Prediction Intervals in Nonlinear Regression

By treating the nonlinear model as if it were linear in the parameterization θ in the neighbourhood of the least squares estimate θ, we construct two-sided nominally-q-prediction intervals by applying the usual linear model theory. The derivation of the truncated series expansion of the expected coverage of the prediction intervals at a feasible value of the parameter vector is described. The quadratic approximation of the expected coverage is then obtained for a two-parameter nonlinear model. Finally we show how we may construct the prediction intervals when a certain type of nonlinear transformation of the parameter vector has been applied.     

A Method for Analyzing Nonlinear Models When the Data are from a Split-plot or Repeated Measures Design

Statistical methods are described which can be used to compare treatments where the response model is nonlinear and the experimental design includes split-plots or repeated measures. The nonlinear analysis of covariance is described for a two-way treatment structure in a split-plot design structure, the usual split-plot experimental design. Evaluating heat tolerance in common beans as a function of temperature is used as an example to demonstrate the methodology.     

A Parameter-Elimination Method for Nonlinear Regression with Linear Parameters and Autocorrelated Errors

In this study, we are interested in the problem of estimating the parameters in a nonlinear regression model when the error terms are correlated. Throughout this work, we restrict ourselves to the special case when the error terms follow a pth order stationary autoregressive model (AR(p)). Following the idea of LAWTON and SYLVESTRE (1971) and GALLANT and GOEBEL (1976), a parameter-elimination method is proposed, which has the advantages that it is not sensitive to the initial values and convergence of the procedure may be more stable because of the reduced dimension of the problem. The parameter-elimination method is compared with the methods by GALLANT and GOEBEL (1976) and GLASBEY (1980) by Monte Carlo Simulation, and the results of applying the first two methods to the real data obtained from the Environmental Protection Administration of the Executive Yuan of the Republic of China are presented.     

删失数据下非线性半参数回归模型中参数的经验似然推断

考察了响应变量在随机删失情形下的非线性半参数回归模型,构造了未知参数的经验对数似然比统计量和调整经验对数似然比统计量,证明在一定条件下,所构造的经验似然比统计量渐近于X~2分布,并由此构造出未知参数的置信域.此外,又构造了未知参数的最小二乘估计量,证明了它的渐近性质.通过模拟研究表明,经验似然方法在置信域的覆盖概率以及精度方面要优于最小二乘法.     

Adjustment uncertainty in effect estimation

Often there is substantial uncertainty in the selection of confounderswhen estimating the association between an exposure and health.We define this type of uncertainty as `adjustment uncertainty'.We propose a general statistical framework for handling adjustmentuncertainty in exposure effect estimation for a large numberof confounders, we describe a specific implementation, and wedevelop associated visualization tools. Theoretical resultsand simulation studies show that the proposed method providesconsistent estimators of the exposure effect and its variance.We also show that, when the goal is to estimate an exposureeffect accounting for adjustment uncertainty, Bayesian modelaveraging with posterior model probabilities approximated usinginformation criteria can fail to estimate the exposure effectand can over- or underestimate its variance. We compare ourapproach to Bayesian model averaging using time series dataon levels of fine particulate matter and mortality.     

Processing of Auditory Midbrain Interspike Intervals by Model Neurons

A question central to sensory processing is how signal information is encoded and processed by single neurons. Stimulus features can be represented through rate coding (via firing rate), temporal coding (via firing synchronization to temporal periodicities), or temporal encoding (via intricate patterns of spike trains). Of the three, examples of temporal encoding are the least documented. One region in which temporal encoding is currently being explored is the auditory midbrain. Midbrain neurons in the plainfin midshipman generate different interspike interval (ISI) distributions depending on the frequencies of the concurrent vocal signals. However, these distributions differ only along certain lengths of ISIs, so that any neurons trying to distinguish the distributions would have to respond selectively to specific ISI ranges. We used this empirical observation as a realistic challenge with which to explore the plausibility of ISI-tuned neurons that could validate this form of temporal encoding. The resulting modeled cells—point neurons optimized through multidimensional searching—were successfully tuned to discriminate patterns in specific ranges of ISIs. Achieving this task, particularly with simplified neurons, strengthens the credibility of ISI coding in the brain and lends credence to its role in auditory processing.     

Optimal Experimental Design and Accuracy of Parameter Estimation for Nonlinear Regression Models Used in Long-term Selection

An experimental design problem is considered for the analysis of long-term selection experiments with nonlinear regression models. For a 3-parametric exponential regression function whose parameters have also a reasonable biological interpretation approximate formulas for the determination of the necessary number of observations at each generation are constructed in such a way that the half expected length of an (1 — α)-confidence interval for a chosen parameter is not greater than a given value. In this sense the accuracy of the parameter estimators can be described.     

