# How to assume the Probability function that will be used in Likelihood

We define Likelihood as follows:

$$\mathcal{L}(\theta | X) = \prod P(x_{i}|\theta)$$

Question: How to assume the probability function $P$, specially in case of complex dataset?

I understand that if we are doing a Coin Toss, I can assume $P$ to be Bernoulli. But what if my dataset is complex (ex: financial data, flu cases) or I am working on some complex use case where I am using a Neural Network to classify images for example and then applying Bayesian inference for identifying the network weights $W$.

$$P(W | D) \propto P(D | W) P(W)$$ where, $$P(W) = N(0, 1)$$ but how do we define / assume, $$P(D | W) = ??$$

• Thank you for your answer. I am aware of the standard distribution functions and their behavior. My question is what if observed data doesn't follow any of these standard distributions. For example: what if I am looking at the weights in Neural Networks. For prior of weight, I can assume that to be gaussian but what distribution will I assume for $P(data | W)$ so that I can calculate $P(W | data)$ ? – The Wanderer Jun 5 '17 at 22:43