A Subsequent Fit of Time Series and Amplitude Histogram of Patch-Clamp Records Reveals Rate Constants up to 1 per Microsecond

Fast gating in time series of patch-clamp current demands powerful tools to reveal the rate constants of the adequate Hidden Markov model. Here, two approaches are presented to improve the temporal resolution of the direct fit of the time series. First, the prediction algorithm is extended to include intermediate currents between the nominal levels as caused by the anti-aliasing filter. This approach can reveal rate constants that are about 4 times higher than the corner frequency of the anti-aliasing filter. However, this approach is restricted to time series with very low noise. Second, the direct fit of the time series is combined with a beta fit, i.e., a fit of the deviations of the amplitude histogram from the Gaussian distribution. Since the “theoretical” amplitude histograms for higher-order Bessel filters cannot be calculated by analytical tools, they are generated from simulated time series. In a first approach, a simultaneous fit of the time series and of the Beta fit is tested. This simultaneous fit, however, inherits the drawbacks of both approaches, not the benefits. More successful is a subsequent fit: The fit of the time series yields a set of rate constants. The subsequent Beta fit uses the slow rate constants of the fit of the time series as fixed parameters and the optimization algorithm is restricted to the fast ones. The efficiency of this approach is illustrated by means of time series obtained from simulation and from the dominant K⁺ channel in Chara. This shows that temporal resolution can reach the microsecond range.     

A probabilistic framework for microarray data analysis: Fundamental probability models and statistical inference

Gene expression studies generate large quantities of data with the defining characteristic that the number of genes (whose expression profiles are to be determined) exceed the number of available replicates by several orders of magnitude. Standard spot-by-spot analysis still seeks to extract useful information for each gene on the basis of the number of available replicates, and thus plays to the weakness of microarrays. On the other hand, because of the data volume, treating the entire data set as an ensemble, and developing theoretical distributions for these ensembles provides a framework that plays instead to the strength of microarrays. We present theoretical results that under reasonable assumptions, the distribution of microarray intensities follows the Gamma model, with the biological interpretations of the model parameters emerging naturally. We subsequently establish that for each microarray data set, the fractional intensities can be represented as a mixture of Beta densities, and develop a procedure for using these results to draw statistical inference regarding differential gene expression. We illustrate the results with experimental data from gene expression studies on Deinococcus radiodurans following DNA damage using cDNA microarrays.     

Strengths and Limits of Beta Distributions as a Means of Reconstructing the True Single-Channel Current in Patch Clamp Time Series with Fast Gating

Single-channel current seems to be one of the most obvious characteristics of ion transport. But in some cases, its determination is more complex than anticipated at first glance. Problems arise from fast gating in time series of patch-clamp current, which can lead to a reduced apparent (measured) single-channel current. Reduction is caused by undetected averaging over closed and open intervals in the anti-aliasing filter. Here it is shown that fitting the measured amplitude histograms by Beta distributions is an efficient tool of reconstructing the true current level from measured data. This approach becomes even more powerful when it is applied to amplitude distributions-per-level. Simulated time series are employed to show that the error sum is a good guideline for finding the correct current level. Furthermore, they show that a Markov model smaller than the one used for gating analysis can be used for current determination (mostly O-C, i.e., open-closed). This increases the reliability of the Beta fit. The knowledge of the true current level is not only important for the understanding of the biophysical properties of the channel. It is also a prerequisite for the correct determination of the rate constants of gating. The approach is applied to measured data. The examples reveal the limits of the analysis imposed by the signal-to-noise ratio and the shape of the amplitude distribution. One application shows that the negative slope of the I-V curve of the human MaxiK channel expressed in HEK293 cells is caused by fast gating.     

Data distributions in magnetic resonance images: A review

Many image processing methods applied to magnetic resonance (MR) images directly or indirectly rely on prior knowledge of the statistical data distribution that characterizes the MR data. Also, data distributions are key in many parameter estimation problems and strongly relate to the accuracy and precision with which parameters can be estimated. This review paper provides an overview of the various distributions that occur when dealing with MR data, considering both single-coil and multiple-coil acquisition systems. The paper also summarizes how knowledge of the MR data distributions can be used to construct optimal parameter estimators and answers the question as to what precision may be achieved ultimately from a particular MR image.     

