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通过小波域马尔可夫树集合高效进行函数型方差分析AI 解读

We introduce a wavelet-domain method for functional analysis of variance (fANOVA). It is based on a Bayesian hierarchical model that employs a graphical hyperprior in the form of a Markov grove (MG)—that is, a collection of Markov trees—for linking the presence/absence of factor effects at all location-scale combinations, thereby incorporating the natural clustering of factor effects in the wavelet-domain across locations and scales. Inference under the model enjoys both…

弹跳粒子采样器：非可逆、无拒绝的马尔可夫链蒙特卡洛方法AI 解读

Many Markov chain Monte Carlo techniques currently available rely on discrete-time reversible Markov processes whose transition kernels are variations of the Metropolis–Hastings algorithm. We explore and generalize an alternative scheme recently introduced in the physics literature (Peters and de With 2012) where the target distribution is explored using a continuous-time nonreversible piecewise-deterministic Markov process. In the Metropolis–Hastings algorithm, a trial move…

基于受访者驱动抽样的隐匿人群规模估计：网络方法AI 解读

Estimating the size of stigmatized, hidden, or hard-to-reach populations is a major problem in epidemiology, demography, and public health research. Capture-recapture and multiplier methods are standard tools for inference of hidden population sizes, but they require random sampling of target population members, which is rarely possible. Respondent-driven sampling (RDS) is a survey method for hidden populations that relies on social link tracing. The RDS recruitment process…

预测分布的贝叶斯非参数校准与组合AI 解读

We introduce a Bayesian approach to predictive density calibration and combination that accounts for parameter uncertainty and model set incompleteness through the use of random calibration functionals and random combination weights. Building on the work of Ranjan and Gneiting, we use infinite beta mixtures for the calibration. The proposed Bayesian nonparametric approach takes advantage of the flexibility of Dirichlet process mixtures to achieve any continuous deformation…

异方差正态均值的分组线性经验贝叶斯估计AI 解读

The problem of estimating the mean of a normal vector with known but unequal variances introduces substantial difficulties that impair the adequacy of traditional empirical Bayes estimators. By taking a different approach that treats the known variances as part of the random observations, we restore symmetry and thus the effectiveness of such methods. We suggest a group-linear empirical Bayes estimator, which collects observations with similar variances and applies a…

用于高维预测与变量选择的贝叶斯回归树AI 解读

Decision tree ensembles are an extremely popular tool for obtaining high-quality predictions in nonparametric regression problems. Unmodified, however, many commonly used decision tree ensemble methods do not adapt to sparsity in the regime in which the number of predictors is larger than the number of observations. A recent stream of research concerns the construction of decision tree ensembles that are motivated by a generative probabilistic model, the most influential…

评估电子邮件营销活动效果的贝叶斯推断AI 解读

Email marketing has been an increasingly important tool for today’s businesses. In this article, we propose a counting-process-based Bayesian method for quantifying the effectiveness of email marketing campaigns in conjunction with customer characteristics. Our model explicitly addresses the seasonality of data, accounts for the impact of customer characteristics on their purchasing behavior, and evaluates effects of email offers as well as their interactions with customer…

利用网络结构估计协方差矩阵AI 解读

In this article, we employ a regression formulation to estimate the high-dimensional covariance matrix for a given network structure. Using prior information contained in the network relationships, we model the covariance as a polynomial function of the symmetric adjacency matrix. Accordingly, the problem of estimating a high-dimensional covariance matrix is converted to one of estimating low dimensional coefficients of the polynomial regression function, which we can…

多工具变量线性 IV 回归的贝叶斯因子模型收缩AI 解读

A Bayesian approach for the many instruments problem in linear instrumental variable models is presented. The new approach has two components. First, a slice sampler is developed, which leverages a decomposition of the likelihood function that is a Bayesian analogue to two-stage least squares. The new sampler permits nonconjugate shrinkage priors to be implemented easily and efficiently. The new computational approach permits a Bayesian analysis of problems that were…

时变协整关系与协整秩的贝叶斯建模AI 解读

A multivariate model that allows for both a time-varying cointegrating matrix and time-varying cointegrating rank is presented. The model addresses the issue that, in real data, the validity of a constant cointegrating relationship may be questionable. The model nests the submodels implied by alternative cointegrating matrix ranks and allows for transitions between stationarity and nonstationarity, and cointegrating and noncointegrating relationships in accordance with the…

动态期限结构模型中的风险价格约束AI 解读

Restrictions on the risk-pricing in dynamic term structure models (DTSMs) tighten the link between cross-sectional and time-series variation of interest rates, and make absence of arbitrage useful for inference about expectations. This article presents a new econometric framework for estimation of affine Gaussian DTSMs under restrictions on risk prices, which addresses the issues of a large model space and of model uncertainty using a Bayesian approach. A simulation study…

序贯资源配置中的贝叶斯指数策略AI 解读

This paper is about index policies for minimizing (frequentist) regret in a stochastic multi-armed bandit model, inspired by a Bayesian view on the problem. Our main contribution is to prove that the Bayes-UCB algorithm, which relies on quantiles of posterior distributions, is asymptotically optimal when the reward distributions belong to a one-dimensional exponential family, for a large class of prior distributions. We also show that the Bayesian literature gives new…

