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Modelling Complexity: Applications of Gibbs Sampling in Medicine

复杂模型建模:Gibbs 抽样在医学中的应用

SUMMARY We review applications of Gibbs sampling in medicine, involving longitudinal, spatial, covariate measurement and survival models. Applications in immunology, pharmacology, transplantation, cancer screening, industrial epidemiology and genetic epidemiology are discussed.

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Spatial Statistics and Bayesian Computation

空间统计与贝叶斯计算

SUMMARY Markov chain Monte Carlo (MCMC) algorithms, such as the Gibbs sampler, have provided a Bayesian inference machine in image analysis and in other areas of spatial statistics for several years, founded on the pioneering ideas of Ulf Grenander. More recently, the observation that hyperparameters can be included as part of the updating schedule and the fact that almost any multivariate distribution is equivalently a Markov random field has opened the way to the use of…

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Spherical Median Axes

球面中位轴

SUMMARY In an earlier paper, Fisher defined the notion of a median direction for data from a unimodal distribution of three-dimensional unit vectors and studied its statistical properties. Corresponding notions of a median axis for bipolar axial or great circle data were also suggested but not analysed. This paper gives a statistical treatment of spherical median axes, including their asymptotic relative efficiencies, and a comparison with the customary principal or polar…

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Maximum Likelihood Estimation of Parameters under a Spatial Sampling Scheme

空间抽样方案下的参数极大似然估计

We study in detail asymptotic properties of maximum likelihood estimators of parameters when observations are taken from a two-dimensional Gaussian random field with a multiplicative Ornstein-Uhlenbeck covariance function. Under the complete lattice sampling plan, it is shown that the maximum likelihood estimators are strongly consistent and asymptotically normal. The asymptotic normality here is normalized by the fourth root of the sample size and is obtained through higher…

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Fitting Continuous ARMA Models to Unequally Spaced Spatial Data

不等间距空间数据的连续ARMA模型拟合

Methods for fitting continuous spatial autoregressive moving average (ARMA) models to unequally spaced observations in two dimensions are reviewed and extended. These are models with rational two-dimensional spectra. Assuming Gaussian input noise and observational errors, maximum likelihood methods are used to estimate the ARMA parameters and the regression coefficients of the deterministic trend. When the number of observations is too large for exact maximum likelihood…

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The Effect of Marijuana Decriminalization on Hospital Emergency Room Drug Episodes: 1975–1978

大麻非刑事化对医院急诊涉药事件的影响:1975—1978年

Between 1973 and 1978, 12 states with collectively over one-third of the total U.S. population enacted laws that decriminalized the possession of marijuana. This article uses standard metropolitan statistical area (SMSA) level data on hospital emergency room drug episodes collected by the Drug Abuse Warning Network to measure the effect of changes in drug penalties on substance abuse crises. The regression models demonstrate that marijuana decriminalization was accompanied…

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Fitting Continuous ARMA Models to Unequally Spaced Spatial Data

不等间距空间数据的连续 ARMA 模型拟合

Methods for fitting continuous spatial autoregressive moving average (ARMA) models to unequally spaced observations in two dimensions are reviewed and extended. These are models with rational two-dimensional spectra. Assuming Gaussian input noise and observational errors, maximum likelihood methods are used to estimate the ARMA parameters and the regression coefficients of the deterministic trend. When the number of observations is too large for exact maximum likelihood…

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Regional Trends in Sulfate Wet Deposition

硫酸盐湿沉降的区域趋势

I propose a multiple time series model for data from a network of monitoring stations that have both temporal and spatial correlation. The model includes a separate mean and trend for each monitoring station and obtains spatial estimates of mean and trend by smoothing the observed values over a rectangular grid using a discrete smoothing prior. Smoothing parameters and covariance estimates can be chosen subjectively or selected using indirect generalized cross-validation.…

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Statistical Theory and Modeling: In Honour of Sir David Cox, FRS.

统计理论与建模:纪念 David Cox 爵士

Part 1 Statistical theory - theoretical concepts significance tests theory of optimal tests estimation asymptotic theory. Part 2 Applied statistics - preliminary considerations statistical models statistical inference model adequancy exploratory and robust methods multi-variate methods use of computers. Part 3 Generalized linear models - a class of non-linear regression models likelihood functions estimation analysis of deviance checking the model. Part 4 Residuals and…

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Testing for neglected nonlinearity in time series models

时间序列模型中遗漏非线性的检验

In this paper a new test, the neural network test for neglected nonlinearity, is compared with the Keenan test, the Tsay test, the White dynamic information matrix test, the McLeod-Li test, the Ramsey RESET test, the Brock-Dechert-Scheinkman test, and the Bispectrum test. The neural network test is based on the approximating ability of neural network modeling techniques recently developed by cognitive scientists. This test is a Lagrange multiplier test that statistically…

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Approximate Inference in Generalized Linear Mixed Models

广义线性混合模型中的近似推断

Statistical approaches to overdispersion, correlated errors, shrinkage estimation, and smoothing of regression relationships may be encompassed within the framework of the generalized linear mixed model (GLMM). Given an unobserved vector of random effects, observations are assumed to be conditionally independent with means that depend on the linear predictor through a specified link function and conditional variances that are specified by a variance function, known prior…

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The Bias of Estimators of Causal Spatial Autoregressive Processes

因果型空间自回归过程估计量的偏差

We study the asymptotic distribution of Yule-Walker and least squares estimators for twodimensional causal autoregressive processes observed on a rectangular part of a lattice. An explicit expression for the asymptotic bias of Yule-Walker estimators is obtained. It is shown that this bias disappears if we use the so-called unbiased sample autocovariance function or least squares estimators.

