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Bayesian Marginal Inference

贝叶斯边际推断

A method is proposed for approximating the marginal posterior density of a continuous function of several unknown parameters, thus permitting inferences about any parameter of interest for nonlinear models when the sample size is finite. Possibly tedious numerical integrations are replaced by conditional maximizations, which are shown to be quite accurate in a number of special cases. There are similarities with the profile likelihood ideas originated by Kalbfleisch and…

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Is Two-Phase Sampling Really Better for Estimating Age Composition?

两阶段抽样真的更适合估计年龄构成吗?

The two-phase sampling design has been traditionally used in ecology applications to estimate age composition. With regard to both economic and statistical considerations, however, the two-phase design may yield estimates of the age composition that are no better than can be obtained using simple random sampling. This article shows that the optimality of the two-phase sampling design depends upon (a) survey objectives, (b) per-unit sampling costs, and (c) the predictive…

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Estimation of Treatment Difference following a Sequential Clinical Trial

序贯临床试验结束后的治疗差异估计

To reduce the number of patients needed to reach a conclusion in a clinical trial, a sequential trial design may be used. In theory the distribution of responses is biased when a sequential trial is stopped. The usual estimation methods of treatment difference applied in nonsequential situations are, therefore, not necessarily applicable following a sequential test. Whitehead (1983) proposed a method for estimating the treatment effect following some types of two-sample…

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Response Surface Analysis with Correlated Data: A Nonlinear Model Approach

相关数据的响应面分析:非线性模型方法

Statistical methods for fitting nonlinear functions to data generated by correlated response variates are discussed. Estimation of the model parameters is performed with an iterative two-stage scheme. The estimation procedure accommodates both within-unit and between-unit variability in fitting a response surface. Under regularity conditions the procedure yields asymptotically normal, strongly consistent estimators. If desired a patterned variance-covariance matrix can be…

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Multiple Test Procedures in Clinical Dose Finding Studies

临床剂量探索研究中的多重检验程序

Test procedures in clinical dose finding studies are considered when it can be assumed that increasing dose levels lead to a larger or at least equal efficacy. If one is interested in various comparisons within the set of dose levels, one arrives at a problem of multiple testing against ordered alternatives. Some multiple test procedures controlling the multiple level of significance are compared in a simulation study. It follows that a simple procedure that only uses…

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Accounting for Misclassification in the Cause-of-Death Test for Carcinogenicity

在致癌性死因检验中考虑死因误分类

The cause-of-death test (Peto 1974; Peto et al. 1980) provides a test for carcinogenicity without requiring extreme lethality assumptions. The approach has been criticized, however, because cause-of-death determinations require subjective decisions by pathologists and may be unreliable. Using a missing data formulation, we derive a simple, intuitive modification of the test that allows for misclassification of cause of death. The modified statistic is a function of the…

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A Model for Informative Censoring

信息性删失的一种模型

In the usual model for censored survival analysis, observations are of the form X = min(T, C), where T and C are nonnegative random variables representing lifetime and censoring time, respectively. Under the usual assumption of independence of T and C, the Kaplan-Meier estimator (KME) is the appropriate estimator of S(t) = Pr(T > t). The KME can lead to substantial overestimates of survival probabilities if the event of censoring indicates an unfavorable prognosis for future…

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A Semiparametric Model for Randomly Truncated Data

随机截断数据的半参数模型

For randomly censored data, it is known that the maximum likelihood estimate (MLE) of the survival curve is not affected by parametric assumption on the censoring variable. The Kaplan-Meier (1958) estimate is the MLE for both nonparametric and semiparametric models. For randomly truncated data, the truncation product-limit estimate is the MLE for nonparametric models. This is not the case if the truncation mechanism is parameterized, however. Specifically, let X be a generic…

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Discretized and Interpolated Kernel Density Estimates