贝叶斯非参数向量自回归模型AI 解读

Vector autoregressive (VAR) models are the main work-horse models for macroeconomic forecasting, and provide a framework for the analysis of complex dynamics that are present between macroeconomic variables. Whether a classical or a Bayesian approach is adopted, most VAR models are linear with Gaussian innovations. This can limit the model’s ability to explain the relationships in macroeconomic series. We propose a nonparametric VAR model that allows for nonlinearity in the…

未知阶异方差 VAR 模型的协整秩确定AI 解读

We investigate the asymptotic and finite sample properties of a number of methods for estimating the cointegration rank in integrated vector autoregressive systems of unknown autoregressive order driven by heteroskedastic shocks. We allow for both conditional and unconditional heteroskedasticity of a very general form. We establish the conditions required on the penalty functions such that standard information criterion-based methods, such as the Bayesian information…

基于软阈值高斯过程的标量对图像回归AI 解读

This work concerns spatial variable selection for scalar-on-image regression. We propose a new class of Bayesian nonparametric models and develop an efficient posterior computational aigorithm. The proposed soft-thresholded Gaussian process provides large prior support over the class of piecewise-smooth, sparse, and continuous spatially-varying regression coefficient functions. In addition, under some mild regularity conditions the soft-thresholded Gaussian proess prior…

信息性抽样下的近似贝叶斯推断AI 解读

Statistical inference with complex survey data is challenging because the sampling design can be informative, and ignoring it can produce misleading results. Current methods of Bayesian inference under complex sampling assume that the sampling design is noninformative for the specified model. In this paper, we propose a Bayesian approach which uses the sampling distribution of a summary statistic to derive the posterior distribution of the parameters of interest. Asymptotic…

高维混合模型成分协方差矩阵的结构检验AI 解读

Summary By studying the family of p-dimensional scale mixtures, the paper shows for the first time a non-trivial example where the eigenvalue distribution of the corresponding sample covariance matrix does not converge to the celebrated Marčenko–Pastur law. A different and new limit is found and characterized. The reasons for failure of the Marčenko–Pastur limit in this situation are found to be a strong dependence between the p-co-ordinates of the mixture. Next, we address…

含少量或大量异质参与者及潜在序列相关状态的动态模型：贝叶斯估计AI 解读

We propose a Bayesian approach to estimating dynamic models that can have state variables that are latent, serially correlated, and heterogeneous. Our approach employs sequential importance sampling and is based on deriving an unbiased estimate of the likelihood within a Metropolis chain. Under fairly weak regularity conditions unbiasedness guarantees that the stationary density of the chain is the exact posterior, not an approximation. Results are verified by Monte Carlo…

多元时间序列多重结构变化的高效贝叶斯方法AI 解读

Summary This paper provides a feasible approach to estimation and forecasting of multiple structural breaks for vector autoregressions and other multivariate models. Owing to conjugate prior assumptions we obtain a very efficient sampler for the regime allocation variable. A new hierarchical prior is introduced to allow for learning over different structural breaks. The model is extended to independent breaks in regression coefficients and the volatility parameters. Two…

采用连续尖峰与厚尾混合先验的稀疏信号贝叶斯估计AI 解读

We introduce a new framework for estimation of sparse normal means, bridging the gap between popular frequentist strategies (LASSO) and popular Bayesian strategies (spike-and-slab). The main thrust of this paper is to introduce the family of Spike-and-Slab LASSO (SS-LASSO) priors, which form a continuum between the Laplace prior and the point-mass spike-and-slab prior. We establish several appealing frequentist properties of SS-LASSO priors, contrasting them with these two…

估计 fMRI 动态功能网络连接的贝叶斯方法AI 解读

Dynamic functional connectivity, i.e., the study of how interactions among brain regions change dynamically over the course of an fMRI experiment, has recently received wide interest in the neuroimaging literature. Current approaches for studying dynamic connectivity often rely on ad-hoc approaches for inference, with the fMRI time courses segmented by a sequence of sliding windows. We propose a principled Bayesian approach to dynamic functional connectivity, which is based…

BNP-Seq：测序计数数据的贝叶斯非参数差异表达分析AI 解读

We perform differential expression analysis of high-throughput sequencing count data under a Bayesian nonparametric framework, removing sophisticated ad hoc pre-processing steps commonly required in existing algorithms. We propose to use the gamma (beta) negative binomial process, which takes into account different sequencing depths using sample-specific negative binomial probability (dispersion) parameters, to detect differentially expressed genes by comparing the posterior…

动态有序回归关系建模：加州岩鱼成熟度估计AI 解读

We develop a Bayesian nonparametric framework for modeling ordinal regression relationships, which evolve in discrete time. The motivating application involves a key problem in fisheries research on estimating dynamically evolving relationships between age, length, and maturity, the latter recorded on an ordinal scale. The methodology builds from nonparametric mixture modeling for the joint stochastic mechanism of covariates and latent continuous responses. This approach…

物种发现的多臂老虎机：贝叶斯非参数方法AI 解读

Marco Battistona, Stefano Favarob* & Yee Whye Tehca Department of Decision Sciences, Bocconi University, Italyb Department of Economics and Statistics, University of Torino and Collegio Carlo Alberto, Torino, Italyc Department of Statistics, University of Oxford, Oxford, United KingdomCONTACT Stefano Favaro stefano.favaro@unito.it Department of Economics and Statistics, University of Torino, 10124 Torino, Italy and Collegio Carlo Alberto, 10024 Moncalieri TO, ItalyColor…