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Student-t 回归模型的客观贝叶斯分析AI 解读

We develop a Bayesian analysis based on two different Jeffreys priors for the Student-t regression model with unknown degrees of freedom. It is typically difficult to estimate the number of degrees of freedom: improper prior distributions may lead to improper posterior distributions, whereas proper prior distributions may dominate the analysis. We show that Bayesian analysis with either of the two considered Jeffreys priors provides a proper posterior distribution. Finally,…

利用目标函数与随机搜索进行聚类AI 解读

Summary A new approach to clustering multivariate data, based on a multilevel linear mixed model, is proposed. A key feature of the model is that observations from the same cluster are correlated, because they share cluster-specific random effects. The inclusion of cluster-specific random effects allows parsimonious departure from an assumed base model for cluster mean profiles. This departure is captured statistically via the posterior expectation, or best linear unbiased…

高维模型选择：基于二次风险的方法AI 解读

Summary We propose a general class of risk measures which can be used for data-based evaluation of parametric models. The loss function is defined as the generalized quadratic distance between the true density and the model proposed. These distances are characterized by a simple quadratic form structure that is adaptable through the choice of a non-negative definite kernel and a bandwidth parameter. Using asymptotic results for the quadratic distances we build a…

贝叶斯层级模型中 Gibbs 采样器的稳定性AI 解读

We characterize the convergence of the Gibbs sampler which samples from the joint posterior distribution of parameters and missing data in hierarchical linear models with arbitrary symmetric error distributions. We show that the convergence can be uniform, geometric or subgeometric depending on the relative tail behavior of the error distributions, and on the parametrization chosen. Our theory is applied to characterize the convergence of the Gibbs sampler on latent Gaussian…

存在设定误差时的回归不连续推断AI 解读

A regression discontinuity (RD) research design is appropriate for program evaluation problems in which treatment status (or the probability of treatment) depends on whether an observed covariate exceeds a fixed threshold. In many applications the treatment-determining covariate is discrete. This makes it impossible to compare outcomes for observations "just above" and "just below" the treatment threshold, and requires the researcher to choose a functional form for the…

狄利克雷过程层级模型的回溯式马尔可夫链蒙特卡洛方法AI 解读

Inference for Dirichlet process hierarchical models is typically performed using Markov chain Monte Carlo methods, which can be roughly categorized into marginal and conditional methods. The former integrate out analytically the infinite-dimensional component of the hierarchical model and sample from the marginal distribution of the remaining variables using the Gibbs sampler. Conditional methods impute the Dirichlet process and update it as a component of the Gibbs sampler.…

学生化与准确 p 值的推导AI 解读

We have a statistic for assessing an observed data point relative to a statistical model but find that its distribution function depends on the parameter. To obtain the corresponding p-value, we require the minimally modified statistic that is ancillary; this process is called Studentization. We use recent likelihood theory to develop a maximal third-order ancillary; this gives immediately a candidate Studentized statistic. We show that the corresponding p-value is…

经验型似然产生的贝叶斯与频率学派置信区间AI 解读

For a general class of empirical-type likelihoods for the population mean, higher-order asymptotics are developed with a view to characterizing its members which allow, for any given prior, the existence of a confidence interval that has approximately correct posterior as well as frequentist coverage. In particular, it is seen that the usual empirical likelihood always allows such a confidence interval, while many of its variants proposed in the literature do not enjoy this…

二元响应数据的灵活广义 t 链接模型AI 解读

A critical issue in modelling binary response data is the choice of the links. We introduce a new link based on the generalized t-distribution. There are two parameters in the generalized t-link: one parameter purely controls the heaviness of the tails of the link and the second parameter controls the scale of the link. Two major advantages are offered by the generalized t-links. First, a symmetric generalized t-link with an unknown shape parameter is much more identifiable…

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多重变点与混合创新模型的高效贝叶斯推断AI 解读

Time series subject to parameter shifts of random magnitude and timing are commonly modeled with a change-point approach using Chib's algorithm to draw the break dates. We outline some advantages of an alternative approach in which breaks come through mixture distributions in state innovations, and for which the sampler of Gerlach, Carter, and Kohn allows reliable and efficient inference. We show how the same sampler can be used to model shifts in variance that occur…

贝叶斯与信息论模型平均在预测中的应用AI 解读

Model averaging often improves forecast accuracy over individual forecasts. It may also be seen as a means of forecasting in data-rich environments. Bayesian model averaging methods have been widely advocated, but a neglected frequentist approach is to use information-theoretic-based weights. We consider the use of information-theoretic model averaging in forecasting U.K. inflation, with a large dataset, and find that it can be a powerful alternative to Bayesian averaging…

