Uncertainty

Whenever we are assigning a probability to something, there is a reason because of which we have to assign it a probability or belief i.e why are you not completely certain about the quantity in question/variable. For example, when you say, there is 50% probability that he has cancer. Then why are you unsure? Are you unsure because you are doubtful about the effectiveness of the test, are you doubtful about your procedure in conducting the test? Almost always you will get a source behind this.

Sometimes, in a not so obvious environment, explicitly finding these sources of uncertainty can be useful to get the final probability of an event.

Typically there are three possible sources of uncertainty:

1. Inherent stochasticity in the system being modeled. For example, most interpretations of quantum mechanics describe the dynamics of subatomic particles as being probabilistic. We can also create theoretical scenarios that we postulate to have random dynamics, such as a hypothetical card game where we assume that the cards are truly shuffled into a random order.

2. Incomplete observability. Even deterministic systems can appear stochastic when we cannot observe all of the variables that drive the behavior of the system. For example, in the Monty Hall problem, a game show contestant is asked to choose between three doors and wins a prize held behind the chosen door. Two doors lead to a goat while a third leads to a car. The outcome given the contestant’s choice is deterministic, but from the contestant’s point of view, the outcome is uncertain.

3. Incomplete modeling. When we use a model that must discard some of the information we have observed, the discarded information results in uncertainty in the model’s predictions. For example, suppose we build a robot that can exactly observe the location of every object around it. If the robot discretizes space when predicting the future location of these objects, then the discretization makes the robot immediately become uncertain about the precise position of objects: each object could be anywhere within the discrete cell that it was observed to occupy.