EEG Activity in the Process of Measuring-off of Time Intervals by Humans

We recorded EEG from sites C3 and C4 in an experimental situation with internal counting-off of a 20-sec-long time interval, whose beginning and end were limited by the tested subject by pushing a button; 65 adult men and women took part in the tests. In the first experimental series, the subject obtained no real information on the accuracy in production of the interval. In the second series, such information was displayed by feedback visual signals. We calculated means of the measured intervals ( ), coefficient of variation of the realizations (CV), and, in the series with the real feedback, successfulness of measuring-off (normalized number of fits within an acceptable range of the standard interval, 19 to 21 sec). Analysis of the data obtained in the first experimental series for the entire tested group demonstrated the existence of a reverse dependence between the modal frequency of EEG beta rhythm recorded from the left hemisphere in the course of measuring-off of the interval and the value. In the second series, we found significant negative correlation between the beta rhythm power in both hemispheres and CV, that between the alpha rhythm power in the left hemisphere and , and positive correlation between the alpha rhythm frequency in the left hemisphere and successfulness of the interval counting-off. Analysis of the dynamics of EEG of each tested subject demonstrated the existence of mostly reverse dependences between the powers of a few EEG rhythms and duration of the produced interval. We hypothesize that the frequencies of the alpha and beta EEG oscillations play the role of significant indices reflecting the speed of the internal clock of the individual. We also emphasize the complex nature and the high individual variability of the EEG pattern in the course of measuring-off of time intervals.     

Scheffy's Confidence Intervals in the Models of Analysis of Covariance

Scheffe's confidence intervals for linear functions of some subvectors of a vector of parameters are presented. The considered subvectors are such that covariance matrices of their estimators are known non-negative definite matrices multiplied by unknown positive constants. This property is characteristic of the least squares estimators of vectors of main and interaction effects in the analysis of covariance models of the following experimental designs: split-block, split-plot, completely randomized two-factor design and randomized complete block design. The formulas for confidence intervals for linear functions of vectors of main or interaction effects in the designs mentioned above are given in the paper. The practical example is given as an illustration.     

肺动脉血流时间间期法评估肺动脉压

为评价肺动脉血流时间间期法评估肺动脉压的价值,本文观察了37例左向右分流先天性心脏病患者。在相同体位及取样容积位置下测量心室射血前期(PEP)、射血时间(ET)、加速时间(AT)、加速度(ACC)、F[F=PEP/(ATET)];计算肺动脉/主动脉血流时间间期比(FPA/FAO),并以各项比例系数与肱动脉压(BAP)的乘积作为肺动脉压的估测值。结果显示:肺动脉/主动脉血流时间间期比与右心导管估测的肺动脉收缩压(PASP)、平均压(PAMP)取得了较好的相关性(r分别为0.84、0.81);ACC次之(r分别为0.72、0.65);PEP/AT较差(r分别为0.53、0.50)。提示:肺动脉/主动脉血流时间间期比为无创定量评估肺动脉压的最佳方法。     

我国洪涝灾害受灾及成灾面积的预测分析

运用ＳＡＳ软件的非线性回归,并结合马尔可夫链方法建立了因洪涝灾害造成的我国农田受灾及成灾面积的２个预测模型,结果表明本文所作的预测效果较好,为我国的灾害预测提供了一种方便实用的方法。     

Estimation of Fixed and Random Effects in the Functional Nonlinear Errors-in-Variable Model

Consider an experiment where a nonlinear continuous functional relationship exists between y and X. Assume that this relationship has been measured at n replicated points of X from each of t treatments or populations. Assume further that the X are fixed unknown vectors and that the location parameter v is either a fixed unknown vector or a vector of random variables. In the first case various linear hypotheses are to be tested about v, such as tests for main effects and interaction; in the second case, the mean and variance of the random variable v are to be estimated. A two-step procedure based on asymptotic theory is presented to test hypotheses or develop estimates for the fixed effects or random effects functional errors-in-variable model. An example of a one-way random effects model is given.     

Nonlinear control for algae growth models in the chemostat

This paper deals with output feedback control of phytoplanktonic algae growth models in the chemostat. The considered class of model is of variable yield type, meaning that the ratio between the environmental nutrient absorption rate and the cells’ growth rate varies, which is different from classical bioprocesses assumptions. On the basis of weak qualitative hypotheses on the analytical expressions of the involved biological phenomena (which guarantee robustness of the procedure toward modeling uncertainties) we propose a nonlinear controller and prove its ability to globally stabilize such processes. Finally, we illustrate our approach with numerical simulations and show its benefits for biological laboratory experiments, especially for ensuring persistence of the culture facing classical experimental problems.     

Nonlinear modelling of renal vasoaction

The control of blood pressure is a complex mixture of neural, hormonal and intrinsic interactions at the level of the heart, kidney and blood vessels. While experimental approaches to understanding these interactions are useful, it remains difficult to conduct experiments to quantify these interactions as the number of parameters increases. Thus, modelling of such physiological systems can offer considerable assistance. Typical mathematical models which describe the ability of the blood vessels to change their diameter (vasoconstriction) assume linearity of operation. However, due to the interaction of multiple vasocontrictive and vasodilative effectors, there is a significant nonlinear response to the influence of neural factors, particularly at higher levels of nerve activity (often seen in subjects with high blood pressure) which leads to low blood flow rates. This paper proposes a number of nonlinear mathematical models for the relationship between neural influences (sympathetic nerve activity (SNA)) and renal blood flow, using a feedback path to model the predominantly nonlinear effect of local vasoactive modulators such as nitric oxide, which oppose the action of SNA. The model structures are motivated by basic physiological principles, while the model parameters are determined using numerical optimisation techniques using open-loop data collected from rabbits. The models were verified by demonstrating correlation between experimental results and model outputs.