Constructing and model-fitting receiver operator characteristics using continuous data.

2018 ◽  
Author(s):  
Josephine Ann Urquhart ◽  
Akira O'Connor
Keyword(s):  
Signal Detection ◽  
Least Squares Method ◽  
Model Fitting ◽  
Simulated Data ◽  
Continuous Variable ◽  
Continuous Data ◽  
Model Parameters ◽  
Operating Characteristics ◽  
Unequal Variance ◽  
Discrete Discrimination

Receiver operating characteristics (ROCs) are plots which provide a visual summary of a classifier’s decision response accuracy at varying discrimination thresholds. Typical practice, particularly within psychological studies, involves plotting an ROC from a limited number of discrete thresholds before fitting signal detection parameters to the plot. We propose that additional insight into decision-making could be gained through increasing ROC resolution, using trial-by-trial measurements derived from a continuous variable, in place of discrete discrimination thresholds. Such continuous ROCs are not yet routinely used in behavioural research, which we attribute to issues of practicality (i.e. the difficulty of applying standard ROC model-fitting methodologies to continuous data). Consequently, the purpose of the current article is to provide a documented method of fitting signal detection parameters to continuous ROCs. This method reliably produces model fits equivalent to the unequal variance least squares method of model-fitting (Yonelinas et al., 1998), irrespective of the number of data points used in ROC construction. We present the suggested method in three main stages: I) building continuous ROCs, II) model-fitting to continuous ROCs and III) extracting model parameters from continuous ROCs. Throughout the article, procedures are demonstrated in Microsoft Excel, using an example continuous variable: reaction time, taken from a single-item recognition memory. Supplementary MATLAB code used for automating our procedures is also presented in Appendix B, with a validation of the procedure using simulated data shown in Appendix C.

scholarly journals Evidence for the Contribution of A Threshold Retrieval Process to Semantic Memory

2017 ◽  
Vol 70 (10) ◽  
pp. 2026-2047 ◽  
Author(s):  
Maria Kempnich ◽  
Josephine A. Urquhart ◽  
Akira R. O'Connor ◽  
Chris J.A. Moulin
Keyword(s):  
Signal Detection ◽  
Semantic Memory ◽  
Target Identification ◽  
Dual Process ◽  
Semantic Retrieval ◽  
Retrieval Process ◽  
Operating Characteristics ◽  
Semantic Task ◽  
Unequal Variance ◽  
Detection Model

It is widely held that episodic retrieval can recruit two processes: a threshold context retrieval process (recollection) and a continuous signal strength process (familiarity). Conversely the processes recruited during semantic retrieval are less well specified. We developed a semantic task analogous to single-item episodic recognition to interrogate semantic recognition receiver-operating characteristics (ROCs) for a marker of a threshold retrieval process. We fitted observed ROC points to three signal detection models: two models typically used in episodic recognition (unequal variance and dual-process signal detection models) and a novel dual-process recollect-to-reject (DP-RR) signal detection model that allows a threshold recollection process to aid both target identification and lure rejection. Given the nature of most semantic questions, we anticipated the DP-RR model would best fit the semantic task data. Experiment 1 (506 participants) provided evidence for a threshold retrieval process in semantic memory, with overall best fits to the DP-RR model. Experiment 2 (316 participants) found within-subjects estimates of episodic and semantic threshold retrieval to be uncorrelated. Our findings add weight to the proposal that semantic and episodic memory are served by similar dual-process retrieval systems, though the relationship between the two threshold processes needs to be more fully elucidated.

An approach to computer analysis of the ligand binding assay data on example of radioligand assay data

2020 ◽  
Vol 18 (02) ◽  
pp. 2050014
Author(s):  
S. N. Fedotov
Keyword(s):  
Least Squares Method ◽  
Main Idea ◽  
Simulated Data ◽  
Real Data ◽  
Model Parameters ◽  
Nonlinear Method ◽  
Ligand Interaction ◽  
Receptor Ligand ◽  
Parameter Values ◽  
True Values

As a rule, receptor-ligand assay data are fitted by logistic functions (4PL model, 5PL model, Feldman’s model). The preparation of the initial estimates for parameters of these functions is an important problem for processing receptor-ligand interaction data. This study represents a new mathematical approach to calculate the initial estimates more closely to the true values of parameters. The main idea of this approach is in using the modified linear least squares method for calculations of the parameters for the 4PL model and the Feldman’s model. In this study, the convergence of model parameters to true values is verified for the simulated data with different statistical scatter. Also, the results of processing real data for the 4PL model and the Feldman’s model are presented. A comparison is made of the parameter values calculated by the presented and a nonlinear method. The developed approach has demonstrated its efficiency in calculating the parameters of the complex Feldman”s models up to 4 ligands and 4 sites.

scholarly journals Estimation of distributed parameters in permittivity models of composite dielectric materials using reflectance

2015 ◽  
Vol 23 (5) ◽  
Author(s):  
H. Thomas Banks ◽  
Jared Catenacci ◽  
Shuhua Hu
Keyword(s):  
Least Squares Method ◽  
Dielectric Material ◽  
Simulated Data ◽  
Dielectric Materials ◽  
Distributed Parameter ◽  
Model Parameters ◽  
Probability Measures ◽  
Computational Algorithms ◽  
The Past ◽  
Distributed Parameters

