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半参数部分样条与广义样条模型中的参数零模型检验AI 解读

Cox and Koh (1986) considered the model $y_i = f(x(i)) + \varepsilon_i, \varepsilon_i$ i.i.d. $N(0, \sigma^2)$, with the (parametric) null hypothesis $f(x), x \in \lbrack 0, 1 \rbrack$, a polynomial of degree $m - 1$ or less, versus the alternative $f$ is "smooth," based on the Bayesian model for $f$ which leads to polynomial smoothing spline estimates for $f$. They showed that there was no uniformly most powerful test and found the locally most powerful (LMP) test. We…

多元 Behrens–Fisher 问题的贝叶斯解法AI 解读

We consider the problem of finding the posterior probabilities of ellipsoids for the difference between two multivariate normal means. We do not require the two population covariance matrices to be equal, therefore, our results pertain to the multivariate Behrens—Fisher problem. A Hotelling T 2-like quantity is defined, and its cdf is expressed as a linear combination of the cdf's of some F distributions. This representation enables us to compute desired probabilities…

摘要暂缺

基于剖面似然的区间估计：强拉格朗日理论及判别分析应用AI 解读

Strong Lagrangian theory is used to illuminate the properties of the profile log likelihood. General conditions are given which lead to a simplification of the computations required to plot this function or calculate interval estimates based upon it. The results presented are rather general with a variety of possible applications. In particular, it is shown that they provide a simple solution to the important practical problem of obtaining an interval estimate for the…

生物测定效力曲线的线性贝叶斯估计量AI 解读

The prior distribution on the class of potency curves in quantal bioassay is assumed to be Ferguson's Dirichlet distribution. Given integrated squared error loss and quantal response data, we derive the Bayes estimator in a linear space generated by the data. Some numerical examples and asymptotic results are also given.

To explain the interactive and causal relationships between gold and silver price movements, time series procedures are used to identify reduced-form parameters corresponding to a general arbitrage model. Enveloped in a framework of expectations about capital gains, current price changes are conjectured to be functions of lagged and present values of the substitute precious metal prices and the interest rate, plus lagged values of its own price. To determine the appropriate…

摘要暂缺

异常值检测与残差分析的贝叶斯方法AI 解读

An approach to detecting outliers in a linear model is developed. An outlier is defined to be an observation with a large random error, generated by the linear model under consideration. Outliers are detected by examining the posterior distribution of the random errors. An augmented residual plot is also suggested as a graphical aid in finding outliers.

贝叶斯自助法的直方样条平滑AI 解读

This paper describes a version of the Bayesian bootstrap that assigns random Dirichlet mass uniformly across statistically equivalent blocks. The method requires prior knowledge that the underlying distribution is continuous with known compact support. Under these conditions, the resulting analysis has three advantages over traditional bootstrap competitors. First, it takes account of the probability integral transformation. Secondly, it often enables exact expressions for…

计量型一次抽样方案的贝叶斯方法AI 解读

In this paper, we develop a model of sampling plans for variables with a polynomial loss function, in which the decision function is either one-sided or two-sided. Based on a Bayesian approach, we suggest a simple finite algorithm for the determination of the optimal single sampling plan. Furthermore, for the case of a symmetric two-sided decision function, we propose an approximate method for determining its optimal single sampling plan.

二项分布参数 N 的推断：层级贝叶斯方法AI 解读

A hierarchical Bayes approach to the problem of estimating N in the binomial distribution is presented. This provides a simple and flexible way of specifying prior information, and also allows a convenient representation of vague prior knowledge. It yields solutions to the problems of interval estimation, prediction and decision making, as well as that of point estimation. The Bayes estimator compares favourably with the best, previously proposed', point estimators in the…

基于剖面似然的区间估计：强拉格朗日理论及判别应用AI 解读

Strong Lagrangian theory is used to illuminate the properties of the profile log likelihood. General conditions are given which lead to a simplification of the computations required to plot this function or calculate interval estimates based upon it. The results presented are rather general with a variety of possible applications. In particular, it is shown that they provide a simple solution to the important practical problem of obtaining an interval estimate for the…

生物测定效价曲线的线性贝叶斯估计AI 解读

The prior distribution on the class of potency curves in quantal bioassay is assumed to be Ferguson's Dirichlet distribution. Given integrated squared error loss and quantal response data, we derive the Bayes estimator in a linear space generated by the data. Some numerical examples and asymptotic results are also given.

