Monte Carlo method

Target entity: Monte Carlo method
Context triple: [Stanislaw Ulam, coInvented, Monte Carlo method]

• A. Markov chain Monte Carlo
  Markov chain Monte Carlo is a class of algorithms that uses Markov chains to generate samples from complex probability distributions, widely used in Bayesian inference, statistical physics, and machine learning.
• B. Euler–Maruyama method
  The Euler–Maruyama method is a basic time-stepping scheme for numerically approximating solutions to stochastic differential equations, widely used in simulations of systems with noise such as Langevin dynamics.
• C. Euler’s method for numerical integration
  Euler’s method for numerical integration is a simple first-order numerical procedure used to approximate solutions to ordinary differential equations by stepping forward in small increments.
• D. Langevin dynamics
  Langevin dynamics is a stochastic approach to modeling the motion of particles in a fluid by combining deterministic forces with random thermal fluctuations, often used to simulate Brownian motion and other nonequilibrium processes.
• E. Ornstein–Uhlenbeck process
  The Ornstein–Uhlenbeck process is a continuous-time stochastic process that models mean-reverting random motion, widely used in physics and quantitative finance to describe systems fluctuating around a long-term equilibrium.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Monte Carlo method
Target entity description: The Monte Carlo method is a computational technique that uses random sampling to approximate numerical results, especially for complex integrals, simulations, and probabilistic systems.

• A. Markov chain Monte Carlo
  Markov chain Monte Carlo is a class of algorithms that uses Markov chains to generate samples from complex probability distributions, widely used in Bayesian inference, statistical physics, and machine learning.
• B. Euler–Maruyama method
  The Euler–Maruyama method is a basic time-stepping scheme for numerically approximating solutions to stochastic differential equations, widely used in simulations of systems with noise such as Langevin dynamics.
• C. Euler’s method for numerical integration
  Euler’s method for numerical integration is a simple first-order numerical procedure used to approximate solutions to ordinary differential equations by stepping forward in small increments.
• D. Langevin dynamics
  Langevin dynamics is a stochastic approach to modeling the motion of particles in a fluid by combining deterministic forces with random thermal fluctuations, often used to simulate Brownian motion and other nonequilibrium processes.
• E. Ornstein–Uhlenbeck process
  The Ornstein–Uhlenbeck process is a continuous-time stochastic process that models mean-reverting random motion, widely used in physics and quantitative finance to describe systems fluctuating around a long-term equilibrium.
• F. None of above. chosen