The use of a modified Fedorov exchange algorithm to optimise sampling times for population pharmacokinetic experiments

We propose a new algorithm for optimising sampling times for population pharmacokinetic experiments using D-optimality. The algorithm was used in conjunction with the population Fisher information matrix as implemented in MATLAB (PFIM 1.1 and 1.2) to evaluate population pharmacokinetic designs. The new algorithm based on the classical Fedorov exchange algorithm optimises the determinant of the population Fisher information matrix. The performance of the new algorithm has been compared with other existing algorithms including simplex, simulated annealing and adaptive random search. The new algorithm performed better especially when dealing with complex designs at the expense of longer computing times.     

Difficulty of singularity in population coding

Fisher information has been used to analyze the accuracy of neural population coding. This works well when the Fisher information does not degenerate, but when two stimuli are presented to a population of neurons, a singular structure emerges by their mutual interactions. In this case, the Fisher information matrix degenerates, and the regularity condition ensuring the Cramér-Rao paradigm of statistics is violated. An animal shows pathological behavior in such a situation. We present a novel method of statistical analysis to understand information in population coding in which algebraic singularity plays a major role. The method elucidates the nature of the pathological case by calculating the Fisher information. We then suggest that synchronous firing can resolve singularity and show a method of analyzing the binding problem in terms of the Fisher information. Our method integrates a variety of disciplines in population coding, such as nonregular statistics, Bayesian statistics, singularity in algebraic geometry, and synchronous firing, under the theme of Fisher information.     

Design of optimal multioutput sampling schedules: Computation of gradients and Hessians

The design of optimal sampling schedules in a dynamic experiment is often accomplished by maximization of a scalar function of the Fisher information matrix, using complex optimization algorithms. In this note exact analytic expressions for the gradients and Hessians of two common design criteria (D- andL-optimality) are derived. The results allow the use of a wealth of efficient gradient search techniques in such designs.     

Optimum experimental designs for dynamic systems in the presence of correlated errors

The problem of determining an optimal measurement time schedule for identification of unknown parameters in multiresponse systems when correlations between observations occur is considered. The measurement process is performed by collecting data at discrete time instants from several outputs. An observation plan is proposed based on a scalar measure of the Fisher information matrix as the design criterion quantifying the accuracy of parameter estimators. A numerical procedure is proposed to determine approximations of optimum designs in the case of correlated measurement errors. The approach is illustrated with an example of the multi-output system of equations describing a chemical kinetic reaction.     

Effect of lateral connections on the accuracy of the population code for a network of spiking neurons.

We study how neuronal connections in a population of spiking neurons affect the accuracy of stimulus estimation. Neurons in our model code for a one-dimensional orientation variable phi. Connectivity between two neurons depends on the absolute difference absolute value(phi - phi') between the preferred orientation of the two neurons. We derive an analytical expression of the activity profile for a population of neurons described by the spike response model with noisy threshold. We estimate the stimulus orientation and the trial-to-trial fluctuations using the population vector method. For stationary stimuli, uniform inhibitory connections produce a more reliable estimation of the stimulus than short-range excitatory connections with long-range inhibitions, although the latter interaction type produces a sharper tuning curve. These results are consistent with previous analytical studies of the Fisher information.     

解WTA问题群智能优化算法的种群初始化问题研究

为提高解武器—目标分配问题(WTA)的群智能优化算法初始种群性能, 从提高初始种群多样性的角度提出了基于密码筒的种群初始化方法, 从提高初始种群解质量的角度分别提出了基于目标威胁—打击效果混合排序的种群初始化方法和装甲分队战术种群初始化方法。最后, 通过一系列不同规模WTA算例的仿真实验对初始化方法进行评估, 结果表明三种种群初始化方法均达到了设计要求, 且各具优势。     

Insights from a simple expression for linear fisher information in a recurrently connected population of spiking neurons

A simple expression for a lower bound of Fisher information is derived for a network of recurrently connected spiking neurons that have been driven to a noise-perturbed steady state. We call this lower bound linear Fisher information, as it corresponds to the Fisher information that can be recovered by a locally optimal linear estimator. Unlike recent similar calculations, the approach used here includes the effects of nonlinear gain functions and correlated input noise and yields a surprisingly simple and intuitive expression that offers substantial insight into the sources of information degradation across successive layers of a neural network. Here, this expression is used to (1) compute the optimal (i.e., information-maximizing) firing rate of a neuron, (2) demonstrate why sharpening tuning curves by either thresholding or the action of recurrent connectivity is generally a bad idea, (3) show how a single cortical expansion is sufficient to instantiate a redundant population code that can propagate across multiple cortical layers with minimal information loss, and (4) show that optimal recurrent connectivity strongly depends on the covariance structure of the inputs to the network.     

