중심합성계획 시뮬레이션 실험에서 공통난수의 활용

An assumption of ordinary least squares (OLS) is constant variance across the domain of a regressor. Often, however, the random error term variance is not constant when modeling biological data and therefore weighted least squares (WLS) is commonly used to estimate parameters. Less emphasis is placed on observations of the dependent variable with larger variances when using WLS, which is thought to produce more “efficient” parameter estimates. Statisticians often use WLS instead of OLS when the random error variance is not constant. However, as natural resource managers, we are often most interested in values of the dependent variable where the variance is greatest. What then are the biological, economic, and management implications of using WLS versus OLS in natural resource modeling? In this article, parameters of the combined-variable volume equation were estimated for individual trees in loblolly pine plantations using both OLS and WLS. A growth-and-yield model was used to predict stand development over time of two planting densities (303 and 1,090 seedlings/ac) and individual tree volumes were predicted using OLS and WLS parameter estimates. Economic analyses were then conducted. Our results show that the choice of OLS or WLS can have a substantial impact on predicted economic returns. Thus, when using WLS, landowners may decide to invest in additional management treatments that may, in fact, not be economically feasible. This study provides further evidence that landowners need to be aware of model structures when basing harvest-age decisions on growth and yield projections.

To analyze simulation runs which use the same random numbers, the blocking concept of experimental design is not needed. Instead, this paper applies a linear regression model with a nondiagonal covariance matrix. This covariance matrix does not need to have a specific pattern such as constant covariances. A simple example yields surprising results. The paper proposes a new framework for the error analysis. This framework consists of three factors (namely, common random numbers, replication, model validity), each with three levels.

Aiming to solve the problem that the significant error between the actual joint torque and the calculated joint torque of a welding robot leads to the vibration of the end-effector, which in turn affects the stability of the end-effector, this paper proposes a identification algorithm based on the Weighted Least Squares Genetic Algorithm (WLS-GA) to construct and solve the dynamical model to obtain the accurate dynamical parameters. Firstly, a linear model of welding robot dynamics is derived. The fifth-order optimal Fourier series excitation trajectory is designed to collect experimental data such as joint torque. Then, a rough solution of the parameters to be recognized is obtained by solving the dynamics model through the Weighted Least Squares (WLS) method, the search space is determined based on the rough solution, and the optimal solution is obtained by using the Genetic Algorithm (GA) to perform a quadratic search in the search space. Finally, the identification data obtained from the algorithm is analyzed and compared with the experimental data. The results show that the error between the identification data obtained using the WLS-GA identification algorithm and the experimental data is relatively small. The results show that the identification data obtained using the WLS-GA identification algorithm have less error than the experimental data, taking the Root Mean Square (RMS) value of the joint torque error obtained using the weighted least squares algorithm as a criterion. The accuracy of the WLS-GA identification algorithm can be improved by up to 66.85% compared with that of the weighted least squares algorithm and by up to 78.0% compared with that of the Ordinary Least Squares (OLS) algorithm. In summary, the WLS-GA identification algorithm can accurately identify the dynamic parameters of the welding robot and more accurately construct a dynamic model to solve the effect of joint torque error on the control characteristics of the welding robot. It can improve the stability of the end-effector of the welding robot to ensure the quality of the automobile body and beam welding and welding speed.

We revisit the problem of blind calibration of uniform linear sensors arrays for narrowband signals and set the premises for the derivation of the optimal blind calibration scheme. In particular, instead of taking the direct (rather involved) Maximum Likelihood (ML) approach for joint estimation of all the unknown model parameters, we follow Paulraj and Kailath’s classical approach in exploiting the special (Toeplitz) structure of the observed covariance. However, we offer a substantial improvement over Paulraj and Kailath’s Least Squares (LS) estimate by using asymptotic approximations in order to obtain simple, (quasi-)linear Weighted LS (WLS) estimates of the sensors’ gains and phases offsets with asymptotically optimal weighting. As we show in simulation experiments, our WLS estimates exhibit near-optimal performance, with a considerable improvement (reaching an order of magnitude and more) in the resulting mean squared errors, w.r.t. the corresponding ordinary LS estimates. We also briefly explain how the methodology derived in this work may be utilized in order to obtain (by certain modifications) the asymptotically optimal ML estimates w.r.t. the raw data via a (quasi)-linear WLS estimate.

