*Bounty: 50*

*Bounty: 50*

I am a student and I am studying machine learning. I am focusing on **probabilistic generative models for classification** and I am having some troubles understanding this topic.

In the slide of my professor it is written the following:

which I don’t understand.

So far, I have understood that in the generative probailistic models, we ant to estimate $P(C_i|x)$, which is the probability of having class $i$ given a data $x$, using the likelihood and the Bayes theorem.

So, it starts by writing the Bayes rule, but the the slides says that we can write this as a sigmoid, **but why?**

If I have to try to give an answer to it, I would say because the sigmoid gives a number from $0$ to $1$, and so a probability, but it is just a guess I am doing.

Moreover, it continues by saying that we can use a gaussian distribution for $P(x|C_i)$, and so $P(x|C_i)=N(mu ,sigma )$, and so :

I don’t understand what it is doing, can somebody please help me?

I don’t know if my question is clear so sorry if it is not but I am really confused. If it is not lcear please tell me I will try to edit it. Thanks in advance.

**Note:** if it can be useful, this has been taken from the Bishop book at **page 197**