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散点图平滑器的选择准则AI 解读

Scatterplot smoothers estimate a regression function y = f(x) by local averaging of the observed data points (xi, yi). In using a smoother, the statistician must choose a “window width,” a crucial smoothing parameter that says just how locally the averaging is done. This paper concerns the data­based choice of a smoothing parameter for splinelike smoothers, focusing on the comparison of two popular methods, Cp and generalized maximum likelihood. The latter is the MLE within…

扩散模型的 MCMC 分析及其金融应用AI 解读

This article proposes a new method for estimation of parameters in diffusion processes from discrete observations. The method is based on Markov-chain Monte Carlo methodology and applies to a wide class of models including systems with unobservable state variables and nonlinearities. The method is applied to the estimation of parameters in one-factor (CEV) interest-rate models and a two-factor model with a latent stochastic volatility component (SV). The CEV model is found…

投资融资约束的跨期变化AI 解读

This article is concerned with understanding how financial constraints on investment vary over the business cycle and whether these constraints are related to macroeconomic policies. These issues are investigated within the framework of a time-varying parameter model using U.S. company panel data from 1971 to 1993. A preliminary investigation of parameter stability in investment equations using cross-sectional estimation techniques indicates a pattern of parameter variation…

资产定价中贝叶斯推断的一则注记AI 解读

In this paper the authors extend results by Harvey and Zhou (1990, Journal of Financial Econometrics 26, 221–254) and Kandel, McCulloch, and Stambaugh (1995, Review of Financial Studies 8(1), 1–53) to derive the posterior distribution of a key parameter in a Bayesian analysis of asset pricing models. It is shown that this distribution depends upon the same terms that constitute the standard asset pricing test of Jobson and Korkie (1985, Canadian Journal of Administrative…

参数模型对非参数备择的贝叶斯与条件频率学派检验AI 解读

Testing the fit of data to a parametric model can be done by embedding the parametric model in a nonparametric alternative and computing the Bayes factor of the parametric model to the nonparametric alternative. Doing so by specifying the nonparametric alternative via a Polya tree process is particularly attractive, from both theoretical and methodological perspectives. Among the benefits is a degree of computational simplicity that even allows for robustness analyses to be…

点源附近疾病风险的贝叶斯建模AI 解读

Recently there has been increased interest, from both the media and the public, in the question, “Is there an excess of disease risk close to a prespecified point source?” To address this question, routinely available public health data may be analyzed. In the United Kingdom, as in many countries, health data and the associated population data that are required for comparison, are available as aggregated counts. In this article we propose to analyze such data using a…

考古磁测调查数据的贝叶斯分析AI 解读

A model is presented for the interpretation of magnetometer data in terms of archeological features beneath the ground. It describes the detector's response to the assemblage of buried features, incorporating both a spread function and a statistical error process as well as appropriate prior beliefs about the nature of archeological features. The problem is to estimate the magnetic susceptibility of the buried features at each horizontal location. A Monte Carlo Markov chain…

实时估计数百万个动态交易时点模式AI 解读

In some business applications, the transaction behavior of each customer is tracked separately with a customer signature. A customer's signature for buying behavior, for example, may contain information on the likely place of purchase, value of goods purchased, type of goods purchased, and timing of purchases. The signature may be updated whenever the customer makes a transaction, and, because of storage limitations, the updating may be able to use only the new transaction…

局部似然估计中模型选择的信息与后验概率准则AI 解读

Local likelihood estimation has proven to be an effective method for obtaining estimates of parameters that vary with a covariate. To obtain useful estimates of such parameters, approximating models are used. In such cases it is useful to consider window based estimates. We may need to choose between competing approximating models. In this article, we propose a modification to the methods used to motivate many information and posterior probability criteria for the weighted…

利用 Metropolis–Hastings 输出估计边际似然AI 解读

This article provides a framework for estimating the marginal likelihood for the purpose of Bayesian model comparisons. The approach extends and completes the method presented in Chib (1995) by overcoming the problems associated with the presence of intractable full conditional densities. The proposed method is developed in the context of MCMC chains produced by the Metropolis–Hastings algorithm, whose building blocks are used both for sampling and marginal likelihood…

折棍先验的 Gibbs 抽样方法AI 解读

A rich and flexible class of random probability measures, which we call stick-breaking priors, can be constructed using a sequence of independent beta random variables. Examples of random measures that have this characterization include the Dirichlet process, its two-parameter extension, the two-parameter Poisson–Dirichlet process, finite dimensional Dirichlet priors, and beta two-parameter processes. The rich nature of stick-breaking priors offers Bayesians a useful class…

多元伯努利观测的平滑样条方差分析及眼科应用AI 解读

We combine a smoothing spline analysis of variance (SS-ANOVA) model and a log-linear model to build a partly flexible model for multivariate Bernoulli data. The joint distribution conditioning on the predictor variables is estimated. The log odds ratio is used to measure the association between outcome variables. A numerical scheme based on the block one-step successive over relaxation SOR–Newton-Ralphson algorithm is proposed to obtain an approximate solution for the…

