Approximate Bayesian computation (ABC) is a family of computational techniques in Bayesian statistics. These techniques allow to fi t a model to data without relying on the computation of the model likelihood. They instead require to simulate a large number of times the model to be fi tted. A number of re finements to the original rejection-based ABC scheme have been proposed, including the sequential improvement of posterior distributions. This technique allows to de- crease the number of model simulations required, but it still presents several shortcomings which are particu- larly problematic for costly to simulate complex models. We here provide a new algorithm to perform adaptive approximate Bayesian computation, which is shown to perform better on both a toy example and a complex social model.
We investigate the problem of deriving adaptive posterior rates of contraction on $\mathbb{L}^{\infty}$ balls in density estimation. Although it is known that log-density priors can achieve optimal rates when the true density is sufficiently smooth, adaptive rates were still to be proven. Here we establish that the so-called spike-and-slab prior can achieve adaptive and optimal posterior contraction rates. Along the way, we prove a generic $\mathbb{L}^{\infty}$ contraction result for log-density priors with independent wavelet coefficients. Interestingly, our approach is different from previou…
Adaptive MC^3 and Gibbs algorithms for Bayesian Model Averaging in Linear Regression Models
MC $^3$（Madigan and York，1995）和Gibbs（George and McCulloch，1997）采样器是线性回归模型中贝叶斯模型平均（BMA）最广泛实现的算法。这些采样器在每次迭代中使用统一的选择概率随机抽取一个变量，然后建议更新该变量。如果变量的数量很大并且许多变量是冗余的，则这在计算上可能是低效的。在这项工作中，我们引入自适应版本的这些采样器，保持其简单的实施，并减少了许多冗余变量的选择概率。在真实和模拟数据集的自适应采样器的效率的改进说明。
A simple and efficient adaptive Markov Chain Monte Carlo (MCMC) method, called the Metropolized Adaptive Subspace (MAdaSub) algorithm, is proposed for sampling from high-dimensional posterior model distributions in Bayesian variable selection. The MAdaSub algorithm is based on an independent Metropolis-Hastings sampler, where the individual proposal probabilities of the explanatory variables are updated after each iteration using a form of Bayesian adaptive learning, in a way that they finally converge to the respective covariates' posterior inclusion probabilities. We prove the ergodicity of …
A fast, flexible simulation framework for Bayesian adaptive designs -- the R package BATSS
MRC Biostatistics Unit, University of Cambridge（剑桥大学医学研究委员会生物统计学单位）；School of Public Health and Preventive Medicine, Monash University（莫纳什大学公共卫生与预防医学院）；Faculty of Informatics and Data Science, University of Regensburg（雷根斯堡大学信息科学与数据科学学院）
The aghq package for implementing approximate Bayesian inference using adaptive quadrature is introduced. The method and software are described, and use of the package in making approximate Bayesian inferences in several challenging low- and high-dimensional models is illustrated. Examples include an infectious disease model; an astrostatistical model for estimating the mass of the Milky Way; two examples in non-Gaussian model-based geostatistics including one incorporating zero-inflation which is not easily fit using other methods; and a model for zero-inflated, overdispersed count data. The …
We introduce a framework for efficient Markov Chain Monte Carlo (MCMC) algorithms targeting discrete-valued high-dimensional distributions, such as posterior distributions in Bayesian variable selection (BVS) problems. We show that many recently introduced algorithms, such as the locally informed sampler and the Adaptively Scaled Individual adaptation sampler (ASI), can be viewed as particular cases within the framework. We then describe a novel algorithm, the Adaptive Random Neighbourhood Informed sampler (ARNI), by combining ideas from both of these existing approaches. We show using several…
We provide the first stochastic convergence rates for a family of adaptive quadrature rules used to normalize the posterior distribution in Bayesian models. Our results apply to the uniform relative error in the approximate posterior density, the coverage probabilities of approximate credible sets, and approximate moments and quantiles, therefore guaranteeing fast asymptotic convergence of approximate summary statistics used in practice. The family of quadrature rules includes adaptive Gauss-Hermite quadrature, and we apply this rule in two challenging low-dimensional examples. Further, we dem…
University of Southern California（南加州大学）；University of California, San Diego（加州大学圣地亚哥分校）
The problem of adaptive sampling for estimating probability mass functions (pmf) uniformly well is considered. Performance of the sampling strategy is measured in terms of the worst-case mean squared error. A Bayesian variant of the existing upper confidence bound (UCB) based approaches is proposed. It is shown analytically that the performance of this Bayesian variant is no worse than the existing approaches. The posterior distribution on the pmfs in the Bayesian setting allows for a tighter computation of upper confidence bounds which leads to significant performance gains in practice. Using…
In Bayesian semi-parametric analyses of time-to-event data, non-parametric process priors are adopted for the baseline hazard function or the cumulative baseline hazard function for a given finite partition of the time axis. However, it would be controversial to suggest a general guideline to construct an optimal time partition. While a great deal of research has been done to relax the assumption of the fixed split times for other non-parametric processes, to our knowledge, no methods have been developed for a gamma process prior, which is one of the most widely used in Bayesian survival analy…
Optimal designs minimize the number of experimental runs (samples) needed to accurately estimate model parameters, resulting in algorithms that, for instance, efficiently minimize parameter estimate variance. Governed by knowledge of past observations, adaptive approaches adjust sampling constraints online as model parameter estimates are refined, continually maximizing expected information gained or variance reduced. We apply adaptive Bayesian inference to estimate transition rates of Markov chains, a common class of models for stochastic processes in nature. Unlike most previous studies, our…
Likelihood-free Bayesian inference algorithms are popular methods for calibrating the parameters of complex, stochastic models, required when the likelihood of the observed data is intractable. These algorithms characteristically rely heavily on repeated model simulations. However, whenever the computational cost of simulation is even moderately expensive, the significant burden incurred by likelihood-free algorithms leaves them unviable in many practical applications. The multifidelity approach has been introduced (originally in the context of approximate Bayesian computation) to reduce the s…
