The paper introduces Annealed Importance Sampling (AIS), a method that combines simulated annealing with importance sampling to estimate expectations and normalizing constants for complex distributions. AIS uses a sequence of intermediate distributions to gradually transition from a tractable distribution to the distribution of interest, allowing for efficient sampling even in high-dimensional problems. The method is particularly useful when dealing with isolated modes, which can be challenging for traditional Markov chain samplers. The paper demonstrates the effectiveness of AIS through various tests, including unimodal and bimodal distributions, and applies it to a linear regression problem with Bayesian models. The results show that AIS can produce accurate estimates and is more efficient than simple importance sampling, especially when the Markov chain transitions are well-designed.The paper introduces Annealed Importance Sampling (AIS), a method that combines simulated annealing with importance sampling to estimate expectations and normalizing constants for complex distributions. AIS uses a sequence of intermediate distributions to gradually transition from a tractable distribution to the distribution of interest, allowing for efficient sampling even in high-dimensional problems. The method is particularly useful when dealing with isolated modes, which can be challenging for traditional Markov chain samplers. The paper demonstrates the effectiveness of AIS through various tests, including unimodal and bimodal distributions, and applies it to a linear regression problem with Bayesian models. The results show that AIS can produce accurate estimates and is more efficient than simple importance sampling, especially when the Markov chain transitions are well-designed.