A program for individual and population optimal design for univariate and multivariate response pharmacokinetic-pharmacodynamic models

The design of pharmacokinetic and pharmacodynamic experiments concerns a number of issues, among which are the number of observations and the times when they are taken. Often a model is used to describe these data and the pharmacokinetic-pharmacodynamic behavior of a drug. Knowledge of the data analysis model at the design stage is beneficial for collecting patient data for parameter estimation. A number of criteria for model-oriented experiments, which maximize the information content of the data, are available. In this paper we present a program, Popdes, to investigate the D-optimal design of individual and population multivariate response models, such as pharmacokinetic-pharmacodynamic, physiologically based pharmacokinetic, and parent drug and metabolites models. A pre-clinical and clinical pharmacokinetic-pharmacodynamic model describing the concentration-time profile and effect of an oncology compound in development is used for illustration.     

Optimal experiment design based on local model networks and multilayer perceptron networks

This paper addresses the topic of model based design of experiments for the identification of nonlinear dynamic systems. Data driven modeling decisively depends on informative input and output data obtained from experiments. Design of experiments is targeted to generate informative data and to reduce the experimentation effort as much as possible. Furthermore, design of experiments has to comply with constraints on the system inputs and the system output, in order to prevent damage to the real system and to provide stable operational conditions during the experiment. For that purpose a model based approach is chosen for the optimization of excitation signals in this paper. Two different modeling architectures, namely multilayer perceptron networks and local model networks are chosen and the experiment design is based on the optimization of the Fisher information matrix of the associated model architecture. The paper presents and discusses feasible problem formulations and solution approaches for the constrained dynamic design of experiments. In this context the effects of the Fisher information matrix in the static and the dynamic configurations are discussed. The effectiveness of the proposed method is demonstrated on a complex nonlinear dynamic engine simulation model and an analysis as well as a comparison of the presented model architectures for model based experiment design is given.     

Obtaining more information from conjoint experiments by best-worst choices

Conjoint choice experiments elicit individuals’ preferences for the attributes of a good by asking respondents to indicate repeatedly their most preferred alternative in a number of choice sets. However, conjoint choice experiments can be used to obtain more information than that revealed by the individuals’ single best choices. A way to obtain extra information is by means of best-worst choice experiments in which respondents are asked to indicate not only their most preferred alternative but also their least preferred one in each choice set. To create D-optimal designs for these experiments, an expression for the Fisher information matrix for the maximum-difference model is developed. Semi-Bayesian D-optimal best-worst choice designs are derived and compared with commonly used design strategies in marketing in terms of the D-optimality criterion and prediction accuracy. Finally, it is shown that best-worst choice experiments yield considerably more information than choice experiments.     

On the accuracy in errors-in-variables identification compared to prediction-error identification

Errors-in-variables estimation problems for single-input–single-output systems with Gaussian signals are considered in this contribution. It is shown that the Fisher information matrix is monotonically increasing as a function of the input noise variance when the noise spectrum at the input is known and the corresponding noise variance is estimated. Furthermore, it is shown that Whittle’s formula for the Fisher information matrix can be represented as a Gramian and this is used to provide a geometric representation of the asymptotic covariance matrix for asymptotically efficient estimators. Finally, the asymptotic covariance of the parameter estimates for the system dynamics is compared for the two cases: (i) when the model includes white measurement noise on the input and the variance of the noise is estimated, and (ii) when the model includes only measurement noise on the output. In both cases, asymptotically efficient estimators are assumed. An explicit expression for the difference is derived when the underlying system is subject only to measurement noise on the output.     