The non-heat-treatable aluminium alloy AA5083 is used widely for marine applications because of its high resistance to sea water and industrial chemical environments. The heat-treatable AA6082 is regarded as structural material exhibiting medium strength and good resistance to corrosion and occupies incredible applications in construction industry. The joining of these alloys is bit challenging in the fusion welding process because of inevitable welding defects like porosity, cracks, distortion. The friction stir welding (FSW) is a potential solid-state joining process which is found more appropriate for such alloys. In this study, dissimilar materials such as AA5083-H111 and AA6082-T6 are selected for the FSW and based on design of experiments 31 trials were chosen with four varying input factors (tool pin profile, tool rotational speed, welding speed and axial force) at five levels to optimize the output responses, namely ultimate tensile strength (UTS) and percentage of elongation (POE). The central composite design (CCD) technique with response surface methodology (RSM) is applied using Design of Expert Version 11 software to develop second-order linear regression quadratic mathematical models using analysis of variance (ANOVA) in order to establish the relationship between input parameters and output responses. Further the confirmation tests revealed that the joints fabricated using tapered square pin profile yield better tensile strength and elongation when compared to other profiles.

On the choice of test for a unit root when the errors are conditionally heteroskedastic

Topographic components analysis of evoked potentials: estimation of model parameters and evaluation of parameter uniqueness

This research article primarily focuses on the estimation of parameters of a linear regression model by the method of ordinary least squares and depicts Gauss-Mark off theorem for linear estimation which is useful to find the BLUE of a linear parametric function of the classical linear regression model. A proof of generalized Gauss-Mark off theorem for linear estimation has been presented in this memoir. Ordinary Least Squares (OLS) regression is one of the major techniques applied to analyse data and forms the basics of many other techniques, e.g. ANOVA and generalized linear models [1]. The use of this method can be extended with the use of dummy variable coding to include grouped explanatory variables [2] and data transformation models [3]. OLS regression is particularly powerful as it relatively easy to check the model assumption such as linearity, constant, variance and the effect of outliers using simple graphical methods [4]. J.T. Kilmer et.al [5] applied OLS method to evolutionary and studies of algometry.

Mathematical modeling provides a rigorous way to quantify immunological processes and discriminate between alternative mechanisms driving specific biological phenomena. It is typical that mathematical models of immunological phenomena are developed by modelers to explain specific sets of experimental data after the data have been collected by experimental collaborators. Whether the available data are sufficient to accurately estimate model parameters or to discriminate between alternative models is not typically investigated. While previously collected data may be sufficient to guide development of alternative models and help estimating model parameters, such data often do not allow to discriminate between alternative models. As a case study, we develop a series of power analyses to determine optimal sample sizes that allow for accurate estimation of model parameters and for discrimination between alternative models describing clustering of CD8 T cells around Plasmodium liver stages. In our typical experiments, mice are infected intravenously with Plasmodium sporozoites that invade hepatocytes (liver cells), and then activated CD8 T cells are transferred into the infected mice. The number of T cells found in the vicinity of individual infected hepatocytes at different times after T cell transfer is counted using intravital microscopy. We previously developed a series of mathematical models aimed to explain highly variable number of T cells per parasite; one of such models, the density-dependent recruitment (DDR) model, fitted the data from preliminary experiments better than the alternative models, such as the density-independent exit (DIE) model. Here, we show that the ability to discriminate between these alternative models depends on the number of parasites imaged in the analysis; analysis of about [Formula: see text] parasites at 2, 4, and 8h after T cell transfer will allow for over 95% probability to select the correct model. The type of data collected also has an impact; following T cell clustering around individual parasites over time (called as longitudinal (LT) data) allows for a more precise and less biased estimates of the parameters of the DDR model than that generated from a more traditional way of imaging individual parasites in different liver areas/mice (cross-sectional (CS) data). However, LT imaging comes at a cost of a need to keep the mice alive under the microscope for hours which may be ethically unacceptable. We finally show that the number of time points at which the measurements are taken also impacts the precision of estimation of DDR model parameters; in particular, measuring T cell clustering at one time point does not allow accurately estimating all parameters of the DDR model. Using our case study, we propose a general framework on how mathematical modeling can be used to guide experimental designs and power analyses of complex biological processes.

