scholarly journals Ensuring Rapid Mixing and Low Bias for Asynchronous Gibbs Sampling

2017 ◽  
Author(s):  
Christopher De Sa ◽  
Kunle Olukotun ◽  
Christopher Ré
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Gibbs Sampling ◽  
Mixing Time ◽  
Markov Chain Analysis ◽  
Empirical Results ◽  
Chain Analysis ◽  
Speed Up ◽  
Theoretical Results

Gibbs sampling is a Markov chain Monte Carlo technique commonly used for estimating marginal distributions. To speed up Gibbs sampling, there has recently been interest in parallelizing it by executing asynchronously. While empirical results suggest that many models can be efficiently sampled asynchronously, traditional Markov chain analysis does not apply to the asynchronous case, and thus asynchronous Gibbs sampling is poorly understood. In this paper, we derive a better understanding of the two main challenges of asynchronous Gibbs: bias and mixing time. We show experimentally that our theoretical results match practical outcomes.

scholarly journals In search of lost mixing time: adaptive Markov chain Monte Carlo schemes for Bayesian variable selection with very large p

Biometrika ◽  
2020 ◽  
Author(s):  
J E Griffin ◽  
K G Łatuszyński ◽  
M F J Steel
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Variable Selection ◽  
Adaptive Design ◽  
Mixing Time ◽  
Bayesian Variable Selection ◽  
Monte Carlo Algorithms ◽  
Large Numbers ◽  
Large P Small N

Summary The availability of datasets with large numbers of variables is rapidly increasing. The effective application of Bayesian variable selection methods for regression with these datasets has proved difficult since available Markov chain Monte Carlo methods do not perform well in typical problem sizes of interest. We propose new adaptive Markov chain Monte Carlo algorithms to address this shortcoming. The adaptive design of these algorithms exploits the observation that in large-$p$, small-$n$ settings, the majority of the $p$ variables will be approximately uncorrelated a posteriori. The algorithms adaptively build suitable nonlocal proposals that result in moves with squared jumping distance significantly larger than standard methods. Their performance is studied empirically in high-dimensional problems and speed-ups of up to four orders of magnitude are observed.

scholarly journals PENDUGAAN ANGKA KEMISKINAN DI KABUPATEN PADANG PARIAMAN MENGGUNAKAN SMALL AREA ESTIMATION DENGAN PENDEKATAN HIERARCHICAL BAYESIAN (HB) LOGLOGISTIK

2019 ◽  
Vol 8 (2) ◽  
pp. 76
Author(s):  
Jusri Repi Basri Yuliani ◽  
Maiyastri Maiyastri ◽  
Rita Diana
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Gibbs Sampling ◽  
Standard Error ◽  
Small Area ◽  
Small Area Estimation ◽  
Hierarchical Bayesian ◽  
Area Estimation ◽  
Level Model

Penelitian ini mengkaji tentang pendekatan Hierarchical Bayesian (HB) Loglogistik yang diaplikasikan pada Small Area Estimation (SAE) dengan tujuan mengestimasi tingkat kemiskinan di Kabupaten Padang Pariaman. Metode pendugaan area kecil yang digunakan pada penelitian ini adalah model level area dasar (basic area level model ) dengan bantuan variabel penyerta yang tersedia pada level kecamatan. Variabel penyerta yang digunakan pada penelitian ini yaitu rasio SLTA/Sederajat (X1), persentase keluarga pertanian (X2), rasio industri mikro kecil (X3), persentase buruh tani dalam setiap anggota keluarga (X4), kepadatan penduduk (X5), dan persentase penduduk pelanggan listrik PLN (X6). Bentuk integrasi yang kompleks dari sebaran peluang bersyarat pada model diselesaikan menggunakan Markov Chain Monte Carlo (MCMC) dengan menerapkan algortima Gibbs Sampling dan bantuan software WinBugs 1.4.3. Hasil estimasi menggunkan model HB yang diperoleh dibandingkan dengan hasil estimasi pendugaan langsung dengan memperhatikan nilai standard error sebagai tolok ukurnya. Hasil pendugaan tingkat kemiskinan untuk level kecamatan di Kabupaten Padang Pariaman dengan model HB menunjukkan nilai standard error yang kecil.Kata Kunci: Tingkat kemiskinan, Small Area Estimation, Hierarchical Bayesian

scholarly journals On the convergence rates of some adaptive Markov chain Monte Carlo algorithms

2015 ◽  
Vol 52 (3) ◽  
pp. 811-825
Author(s):  
Yves Atchadé ◽  
Yizao Wang
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Convergence Rates ◽  
Mixing Time ◽  
Regularity Conditions ◽  
Monte Carlo Algorithms ◽  
Mcmc Algorithms ◽  
Variation Distance ◽  
Importance Resampling

In this paper we study the mixing time of certain adaptive Markov chain Monte Carlo (MCMC) algorithms. Under some regularity conditions, we show that the convergence rate of importance resampling MCMC algorithms, measured in terms of the total variation distance, is O(n-1). By means of an example, we establish that, in general, this algorithm does not converge at a faster rate. We also study the interacting tempering algorithm, a simplified version of the equi-energy sampler, and establish that its mixing time is of order O(n-1/2).

Sign in / Sign up

Export Citation Format

Share Document