二项自回归移动平均模型及其在美国经济衰退中的应用AI 解读

Binary Autoregressive Moving Average (BARMA) models provide a modeling technology for binary time series analogous to the classic Gaussian ARMA models used for continuous data. BARMA models mitigate the curse of dimensionality found in long lag Markov models and allow for non-Markovian persistence. The autopersistence function (APF) and autopersistence graph (APG) provide analogs to the autocorrelation function and correlogram. Parameters of the BARMA model may be estimated…

多条时间序列的模型聚类AI 解读

We propose to pool multiple time series into several groups using finite-mixture models. Within each group, the same econometric model holds. We estimate the groups of time series simultaneously with the group-specific model parameters using Bayesian Markov chain Monte Carlo simulation methods. We discuss model identification and base model selection on marginal likelihoods. With a simulation study, we document the efficiency gains in estimation and forecasting realized…

产出缺口的贝叶斯分析AI 解读

Our objective is to build output gap estimates that benefit from information provided by Phillips curve theory and business cycle studies. For this, we develop a Bayesian analysis of the bivariate Phillips curve model proposed by Kuttner for estimating potential output. Given our priors, we obtain samples from parameters and state variables joint posterior distribution following a Gibbs sampling strategy. We sample the state variables given parameters using the Carter–Kohn…

财务比率的多变量部分调整：贝叶斯层级方法AI 解读

Abstract In this paper we propose a multivariate extension of the partial adjustment model of financial ratios. To that end, we use a dynamic factor model which assumes that financial ratios measuring, essentially, the same economic–financial dimension of the firm evolve in a similar way, reflecting the evolution of the common factor. The proposed model is hierarchical with three levels. The first describes the relationship between each ratio and its common factor; the…

等位基因丢失频率数据的贝叶斯分析AI 解读

One objective of allelic-loss studies is to identify chromosomal locations that may harbor tumor-suppressor genes. An instability-selection model has been developed for allelic-loss data in which the loss events are available for each tumor and each marker (allelotypes). In performing pooled analyses of published allelic-loss experiments, however, only summaries of the frequency of allelic loss (FAL) may be available. The instability-selection model can be applied to these…

非齐次泊松过程的贝叶斯预测及呼叫中心应用AI 解读

A call center is a centralized hub where customer and other telephone calls are handled by an organization. In today's economy, call centers have become the primary points of contact between customers and businesses. Thus accurate predictions of call arrival rates are indispensable to help call center practitioners staff their call centers efficiently and cost-effectively. This article proposes a multiplicative model for modeling and forecasting within-day arrival rates to a…

多中心生存研究的多分辨率风险模型AI 解读

In multicenter studies, one often needs to make inference about a population survival curve based on multiple, possibly heterogeneous survival data from individual centers. We investigate a flexible Bayesian method for estimating a population survival curve based on a semiparametric multiresolution hazard model that can incorporate covariates and account for center heterogeneity. The method yields a smooth estimate of the survival curve for "multiple resolutions" or time…

贝叶斯多元保序回归样条AI 解读

In many applications, interest focuses on assessing the relationship between a predictor and a multivariate outcome variable, and there may be prior knowledge about the shape of the regression curves. For example, regression functions that relate dose of a possible risk factor to different adverse outcomes can often be assumed to be nondecreasing. In such cases, interest focuses on (1) assessing evidence of an overall adverse effect, (2) determining which outcomes are most…

协变量缺失下的统计分类AI 解读

Summary Some results related to statistical classification in the presence of missing covariates are presented. We derive representations for the best (Bayes) classifier when some of the covariates can be missing; this is done without imposing any assumptions on the underlying missing probability mechanism. Furthermore, without assuming any missingness-at-random type of conditions, we also construct Bayes consistent classifiers that do not require any imputation-based…

不依赖变量顺序的区域数据协同区域化模型及多疾病制图应用AI 解读

Summary With the ready availability of spatial databases and geographical information system software, statisticians are increasingly encountering multivariate modelling settings featuring associations of more than one type: spatial associations between data locations and associations between the variables within the locations. Although flexible modelling of multivariate point-referenced data has recently been addressed by using a linear model of co-regionalization, existing…

使用近似工具变量的测量误差建模AI 解读

Summary Consider using regression modelling to relate an exposure (predictor) variable to a disease outcome (response) variable. If the exposure variable is measured with error, but this error is ignored in the analysis, then misleading inferences can result. This problem is well known and has spawned a large literature on methods which adjust for measurement error in predictor variables. One theme is that the requisite assumptions about the nature of the measurement error…