离散化与插值后的核密度估计

The kernel estimate of a probability density function inherits its smoothness properties from the kernel density chosen by the investigator. Nevertheless, for computational (and especially graphical) reasons, exact kernel density estimates are often presented in (piecewise constant) discretized or (piecewise linear) interpolated form, using the exact estimate only at some grid of points. The asymptotic integrated mean squared error properties of these modifications are…

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Fully Exponential Laplace Approximations to Expectations and Variances of Nonpositive Functions

非正函数期望与方差的完全指数型拉普拉斯近似

Tierney and Kadane (1986) presented a simple second-order approximation for posterior expectations of positive functions. They used Laplace's method for asymptotic evaluation of integrals, in which the integrand is written as f(θ)exp(-nh(θ)) and the function h is approximated by a quadratic. The form in which they applied Laplace's method, however, was fully exponential: The integrand was written instead as exp[− nh(θ) + log f(θ)]; this allowed first-order approximations to…

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An Application of Nonlinear Bounded Influence Estimation to Aggregate Bank Borrowing from the Federal Reserve

非线性有界影响估计在美联储银行总借款中的应用

Forecasting aggregate discount window borrowing has posed difficulties for the Federal Reserve, due in part to outliers resulting from numerous institutional changes and special borrowing situations. This article applies bounded influence estimation and influence diagnostics to identify and adjust for outliers in the case of discount window borrowing. Since most banks borrow from the Federal Reserve infrequently, the model is nonlinear and of the switching regression class.…

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Multivariate Time Series Projections of Parameterized Age-Specific Fertility Rates

参数化年龄别生育率的多元时间序列预测

Projection of individual age-specific fertility rates is a forecasting problem of high dimension. We solve this dimensionality problem by using parametric curves to approximate the annual age-specific rates and a multivariate time series model to forecast the curve parameters. These yield forecasts of future fertility curves, which are then used to compute age-specific fertility rate forecasts. This reduces the dimensionality of the forecasting problem and also guarantees…

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The Ames Salmonella /Microsome Mutagenicity Assay: Issues of Inference and Validation

Ames 沙门氏菌/微粒体致突变试验:推断与验证

The importance of chemically induced mutation for human health is discussed briefly, and the biological basis for the primary in vitro assay for mutagenicity, the Ames Salmonella/microsome assay, is reviewed. A previous analysis for Ames test data, based on two mathematical models of the competing risks of mutation and toxicity, is shown to have inflated false-positive rates. A reason for this is the existence of local singularities in the Fisher information matrix. A new…

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Empirical Bayes Procedures for Stabilizing Maps of U.S. Cancer Mortality Rates

稳定美国癌症死亡率地图的经验贝叶斯方法

"The geographic mapping of age-standardized, cause-specific death rates is a powerful tool for identifying possible etiologic factors, because the spatial distribution of mortality risks can be examined for correlations with the spatial distribution of disease-specific risk factors. This article presents a two-stage empirical Bayes procedure for calculating age-standardized cancer death rates, for use in mapping, which are adjusted for the stochasticity of rates in small…

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Application of Bayesian Decision Procedure to the Inference of Genetic Linkage

贝叶斯决策程序在遗传连锁推断中的应用

The purpose of this article is to introduce the concept of O-Ki loss to the inference of genetic linkage. The prior information proposed by Elston and Lange (1975) was used. To help geneticists to understand the implications of the loss function and the Bayes decision rule, the Bayes decision procedure proposed in this article was suggested to be treated as a conventional test statistic. Then it seems almost natural to compare the performance of power of the statistic…

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Estimation of Treatment Difference Following a Sequential Clinical Trial

序贯临床试验结束后的治疗差异估计

To reduce the number of patients needed to reach a conclusion in a clinical trial, a sequential trial design may be used. In theory the distribution of responses is biased when a sequential trial is stopped. The usual estimation methods of treatment difference applied in nonsequential situations are, therefore, not necessarily applicable following a sequential test. Whitehead (1983) proposed a method for estimating the treatment effect following some types of two-sample…

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