3 + missing important bit "(with mean *m* and variance 1)"

Say I have a black box generating data samples, and I want to estimate the parameters of the black box from the samples.

The black box works like this: it has a parameter m (a real number), and to generate a value v, it first generates v0 according to a normal distribution (with mean m and variance 1), and if v0 is positive it returns v0, if not it returns 0.

So my data samples will be a bunch of zeroes and positive real numbers.

So my question is, from a sample, how do I estimate m?

To me, this looks like a straightforward case of bayesian probability, where I would use p(samples|m) to get p(m|samples) and have some prior on the distribution of m.

So uncle Bayes would say: $p(m|series) = p(series|m) * p(m) / p(series)$

Since the samples are independant, $p(samples|m) = \prod p(sample|m)$

...but some of those $p(sample|m)$ are "discrete probabilities" (when the value is 0), and some are continuous probabilities! Can I muliply them just like that?

(Same goes for calculating $p(samples)$)

Can someone help me clear the confusion?

2 (edit: better formatting); + added some Bayes.

Say I have a black box generating data samples, and I want to estimate the parameters of the black box from the samples.

The black box works like this: it has a parameter m (a real number), and to generate a value v, it first generates v0 according to a normal distribution, and if v0 is positive it returns v0, if not it returns 0.

So my data samples will be a bunch of zeroes and positive real numbers.

So my question is, from a sample, how do I estimate m?

To me, this looks like a straightforward case of bayesian probability, where I would use p(samples|m) to get p(m|samples) and have some prior on the distribution of m.

So uncle Bayes would say: $p(m|series) = p(series|m) * p(m) / p(series)$

Since the samples are independant, p(samples|m) = $\prod$p(sample|m)p(samples|m) = \prod p(sample|m)$...but some of those p(sample|m)$p(sample|m)$are "discrete probabilities" (when the value is 0), and some are continuous probabilities! Can I muliply them just like that? (Same goes for calculating$p(samples)$) Can someone help me clear the confusion? 1 # Estimating the mean of a truncated gaussian curve Say I have a black box generating data samples, and I want to estimate the parameters of the black box from the samples. The black box works like this: it has a parameter m (a real number), and to generate a value v, it first generates v0 according to a normal distribution, and if v0 is positive it returns v0, if not it returns 0. So my data samples will be a bunch of zeroes and positive real numbers. So my question is, from a sample, how do I estimate m? And what kind of mathematical tools do I use to reason about this? To me, this looks like a straightforward case of bayesian probability, where I would use p(samples|m) to get p(m|samples) and have some prior on the distribution of m. Since the samples are independant, p(samples|m) =$\prod\$p(sample|m)

...but some of those p(sample|m) are "discrete probabilities" (when the value is 0), and some are continuous probabilities! Can I muliply them just like that?

Can someone help me clear the confusion?