Ensemble samplers with affine invariance are Markov chain Monte Carlo (MCMC) methods that are unaffected by affine transformations of space. These methods are easy to construct and require little computational overhead, making them particularly useful for sampling badly scaled distributions. Computational tests show that affine invariant methods can be significantly faster than standard MCMC methods on highly skewed distributions. The paper introduces a family of ensemble MCMC samplers with affine invariance. An ensemble consists of multiple walkers, each in a high-dimensional space. The target probability density for the ensemble is the product of individual densities. The ensemble MCMC algorithm is a Markov chain on the state space of ensembles. The algorithm is affine invariant, meaning its performance is independent of the aspect ratio in highly anisotropic distributions. The paper describes two affine invariant methods: the stretch move and the walk move. The stretch move involves moving a walker using a complementary walker, while the walk move uses a proposal based on the mean and covariance of a subset of walkers. The replacement move is another method that replaces a walker with an independent sample from the density estimated by a subset of walkers. The paper also discusses the evaluation of ensemble sampling methods using integrated autocorrelation time as a measure of performance. Computational tests show that affine invariant methods outperform standard single-particle methods on difficult distributions, such as the Rosenbrock density and a 101-dimensional distribution. The methods are efficient and effective for a wide range of problems, including those with high-dimensional and skewed distributions. The paper concludes that affine invariant ensemble MCMC methods are a valuable tool for sampling in complex and high-dimensional spaces.Ensemble samplers with affine invariance are Markov chain Monte Carlo (MCMC) methods that are unaffected by affine transformations of space. These methods are easy to construct and require little computational overhead, making them particularly useful for sampling badly scaled distributions. Computational tests show that affine invariant methods can be significantly faster than standard MCMC methods on highly skewed distributions. The paper introduces a family of ensemble MCMC samplers with affine invariance. An ensemble consists of multiple walkers, each in a high-dimensional space. The target probability density for the ensemble is the product of individual densities. The ensemble MCMC algorithm is a Markov chain on the state space of ensembles. The algorithm is affine invariant, meaning its performance is independent of the aspect ratio in highly anisotropic distributions. The paper describes two affine invariant methods: the stretch move and the walk move. The stretch move involves moving a walker using a complementary walker, while the walk move uses a proposal based on the mean and covariance of a subset of walkers. The replacement move is another method that replaces a walker with an independent sample from the density estimated by a subset of walkers. The paper also discusses the evaluation of ensemble sampling methods using integrated autocorrelation time as a measure of performance. Computational tests show that affine invariant methods outperform standard single-particle methods on difficult distributions, such as the Rosenbrock density and a 101-dimensional distribution. The methods are efficient and effective for a wide range of problems, including those with high-dimensional and skewed distributions. The paper concludes that affine invariant ensemble MCMC methods are a valuable tool for sampling in complex and high-dimensional spaces.