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Semiparametric Analysis of Variance with Tensor Product Thin Plate Splines

采用张量积薄板样条的半参数方差分析

SUMMARY We consider fitting multivariate models to response data based on analysis-of-variance (ANOVA)-like decompositions of functions of several variables, f(t 1,..., td) = C + σα f α(ta + σα < β f αβ(t α, t β) + · · · · A theory for fitting (some components of) these models with polynomial smoothing splines exists when each tα is in a subset of the real line. In this case the various estimated components turn out to be certain tensor sums and products of polynomial…

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On median-type estimators of direction for the von Mises—Fisher distribution

von Mises–Fisher 分布方向参数的中位数型估计

We study three median-type estimators of direction: the normalized spatial median, L1-estimator on the sphere and spherical median. Their asymptotic distributions, efficiencies, influence functions and sensitivities are given at the von Mises-Fisher model. A simulation study is also carried out to compare their finite sample performance in terms of mean squared errors. We conclude that overall the normalized spatial median is the preferred estimator.

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The bias of estimators of causal spatial autoregressive processes

因果型空间自回归过程估计量的偏差

We study the asymptotic distribution of Yule-Walker and least squares estimators for twodimensional causal autoregressive processes observed on a rectangular part of a lattice. An explicit expression for the asymptotic bias of Yule-Walker estimators is obtained. It is shown that this bias disappears if we use the so-called unbiased sample autocovariance function or least squares estimators.

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Parameter Updating in a Bayes Network

贝叶斯网络中的参数更新

A Bayes network is a directed acyclic graph in which the links are quantified by fixed conditional probabilities and the nodes represent random variables. The primary use of the network is to provide an efficient method for updating conditional probabilities in the graph. We consider the consequences of using the network as the computational device for updating parameter estimates in the dynamic linear model, a discrete time Bayesian model. We show that using the network…

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Parameter Updating in a Bayes Network

贝叶斯网络中的参数更新

A Bayes network is a directed acyclic graph in which the links are quantified by fixed conditional probabilities and the nodes represent random variables. The primary use of the network is to provide an efficient method for updating conditional probabilities in the graph. We consider the consequences of using the network as the computational device for updating parameter estimates in the dynamic linear model, a discrete time Bayesian model. We show that using the network…

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Lyapunov exponents as a nonparametric diagnostic for stability analysis

作为稳定性分析非参数诊断工具的 Lyapunov 指数

The common observation made in the empirical nonlinear dynamics literature is the constraints imposed by the availability of a limited number of observations in the implementation of the existing algorithms of Lyapunov exponents. The algorithm discussed here can estimate all "n" Lyapunov exponents of an unknown "n"-dimensional dynamical system accurately with limited number of observations. This makes the algorithm attractive for applications to economic as well as financial…

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A New Method of Prediction for Spatial Regression Models with Correlated Errors

相关误差空间回归模型的一种新预测方法

SUMMARY This paper deals with minimum mean-squared error, unbiased linear interpolation of a continuous domain spatial process based on a sparse set of irregularly spaced observations. The process is assumed to be governed by a linear regression model with errors that follow a second-order stationary Gaussian random field. A new method of prediction is developed that is compatible with the parameter estimation procedures of Vecchia. The result is a new likelihood-based…

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Polynomial approximations in cross‐sectional models

横截面模型中的多项式近似

Abstract The time‐series distributed lag techniques of econometrics can be usefully applied to cross‐sectional, spatial and cross‐section time‐series situations. The application is perfectly natural in cross‐section, time‐series models when regression coefficients evolve systematically as the cross‐section grouping variable changes. The evolution of such coefficients lends itself to polynomial approximation or more general smoothing restrictions. These ideas are not new,…

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A Spatial Statistical Analysis of Tumor Growth

肿瘤生长的空间统计分析

Growth models for tumors commonly are developed for a one-dimensional summary (e.g., number of cells, volume). At the supracellular level, however, ignoring tumor shape leads to oversimplification of the growth mechanism. For example, an oncologist would view the discovery of a compact tumor of volume v differently from the discovery of two osculatory compact tumors each of volume v/2. This article presents a growth model that uses shape information at a previous time to…

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Randomization and Monte Carlo Methods in Biology.

生物学中的随机化与蒙特卡洛方法

Part 1 Randomization tests and confidence intervals: the idea of a randomization test examples of a randomization test aspects of randomization testing raised by the examples confidence intervals from randomization. Part 2 Monte Carlo and other computer intensive methods: Monte Carlo tests jackknifing bootstrapping bootstrap tests of significance and confidence intervals. Part 3 Some general considerations: power determining how many randomizations are needed determining a…

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A Spatial Statistical Analysis of Tumor Growth

肿瘤生长的空间统计分析

Growth models for tumors commonly are developed for a one-dimensional summary (e.g., number of cells, volume). At the supracellular level, however, ignoring tumor shape leads to oversimplification of the growth mechanism. For example, an oncologist would view the discovery of a compact tumor of volume v differently from the discovery of two osculatory compact tumors each of volume v/2. This article presents a growth model that uses shape information at a previous time to…

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