统计证据的信念函数表示AI 解读

In Glenn Shafer's theory of parametric statistical inference, observational evidence and prior evidence are separately represented by belief or commonality functions $Q$ and $R$, which are then combined by Dempster's rule. We characterise, for finite parameter spaces, the functionals $Q$ and $R$ for which statistically independent observations may be combined by Dempster's rule, and those for which Dempster's rule is consistent with Bayes' rule. The functionals are…

若干类全局 Cramér–Rao 界AI 解读

This paper considers Cramer-Rao type bounds for the estimation error of a parameter in a Bayesian setup. This class of bounds, introduced by Van Trees, proved useful in various stochastic communications and control problems. Two issues are considered in this paper. The first deals with a comparison of the tightness of several different versions of the bound in the multivariate case. The second introduces several useful generalizations of the original version of the bound.

分层样本均值的稳健经验贝叶斯估计AI 解读

This article considers simultaneous estimation of means from several strata, where each stratum contains a finite number of elements. For example, quite often estimates of annual incomes, unemployment rates, and so forth must be made simultaneously for many areas. Our results find application in small area estimation where very few samples are available from an individual area, and an estimate of a certain area mean or simultaneous estimates of several area means can be…

模型选择后推断：变换型与自适应推断的决策论方法AI 解读

A decision-theory approach is formulated for inference following model selection. Inference here refers to either testing, point estimation, or confidence estimation. The loss function includes components for model selection as well as for inference and allows for flexibility in emphasis on one or the other, if such emphasis is desired. A general prescription for Bayes and generalized Bayes procedures is given. A procedure consists of model selection and inference. The…

总体规模未知的一般次序统计量模型：推断与预测AI 解读

Suppose that the first n order statistics from a random sample of N positive random variables are observed, where N is unknown. This, the general order statistic model, has been applied to the study of market penetration, capture—recapture, burn-in in repairable systems, software reliability growth, the estimation of the number of individuals exposed to radiation, and the estimation of the number of unseen species. Inference is to be made about the unknown parameters,…

估计总体与词汇规模的多项分布贝叶斯方法AI 解读

We approach estimation of the size of a population or a vocabulary through a Bayesian analysis of the multinomial distribution. We view the sample as being generated from such a distribution with an unknown number of cells and unknown cell probabilities, and develop a Bayesian procedure to estimate the number of cells and the coverage of the sample. The prior distribution of the number of cells is arbitrary. Given that number, the cell probabilities are assumed to follow a…

删失生存数据的近似贝叶斯分析AI 解读

The Bayesian analysis of data arising from a location-scale regression model, and which may include a number of right-censored observations, is considered. The posterior distributions of the suitably normalized precision parameter and regression coefficient vector are shown to be well approximated by X2 and multivariate t distributions respectively. The ideas are illustrated using some clinical survival data.

测量误差诊断与性别歧视问题AI 解读

Numerical and graphical diagnostic tools are presented for studying the effect of explanatory-variable measurement errors on regression results when very rough knowledge about the measurement-error variances or reliabilities is available. These methods are exhibited on an example of sex discrimination in which male and female salaries are compared after adjustment for individual qualifications but the observed qualification variables are only proxies for what is actually…

自适应处理分配与多臂老虎机问题AI 解读

A class of simple adaptive allocation rules is proposed for the problem (often called the "multi-armed bandit problem") of sampling $x_1, \cdots x_N$ sequentially from $k$ populations with densities belonging to an exponential family, in order to maximize the expected value of the sum $S_N = x_1 + \cdots + x_N$. These allocation rules are based on certain upper confidence bounds, which are developed from boundary crossing theory, for the $k$ population parameters. The rules…

摘要暂缺

贝叶斯方法在家庭用水日记分析中的应用AI 解读

One of the objectives of a comprehensive domestic water use study conducted in Perth, Western Australia, was the quantification of components of water usage. Each household in a sample of about 3,000 was asked to record all water uses in a specially provided diary for a 2-week period, and the total water usage, both in-house and ex-house, was metered daily during this time. This article describes an application of Bayesian methodology to the estimation of usage for each…