The key insight is that instead of treating each sample independently, dependent sampling uses the information from the previous sample to determine the next one. This creates a chain of information that flows from sample to sample, allowing the sampler to intelligently explore high-probability regions.
Conditions: Each new sample is drawn from a probability distribution conditioned on the previous sample.; The formula is Xn+1∼P(⋅∣Xn).; Applies to complex probability distributions with multiple peaks and weird shapes.
The key insight is that instead of treating each sample independently, dependent sampling uses the information from the previous sample to determine the next one. This creates a chain of information that flows from sample to sample, allowing the sampler to intelligently explore high-probability regions.
Conditions: Each new sample is drawn from a probability distribution conditioned on the previous sample.; The formula is Xn+1∼P(⋅∣Xn).; Applies to complex probability distributions with multiple peaks and weird shapes.
A Markov chain is a mathematical system that undergoes transitions from one state to another according to certain probabilistic rules. Its defining characteristic is the memoryless property: the probability of transitioning to any particular state depends solely on the current state and time elapsed, not on the sequence of events that preceded it.
Conditions: The future state depends only on the present state.; Transition probabilities are defined between states.; The system is a Markov chain.
A Markov chain is a mathematical system that undergoes transitions from one state to another according to certain probabilistic rules. Its defining characteristic is the memoryless property: the probability of transitioning to any particular state depends solely on the current state and time elapsed, not on the sequence of events that preceded it.
Conditions: The future state depends only on the present state.; Transition probabilities are defined between states.; The system is a Markov chain.