Probabilistic Modelling

Models

A model describes data that one could observe from a system.

Whenever you are working with probability, you are essentially working with Random Variables. Now if you have random variables, there might be connections between them.

Let's say you have some system which get's some input and produces some output. Now you define these input and output as random variables. These random variables are now related to each other by the dynamics of the system.

So the probabilistic model is basically a representation of some system or process of random variables.

Few example of models:

• Bayesian Networks/Graphical Models

• Hidden Markov Models

• State Space Models

Models will generally we some equations having random variables, hence relate these random variables to each other.

$$Y = \beta_0X+\beta_1 + \epsilon$$

The above is equations is model of linear regression. $X,Y,\epsilon$are all random variables.