利用家庭和社区随机效应研究马拉维儿童死亡率AI 解读

The Malawi Demographic and Health Survey conducted in 1992 collected the retrospective birth histories for a national sample of 4,878 women aged between 15 and 49 years. The sample was randomly selected by a two-stage sampling design. The data consist of biological, demographic, and social variables collected for each birth. This article models the infant and early childhood survival using family and community random effect multipliers on the fixed effect proportional…

经典与动态切换及混合模型的马尔可夫链蒙特卡洛估计AI 解读

Bayesian estimation of a very general model class, where the distribution of the observations depends on a latent process taking values in a discrete state space, is discussed in this article. This model class covers finite mixture modeling, Markov switching autoregressive modeling, and dynamic linear models with switching. The consequences the unidentifiability of this type of model has on Markov chain Monte Carlo (MCMC) estimation are explicitly dealt with. Joint Bayesian…

用于错误检测与总体规模估计的贝叶斯捕获—再捕获方法：异质性与依赖性AI 解读

This paper considers estimation of the unknown size N of a population based on multiple capture‐recapture samples. We extend the Bayesian multiple recapture model to accommodate possible heterogeneity and dependence among the samples and possible heterogeneity within the samples. In the dependent model, we show that posterior inference for N is independent of almost all the nuisance parameters. We develop a flexible Bayesian model for heterogeneity within samples and…

贝叶斯模型平均的基准先验AI 解读

In contrast to a posterior analysis given a particular sampling model, posterior model probabilities in the context of model uncertainty are typically rather sensitive to the specification of the prior. In particular, 'diffuse' priors on model-specific parameters can lead to quite unexpected consequences. Here we focus on the practically relevant situation where we need to entertain a (large) number of sampling models and we have (or wish to use) little or no subjective…

多元线性样条的贝叶斯回归AI 解读

Summary We present a Bayesian analysis of a piecewise linear model constructed by using basis functions which generalizes the univariate linear spline to higher dimensions. Prior distributions are adopted on both the number and the locations of the splines, which leads to a model averaging approach to prediction with predictive distributions that take into account model uncertainty. Conditioning on the data produces a Bayes local linear model with distributions on both…

追踪移动目标：动态贝叶斯模型的蒙特卡洛推断AI 解读

Summary Markov chain Monte Carlo (MCMC) sampling is a numerically intensive simulation technique which has greatly improved the practicality of Bayesian inference and prediction. However, MCMC sampling is too slow to be of practical use in problems involving a large number of posterior (target) distributions, as in dynamic modelling and predictive model selection. Alternative simulation techniques for tracking moving target distributions, known as particle filters, which…

摘要暂缺

基于部分累计数据预测累计总量AI 解读

We present a Bayesian solution to forecasting a time series when few observations are available. The quantity to predict is the accumulated value of a positive, continuous variable when partially accumulated data are observed. These conditions appear naturally in predicting sales of style goods and coupon redemption. A simple model describes the relation between partial and total values, assuming stable seasonality. Exact analytic results are obtained for point forecasts and…

离散持续时间模型的贝叶斯半参数估计：Dirichlet 过程先验应用AI 解读

Abstract This paper proposes a Bayesian estimator for a discrete time duration model which incorporates a non‐parametric specification of the unobserved heterogeneity distribution, through the use of a Dirichlet process prior. This estimator offers distinct advantages over the Nonparametric Maximum Likelihood estimator of this model. First, it allows for exact finite sample inference. Second, it is easily estimated and mixed with flexible specifications of the baseline…

贝叶斯图像复原中Gibbs采样器收敛时间的界AI 解读

This paper shows how coupling methodology can be used to give precise, a priori bounds on the convergence time of Markov chain Monte Carlo algorithms for which a partial order exists on the state space which is preserved by the Markov chain transitions. This methodology is applied to give a bound on the convergence time of the random scan Gibbs sampler used in the Bayesian restoration of an image of N pixels. For our algorithm, in which only one pixel is updated at each…

校准与经验贝叶斯变量选择AI 解读

For the problem of variable selection for the normal linear model, selection criteria such as aic, Cp , bic and ric have fixed dimensionality penalties. Such criteria are shown to correspond to selection of maximum posterior models under implicit hyperparameter choices for a particular hierarchical Bayes formulation. Based on this calibration, we propose empirical Bayes selection criteria that use hyperparameter estimates instead of fixed choices. For obtaining these…

BIC 马尔可夫阶数估计量的一致性AI 解读

The Bayesian Information Criterion (BIC) estimates the order of a Markov chain (with finite alphabet $A$) from observation of a sample path $x_1, x_2,\dots, x_n$, as that value $k = \hat{k}$ that minimizes the sum of the negative logarithm of the $k$th order maximum likelihood and the penalty term $\frac{|A|^k(|A|-1)}{2}\log n$. We show that $\hat{k}$ equals the correct order of the chain, eventually almost surely as $n \rightarrow \infty$, thereby strengthening earlier…