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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 $X_{n+1} \sim P(\cdot|X_n)$.; 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 $X_{n+1} \sim P(\cdot|X_n)$.; Applies to complex probability distributions with multiple peaks and weird shapes.