Almost rejectionless sampling from Nakagami-m distributions (m≥1)

Luengo, David; Martino, Luca

doi:10.1049/el.2012.3513

Cited by 16 publications

(12 citation statements)

References 10 publications

(12 reference statements)

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“…On the one hand, sticky MCMC methods can be employed as stand-alone algorithms. Indeed, in many applications, it is necessary to draw samples from complicated univariate target pdf (as example in signal processing, see [38]). In this case, the sticky schemes provide virtually independent samples (i.e., with correlation close to zero) very efficiently.…”

Section: Range Of Applicability and Multivariate Generationmentioning

confidence: 99%

“…Given the support set S t and the state x t−1 , the expected probability of adding a new point to S t at the t-th iteration is given by (38) represents the kernel function of AISM given x t−1 and S t . Since candidate points x ∈ X are directly drawn from the proposal pdf, we have p t x |x t−1 , S t = q t x |S t , and from the structure of the AISM in Table 1 it is straightforward to see that…”

Section: Appendix A: Proof Of Theoremmentioning

confidence: 99%

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Adaptive independent sticky MCMC algorithms

Martino

Casarin

Leisen

et al. 2018

EURASIP J. Adv. Signal Process.

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Monte Carlo methods have become essential tools to solve complex Bayesian inference problems in different fields, such as computational statistics, machine learning, and statistical signal processing. In this work, we introduce a novel class of adaptive Monte Carlo methods, called adaptive independent sticky Markov Chain Monte Carlo (MCMC) algorithms, to sample efficiently from any bounded target probability density function (pdf). The new class of algorithms employs adaptive non-parametric proposal densities, which become closer and closer to the target as the number of iterations increases. The proposal pdf is built using interpolation procedures based on a set of support points which is constructed iteratively from previously drawn samples. The algorithm's efficiency is ensured by a test that supervises the evolution of the set of support points. This extra stage controls the computational cost and the convergence of the proposal density to the target. Each part of the novel family of algorithms is discussed and several examples of specific methods are provided. Although the novel algorithms are presented for univariate target densities, we show how they can be easily extended to the multivariate context by embedding them within a Gibbs-type sampler or the hit and run algorithm. The ergodicity is ensured and discussed. An overview of the related works in the literature is also provided, emphasizing that several well-known existing methods (like the adaptive rejection Metropolis sampling (ARMS) scheme) are encompassed by the new class of algorithms proposed here. Eight numerical examples (including the inference of the hyper-parameters of Gaussian processes, widely used in machine learning for signal processing applications) illustrate the efficiency of sticky schemes, both as stand-alone methods to sample from complicated one-dimensional pdfs and within Gibbs samplers in order to draw from multi-dimensional target distributions.

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Section: Range Of Applicability and Multivariate Generationmentioning

confidence: 99%

Section: Appendix A: Proof Of Theoremmentioning

confidence: 99%

Adaptive independent sticky MCMC algorithms

Martino

Casarin

Leisen

et al. 2018

EURASIP J. Adv. Signal Process.

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“…The Nakagami distribution is widely used for the simulation of fading channels in wireless communications [31][32][33]. When β is an integer or half-integer (i.e., β = n 2 with n ∈ N), independent samples can be directly generated through the square root of a sum of squares of n zero-mean i.i.d.…”

Section: Unimodal Target Pdf: Nakami Distributionmentioning

confidence: 99%

“…Gaussian random variables [33]. However, for generic values of β there is not direct method to sample from it, and several alternative approaches have been considered [31,32]. Here, our goal is to esti- 1 2 ) (β) 2 for = 1 and β = 4.6.…”

Section: Unimodal Target Pdf: Nakami Distributionmentioning

confidence: 99%

A fast universal self-tuned sampler within Gibbs sampling

Martino

Yang

Luengo

et al. 2015

Digital Signal Processing

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“…Random variate generation is required in different fields and several applications, such as Bayesian inference and simulation of complex systems [Devroye, 1986, Hörmann et al, 2003, Robert and Casella, 2004, Luengo and Martino, 2012. Rejection sampling (RS) [Robert and Casella, 2004, Chapter 2] is a universal sampling method which generates independent samples from a target probability density function (pdf).…”

Section: Introductionmentioning

confidence: 99%

Adaptive rejection sampling with fixed number of nodes

Martino

Louzada

2017

Communications in Statistics - Simulation and Computation

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The adaptive rejection sampling (ARS) algorithm is a universal random generator for drawing samples efficiently from a univariate log-concave target probability density function (pdf). ARS generates independent samples from the target via rejection sampling with high acceptance rates. Indeed, ARS yields a sequence of proposal functions that converge toward the target pdf, so that the probability of accepting a sample approaches one. However, sampling from the proposal pdf becomes more computational demanding each time it is updated. In this work, we propose a novel ARS scheme, called Cheap Adaptive Rejection Sampling (CARS), where the computational effort for drawing from the proposal remains constant, decided in advance by the user. For generating a large number of desired samples, CARS is faster than ARS.

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Almost rejectionless sampling from Nakagami-m distributions (m≥1)

Cited by 16 publications

References 10 publications

Adaptive independent sticky MCMC algorithms

Adaptive independent sticky MCMC algorithms

A fast universal self-tuned sampler within Gibbs sampling

Adaptive rejection sampling with fixed number of nodes

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