Please enable JavaScript.
Coggle requires JavaScript to display documents.
Uncertainty - Probability and Markov chains - Coggle Diagram
Uncertainty - Probability and Markov chains
Uncertainty
Aleatory Uncertainty
: Refers to uncertainty caused by inherent randomness or variability in the system, like rolling a dice or weather predictions. It's a type of uncertainty that can’t be reduced by gaining more information; it’s part of the system's nature
Epistemic Uncertainty
: Refers to uncertainty due to incomplete knowledge or information. This type of uncertainty can be reduced by acquiring more data or improving the model's understanding of the environment.
Probability Theory
Probability theory is a branch of mathematics that focuses on calculating the likelihood of events occurring. It provides tools to model and analyze uncertainty and randomness in various situations.
Decision Theory
Decision theory is a framework used to evaluate and make choices under uncertainty. It combines probability theory (to model uncertainty) and utility theory (to model preferences and outcomes).
Utility Theory
Utility is a way to represent an individual’s preferences over different outcomes. It quantifies the satisfaction, value, or benefit derived from each outcome.
In decision theory, the goal is often to maximize expected utility, which is a weighted sum of utilities, where each utility is weighted by the probability of the corresponding outcome.
Probability
Theoretical Probability
: Based on reasoning or known outcomes.
Experimental Probability
: Based on actual experiments and data.
Subjective Probability
: Based on personal belief or experience.
Markov Chains
A Markov Chain is a type of mathematical model for a system that moves between different states, where the probability of moving to the next state depends only on the current state — not on how you got there.
Stochastic process
A stochastic process is a mathematical model of a system that changes over time in a random (probabilistic) way.
Chaos Theory
Chaos Theory studies the behavior of deterministic systems that are highly sensitive to initial conditions — a concept famously known as the butterfly effect.