Ozone owns high oxidative potential against a broad microbial spectrum and can be applied directly in grain and seed for decontamination fungal and mycotoxin reduction. Thus, the objective of this work was to evaluate the effect of ozonation in the control of fungi and on sunn hemp seeds quality. For this, a cylindrical column of 15 cm diameter PVC was used for ozonation at different heights of the seed layer 2.95 to 17.05 cm and in different times of exposure ozone (17.7, 30, 60, 90 and 102.3 min) according to central composite rotatable design (CCRD). It was evaluated the effect of ozone on decontamination by fungi, moisture content and electric conductivity of sunn hemp seeds. Results of CCRD show different reductions of fungi and a second-order linear model was proposed (average absolute deviation 7.79% and R²=0.67). Fungi reduction (92.37%) was significantly higher in lower layers of the seed column and in longer ozone exposure times, values corresponding to 10 cm and 102.7 min, respectively. Results also showed that ozonation did not influence significantly electrical conductivity and moisture content of seeds (p-value<0.05). Thus, application of ozone can ensure maintenance of sunn hemp seeds in post-harvest without damaging your quality.

In this work, a statistical damage diagnosis scheme using stochastic time series models in the context of acousto ultrasound guided wave-based structural health monitoring (SHM) has been proposed and its performance has been assessed experimentally. Three different methods of damage diagnosis were employed, namely: i) standard autoregressive (AR)-based method, ii) singular value decomposition (SVD)-based method, and iii) principal component analysis-based method. For estimating the AR model parameters, the asymptotically efficient weighted least squares (WLS) method was used. The estimated model parameters were then used to estimate a statistical characteristic quantity that follows a chi-squared distribution. A statistical threshold derived from the chi-squared distribution that depends on the number of degrees of freedom was used instead of a user-defined margin to facilitate automatic damage detection. The method's effectiveness is assessed via multiple experiments under various damage scenarios using damage intersecting as well as non-intersecting paths.

For the conventional four-parameter model of photovoltaic (PV) cell, to simplify the number of its mathematical equations, in this paper, a variable-weather-parameter cell model (VWP model) is proposed. Furthermore, to decrease the number of its model parameters, a simplified variable-weather-parameter cell model (SVWP model) is also proposed. Based on them, the model parameters of linear equivalent models can be replaced by the conventional four-parameter model parameters, which finds the direct relationships between linear equivalent cell model and four-parameter cell model. Finally, some simulation experiments are done by comparing the proposed VWP and SVWP models with conventional four-parameter model of PV cell. The results show that, on the one hand, their output characteristics almost correspond with each other. On the other hand, these proposed cell models are very accurate under varying irradiance or temperature conditions. Meanwhile, some simulation experiments also verify that the linear equivalent models expressed by the VWP model and SVWP model are feasible, available and reasonable. By this work, both the conventional four-parameter model and linear equivalent models are greatly evolved and improved. On the one hand, the conventional four-parameter model can be greatly simplified, which makes its modeling and application easier. On the other hand, the bridge between it and linear equivalent models can be built successfully, which makes these linear models more standard and practical.

A widely applied method of experimental design in stochastic simulation is to use the same pseudo random-number stream for each of the systems or alternatives to be compared. If there are only two alternatives, there is a well-known simple method of statistical analysis. This paper presents Graybill's3 extension of that analysis technique to the case of several systems or alternatives and points out its applicability in the simulation environment. The technique is illustrated using a stochastic simula tion model of a small inventory system. An empirical comparison with other methods of design and analysis is included.

Estimation in linear regression models with measurement errors subject to single-indexed distortion

Use of Simulation Tools To Illustrate the Effect of Data Management Practices for Low and Negative Plate Counts on the Estimated Parameters of Microbial Reduction Models