This paper introduces a novel Markov chain Monte Carlo (MCMC) method, inspired by simulated annealing, designed to address the slow mixing issue in high-dimensional statistical problems. The proposed method, called "simulated tempering," involves simulating realizations from a sequence of distributions, allowing the distribution being simulated to vary randomly over time. This approach is particularly useful for problems where other methods require excessive computational time. The authors demonstrate the effectiveness of their method through an application in statistical genetics, specifically ancestral inference on a large genealogy (7 generations, 2024 individuals), where the goal is to estimate the probabilities of individuals being carriers of cystic fibrosis. The method is shown to mix rapidly, achieving results in a few hours, compared to the impractical run times of traditional Gibbs samplers. The paper also discusses the determination of the pseudo-prior, which is crucial for the sampler's performance, and provides guidelines for choosing the number and spacing of distributions. Additionally, the authors illustrate the method's application to the "witch's hat" distribution and the conditional Strauss process, highlighting its broader utility in various statistical problems.This paper introduces a novel Markov chain Monte Carlo (MCMC) method, inspired by simulated annealing, designed to address the slow mixing issue in high-dimensional statistical problems. The proposed method, called "simulated tempering," involves simulating realizations from a sequence of distributions, allowing the distribution being simulated to vary randomly over time. This approach is particularly useful for problems where other methods require excessive computational time. The authors demonstrate the effectiveness of their method through an application in statistical genetics, specifically ancestral inference on a large genealogy (7 generations, 2024 individuals), where the goal is to estimate the probabilities of individuals being carriers of cystic fibrosis. The method is shown to mix rapidly, achieving results in a few hours, compared to the impractical run times of traditional Gibbs samplers. The paper also discusses the determination of the pseudo-prior, which is crucial for the sampler's performance, and provides guidelines for choosing the number and spacing of distributions. Additionally, the authors illustrate the method's application to the "witch's hat" distribution and the conditional Strauss process, highlighting its broader utility in various statistical problems.