity?

3. Apr 20, 2014

keliu

In fact I am reading a paper about Microsoft's Adpredictor model. And here is a web article about the model's derivative process.

In the Step 7 of the web article, the author says that :
p(t) = N(t; μ, σ2)δ(y = sign(t)) and when y = 1, p(t) = N(t; μ, σ2)δ(t > 0) and then t has a truncated normal distribution. I don't understand how he could do that how he finish the full step 7.

Because the blog does not have any contact information about the owner, so I came here.

Thanks!

4. Apr 20, 2014

Matterwave

I...I can't make heads or tails of that at all, sorry. Hopefully someone better versed in this than me can help you.

5. Apr 21, 2014

jasonRF

As far as I can tell from the paper, it seems like either they goofed or the rendering in the pdf file had a problem. I could be wrong, but it seems to me that the two "delta" equations on the fourth page should read:
$$p(s|\mathbf{x,w}) = \delta(s - \mathbf{w^T x}).$$
and
$$p(y|t)= \delta(y - sign(t)).$$
These interpretations seem consistent with the words that precede each equation.

jason

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