Robust Classification of Functional and Quantitative Image Data Using Functional Mixed Models

Summary This article introduces new methods for performing classification of complex, high‐dimensional functional data using the functional mixed model (FMM) framework. The FMM relates a functional response to a set of predictors through functional fixed and random effects, which allows it to account for various factors and between‐function correlations. The methods include training and prediction steps. In the training steps we train the FMM model by treating class designation as one of the fixed effects, and in the prediction steps we classify the new objects using posterior predictive probabilities of class. Through a Bayesian scheme, we are able to adjust for factors affecting both the functions and the class designations. While the methods can be used in any FMM framework, we provide details for two specific Bayesian approaches: the Gaussian, wavelet‐based FMM (G‐WFMM) and the robust, wavelet‐based FMM (R‐WFMM). Both methods perform modeling in the wavelet space, which yields parsimonious representations for the functions, and can naturally adapt to local features and complex nonstationarities in the functions. The R‐WFMM allows potentially heavier tails for features of the functions indexed by particular wavelet coefficients, leading to a down‐weighting of outliers that makes the method robust to outlying functions or regions of functions. The models are applied to a pancreatic cancer mass spectroscopy data set and compared with other recently developed functional classification methods.     

Testing Equality of Means in the Presence of Correlation and Missing Data

A statistic, derived from the combination of two dependent tests, is proposed for testing the hypothesis of equality of the means of a bivariate normal distribution with unknown common variance and correlation coefficient when observations are missing on one or both variates. The null distribution of the statistic is approximated by a well-known distribution. The empirical powers of the statistic are computed and compared with some of the known statistics. The comparisons support the use of the proposed test.     

DNA进化马尔可夫过程模型的评价与推广

本文对ＤＮＡ序列进化过程中核苷酸替代的随机模型进行了评价,对替代速率在时间和空间上不恒定的情形进行了考察和推广。Ｌａｎａｖｅ等（１９８４）曾提出一个模型,宣称对替代的模式未做任何假定,但事实上我们证明它假定替代过程是可逆的。运用２－ｐ、４－ｐ和６－ｐ模型进行的计算表明替代速度在位点间的差异会造成估计的替代数严重偏低,并且替代数越大,偏差也越大。替代模式在位点间的差异也会造成估计值偏低,但偏差不严重     

On Testing Equality of Means of Correlated Variates with Missing Data on One Response

A statistic is proposed for testing the hypothesis of equality of the means of a bivariate normal distribution with unknown common variance and correlation coefficient when observations are missing on one of the variates. The distribution of the statistic is approximated by a normal distribution under the null hypothesis. The empirical powers of the statistic are computed and compared with those of the conventional paired t and the other known statistics. The power comparisons support the use of the proposed test.     

On Testing Equality of Means in the Paired Case with Incomplete Data on Both Responses

Several non iterative tests for the equality of two correlated means with missing data on both responses are compared by means of Monte Carlo studies. The main results are that a test due to LIN and STIVERS (1974) is to be preferred when the number of complete pairs is large, a WELCH type statistic with degrees of freedom modified in this paper when the correlation between the two responses is known to be low, and one of four suggested, one in this paper, maximum likelihood based tests when the number of complete pairs is small and there is no large variance inequality believed to exist.     

Marginal Models Via GLS: A Convenient Yet Neglected Tool for the Analysis of Correlated Data in the Behavioural Sciences

Behavioural research often produces data that have a complicated structure. For instance, data can represent repeated observations of the same individual and suffer from heteroscedasticity as well as other technical snags. The regression analysis of such data is often complicated by the fact that the observations (response variables) are mutually correlated. The correlation structure can be quite complex and might or might not be of direct interest to the user. In any case, one needs to take correlations into account (e.g. by means of random‐effect specification) in order to arrive at correct statistical inference (e.g. for construction of the appropriate test or confidence intervals). Over the last decade, such data have been more and more frequently analysed using repeated‐measures ANOVA and mixed‐effects models. Some researchers invoke the heavy machinery of mixed‐effects modelling to obtain the desired population‐level (marginal) inference, which can be achieved by using simpler tools – namely marginal models. This paper highlights marginal modelling (using generalized least squares [GLS] regression) as an alternative method. In various concrete situations, such marginal models can be based on fewer assumptions and directly generate estimates (population‐level parameters) which are of immediate interest to the behavioural researcher (such as population mean). Sometimes, they might be not only easier to interpret but also easier to specify than their competitors (e.g. mixed‐effects models). Using five examples from behavioural research, we demonstrate the use, advantages, limits and pitfalls of marginal and mixed‐effects models implemented within the functions of the ‘nlme’ package in R.     

