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This work aims to present a simple explanation about the ABC, Approximate Bayesian Computation or likelihood-free methods, a sampler algorithm class made to sampling from a posteriori distribution π(θ|x) in an independent way of the likelihood function. Along of this paper is to present a couple of ABC algorithms such as the ABC Rejection and the ABC MCMC. These algorithms are also applied to the beta model and to the normal-gamma model, in order to generate an univariate posterior distribution and a bivariate distribution, respectively. [ABSTRACT FROM AUTHOR]

We consider the problem of quickly estimating the best κ-term Fourier representation for a given frequency-sparse band-limited signal (i.e., function) f: [0,2π]→¢. In essence, this requires the identification of κ of the largest magnitude frequencies of fˇ∈¢N, and the estimation their Fourier coefficients. Randomized sublinear-time Monte Carlo algorithms, which have a small probability of failing to output accurate answers for each input signal, have been developed for solving this problem [1, 2]. These methods were implemented as the Ann Arbor Fast Fourier Transform (AAFFT) and empirically evaluated in [3]. In this paper we present and evaluate the first implementation, called the Gopher Fast Fourier Transform (GFFT), of the more recently developed sparse Fourier transform techniques from [4]. Our experiments indicate that different variants of GFFT generally outperform AAFFT with respect to runtime and sample usage. [ABSTRACT FROM AUTHOR]