ATAIS is an adaptive importance sampler that alternates between sampling nonlinear-model parameters and analytically updating the noise covariance matrix, then reweights old samples to approximate the joint posterior over both.
Gradient Importance Sampling
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abstract
Adaptive Monte Carlo schemes developed over the last years usually seek to ensure ergodicity of the sampling process in line with MCMC tradition. This poses constraints on what is possible in terms of adaptation. In the general case ergodicity can only be guaranteed if adaptation is diminished at a certain rate. Importance Sampling approaches offer a way to circumvent this limitation and design sampling algorithms that keep adapting. Here I present a gradient informed variant of SMC (and its special case Population Monte Carlo) for static problems.
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Adaptive posterior distributions for uncertainty analysis of covariance matrices in Bayesian inversion problems for multioutput signals
ATAIS is an adaptive importance sampler that alternates between sampling nonlinear-model parameters and analytically updating the noise covariance matrix, then reweights old samples to approximate the joint posterior over both.