Extrapolation for Exposure Duration in Oral Toxicity: A Quantitative Analysis of Historical Toxicity Data

For human risk assessment, experimental data often have to be extrapolated for exposure duration, which is generally done by means of default values. The purpose of the present study was twofold. First, to derive a statistical distribution for differences in exposure duration that can be used in a probabilistic concept for combining assessment factors in risk characterization. Second, to obtain insight in the magnitude of the change in No-Observed-Adverse-Effect-Level (NOAEL) with exposure duration, which will lead to more science-based assessment factors for exposure duration. A large historical database, including 198 substances, was consulted. Ratios were calculated for pairs of NOAELs for systemic toxicity from oral toxicity studies with the same species (rats or mice, various strains) and different exposure duration categories. The Geometric Mean (GM), Geometric Standard Deviation (GSD), and the 90th and 95th percentile values were determined. The traditionally applied default factors for subacute to semichronic (10), for semichronic to chronic (10), and for subacute to chronic exposure (100) corresponded with the 93, 87, and 99-percentiles of the respective distributions. Options are presented for a set of default values and probabilistic distributions for assessment factors for exposure duration based on data from the consulted historical database.     

Testing Equality of Means and Simultaneous Confidence Intervals in Repeated Measures with Missing Data

In this paper, repeated measures with intraclass correlation model is considered when the observations are missing at random. An exact test for the equality of the mean components and simultaneous confidence intervals (Scheffé and Bonferroni inequality types) are given for linear contrasts of the mean components when the missing observations are of a monotone type. When the missing observations are not of the monotone type, the maximum likelihood estimates are obtained numerically by iterative methods given in Srivastava and Carter (1986). These estimators are then used to obtain asymptotic tests and confidence intervals for the equality of mean components and linear contrasts, respectively. An example is given to illustrate the method.     

Evaluation and Estimation of Various Markov Models with Applications to Membrane Channel Kinetics

Hidden Markov modelling is a powerful and efficient digital signal processing strategy for extracting the maximum likelihood model from a finite length sample of noisy data. Assuming the number of states in the model is known, then the state levels, transition probabilities, initial state distribution and the noise variance can be estimated. We investigate the applicability of this technique in membrane channel kinetics not only as a parameter estimator, but also as an aid to discriminating between various model types according to their statistical likelihood. We survey three representative classes of channel dynamics, namely: aggregated Markov models, semi-Markov models (with asymptotically convergent transition probabilities), and coupled Markov models; reformulating each within a discrete-time hidden Markov model framework. We then provide numerical evidence of the effectiveness of the procedure using simulated channel data and hence show that the correct model, as well as the model parameters, can be discerned. We also demonstrate that the model likelihood can be used to indicate the approximate number of states in the model.     

A General Class of Semiparametric Transformation Frailty Models for Nonproportional Hazards Survival Data

Summary We propose a semiparametrically efficient estimation of a broad class of transformation regression models for nonproportional hazards data. Classical transformation models are to be viewed from a frailty model paradigm, and the proposed method provides a unified approach that is valid for both continuous and discrete frailty models. The proposed models are shown to be flexible enough to model long‐term follow‐up survival data when the treatment effect diminishes over time, a case for which the PH or proportional odds assumption is violated, or a situation in which a substantial proportion of patients remains cured after treatment. Estimation of the link parameter in frailty distribution, considered to be unknown and possibly dependent on a time‐independent covariates, is automatically included in the proposed methods. The observed information matrix is computed to evaluate the variances of all the parameter estimates. Our likelihood‐based approach provides a natural way to construct simple statistics for testing the PH and proportional odds assumptions for usual survival data or testing the short‐ and long‐term effects for survival data with a cure fraction. Simulation studies demonstrate that the proposed inference procedures perform well in realistic settings. Applications to two medical studies are provided.     

Estimation of Covariance Matrices in Unbalanced Random and Mixed Multivariate Models

Three HENDERSON'S Methods of estimating the variance components are generalized from one to p variables using a compact matrix notation. These results are obtained using a generalized Kronecker product of matrices, generalized trace of order p and a generalized quadratic form.     

农作物种子检验中发芽试验的容许误差的统计模型与计算

当代计算手段远远优于计算种子检验规程发芽试验现行标准中容许误差数值的20 世纪60年代,鉴于此,本文在提出发芽试验统计检验模型的基础上,利用MATLAB编程重新计算了容许误差值．过去计算的三种容许误差有较大的正偏差,另一种有很小的负偏差．建议对现行的种子检验规程有关计数型的容许误差数值进行修订．     

华南南亚热带植被第一性生产量的影响因素及预测模型

讨论植被类型、降雨、湿度、土壤条件对华南南亚热带植被第一性生产量的影响。比较各种预测第一性生产量的气候模型,为更好地预测和提高华南南亚热带植被第一性生产量提供依据。