基于GIS的人口管理信息系统的设计与实现

传统的人口管理信息系统已无法满足信息时代经济快速发展的需要，为科学、高效地管理人口数据，开发了基于GIS的人口管理信息系统。介绍了该系统的主要内容，包括系统体系结构设计、功能设计、数据库设计以及系统的技术特点，并给出了系统实现中对一些关键技术问题的解决方案。     

A program for the optimum design of pharmacokinetic, pharmacodynamic, drug metabolism and drug-drug interaction models

Planning any experiment includes issues such as how many samples are to be taken and their location given some predictor variable. Often a model is used to explain these data; hence including this formally in the design will be beneficial for any subsequent parameter estimation and modelling. A number of criteria for model oriented experiments, which maximise the information content of the collected data are available. In this paper we present a program, Optdes, to investigate the optimal design of pharmacokinetic, pharmacodynamic, drug metabolism and drug-drug interaction models. Using the developed software the location of either a predetermined number of design points (exact designs) or together with the proportion of samples at each point (continuous designs) can be determined. Local as well as Bayesian designs can be optimised by either D- or A-optimality criteria. Although often the optimal design cannot be applied for practical reasons, alternative designs can be readily evaluated.     

On the Fernández-Steel distribution: Inference and application

In this article, we perform statistical inference on a skew model that belongs to a class of distributions proposed by Fernández and Steel (1998). Specifically, we introduce two ways to represent this model by means of which moments and generation of random numbers can be obtained. In addition, we carry out estimation of the model parameters by moment and maximum likelihood methods. Asymptotic inference based on both of these methods is also produced. We analyze the expected Fisher information matrix associated with the model and highlight the fact that this does not have the singularity problem, as occurs with the corresponding information matrix of the skew-normal model introduced by Azzalini (1985). Furthermore, we conduct a simulation study to compare the performance of the moment and maximum likelihood estimators. Finally, an application based on real data is carried out.     

Optimal experiment design under process noise using Riccati differential equations

In this paper, we present a numerical method for optimal experiment design of nonlinear dynamic processes. Here, we suggest to optimize an approximation of the predicted variance–covariance matrix of the parameter estimates, which can be computed as the solution of a Riccati differential equation. In contrast to existing approaches, the proposed method allows us to take process noise into account and requires less derivative states to be computed compared to the traditional Fisher information matrix based approach. This process noise is assumed to be a time-varying random disturbance which is not known at the time when the experiment is designed. We illustrate the technique by solving an optimal experiment design problem for a fed-batch bioreactor benchmark case study. Here, we concentrate on how the optimal input design and associated accuracy of the parameter identification is influenced when process noise is present.     

Computation of the exact Cramer–Rao lower bound for the parameters of a nonsymmetric half-plane 2-D ARMA model

The Cramer–Rao lower bound (CRLB) that gives the minimal achievable variance/standard deviation for any unbiased estimator offers a useful tool for an assessment of the consistency of parameter estimation techniques. In this paper, a closed-form expression for the computation of the exact CRLB on unbiased estimates of the parameters of a two-dimensional (2-D) autoregressive moving average (ARMA) model with a nonsymmetric half-plane (NSHP) region of support is developed. The proposed formulation is mainly based on a matrix representation of 2-D real-valued discrete and homogeneous random field characterized by the NSHP ARMA model. Assuming that the random field is Gaussian, the covariance matrix of the NSHP ARMA random field is first expressed in terms of the model parameters. Then, using this matrix structure, a closed-form expression of the exact Fisher information matrix required for the CRLB computation of the NSHP ARMA model parameters is developed. Finally, the main formulas derived for the NSHP ARMA model are rearranged for its autoregressive and moving average counterparts, separately. Numerical simulations are included to demonstrate the behavior of the derived CRLB formulas.     

Progressively Type-II censored competing risks data from Lomax distributions

A competing risks model based on Lomax distributions is considered under progressive Type-II censoring. Maximum likelihood estimates for the distribution parameters are established. Moreover, the expected Fisher information matrix is computed and optimal Fisher information based censoring plans are discussed. In particular, it turns out that the optimal censoring scheme depends on the particular parametrization of the Lomax distributions.