AbstractWe investigate the feasibility of quantifying properties of a composite dielectric material through the reflectance, where the permittivity is described by the Lorentz model in which an unknown probability measure is placed on the model parameters. We summarize the computational and theoretical framework (the Prohorov metric framework) developed by our group in the past two decades for nonparametric estimation of probability measures using a least-squares method, and point out the limitation of the existing computational algorithms for this particular application. We then improve the algorithms, and demonstrate the feasibility of our proposed methods by numerical results obtained for both simulated data and experimental data for inorganic glass when considering the resonance wavenumber as a distributed parameter. Finally, in the case where the distributed parameter is taken as the relaxation time, we show using simulated data how the addition of derivative measurements improves the accuracy of the method.

scholarly journals Determination of synchronous generator nonlinear model parameters based on power rejection tests using a gradient optimization algorithm

2017 ◽  
Vol 65 (4) ◽  
pp. 479-488 ◽  
Author(s):  
A. Boboń ◽  
A. Nocoń ◽  
S. Paszek ◽  
P. Pruski
Keyword(s):  
Parameter Estimation ◽  
Objective Function ◽  
Optimization Algorithm ◽  
Least Squares Method ◽  
Synchronous Generator ◽  
Operating Conditions ◽  
Model Parameters ◽  
State Variables ◽  
Starting Point ◽  
Gradient Optimization

AbstractThe paper presents a method for determining electromagnetic parameters of different synchronous generator models based on dynamic waveforms measured at power rejection. Such a test can be performed safely under normal operating conditions of a generator working in a power plant. A generator model was investigated, expressed by reactances and time constants of steady, transient, and subtransient state in the d and q axes, as well as the circuit models (type (3,3) and (2,2)) expressed by resistances and inductances of stator, excitation, and equivalent rotor damping circuits windings. All these models approximately take into account the influence of magnetic core saturation. The least squares method was used for parameter estimation. There was minimized the objective function defined as the mean square error between the measured waveforms and the waveforms calculated based on the mathematical models. A method of determining the initial values of those state variables which also depend on the searched parameters is presented. To minimize the objective function, a gradient optimization algorithm finding local minima for a selected starting point was used. To get closer to the global minimum, calculations were repeated many times, taking into account the inequality constraints for the searched parameters. The paper presents the parameter estimation results and a comparison of the waveforms measured and calculated based on the final parameters for 200 MW and 50 MW turbogenerators.

scholarly journals The Effect of Crown Dimensions on Stem Profile for Dahurian Larch, Korean Spruce, and Manchurian Fir in Northeast China

Forests ◽  
2021 ◽  
Vol 12 (4) ◽  
pp. 398
Author(s):  
Amna Hussain ◽  
Muhammad Khurram Shahzad ◽  
Lichun Jiang
Keyword(s):  
Northeast China ◽  
Least Squares Method ◽  
Model Fitting ◽  
Nonlinear Least Squares ◽  
Dahurian Larch ◽  
Fit Statistics ◽  
Crown Length ◽  
Crown Shape ◽  
Natural Stands ◽  
Crown Dimensions

Crown architecture has long been evaluated for its impact on taper modeling. However, most of the research has focused on a limited number of crown dimensions. This study examined the effect of adding several crown dimensions in improving the diameter and volume estimates of Dahurian larch, Korean spruce, and Manchurian fir in northeast China. The crown dimensions included crown length, crown ratio, crown width, height to live crown base, diameter at the crown base, and crown shape. A well-known taper model of Clark et al. (1991) was fitted to the data of 276 trees from natural stands. To adjust the inherent autocorrelation in the data, we added a third-order continuous-time error structure in the model fit. Model fitting was carried out with the NLMIXED procedure (Non-linear Mixed Procedure), followed by the MODEL procedure of SAS using the generalized nonlinear least-squares method. Fit statistics and graphical assessments were used to evaluate the original and modified models. Above 98% of the total variance of d was explained by the models for all species. The addition of crown variables showed slight improvements for root mean square error (RMSE) values in the analyzed species. The RMSE plots indicated that the models with crown variables slightly improved the diameter and volume predictions for the species but only for the upper stem (>50%–90%). The study demonstrated that crown dimensions influence the stem taper, but the original model of Clark et al. (1991) reasonably realized that effect.

scholarly journals Spectral Convolution Feature-Based SPD Matrix Representation for Signal Detection Using a Deep Neural Network

Entropy ◽  
2020 ◽  
Vol 22 (9) ◽  
pp. 949
Author(s):  
Jiangyi Wang ◽  
Min Liu ◽  
Xinwu Zeng ◽  
Xiaoqiang Hua
Keyword(s):  
Neural Network ◽  
Signal Detection ◽  
Convolutional Neural Network ◽  
Deep Neural Network ◽  
Detection Method ◽  
Learning Algorithm ◽  
Simulated Data ◽  
Data Sets ◽  
Feature Maps ◽  
Simulated Data Sets

Convolutional neural networks have powerful performances in many visual tasks because of their hierarchical structures and powerful feature extraction capabilities. SPD (symmetric positive definition) matrix is paid attention to in visual classification, because it has excellent ability to learn proper statistical representation and distinguish samples with different information. In this paper, a deep neural network signal detection method based on spectral convolution features is proposed. In this method, local features extracted from convolutional neural network are used to construct the SPD matrix, and a deep learning algorithm for the SPD matrix is used to detect target signals. Feature maps extracted by two kinds of convolutional neural network models are applied in this study. Based on this method, signal detection has become a binary classification problem of signals in samples. In order to prove the availability and superiority of this method, simulated and semi-physical simulated data sets are used. The results show that, under low SCR (signal-to-clutter ratio), compared with the spectral signal detection method based on the deep neural network, this method can obtain a gain of 0.5–2 dB on simulated data sets and semi-physical simulated data sets.

scholarly journals MGMM: An R Package for fitting Gaussian Mixture Models on Incomplete Data

2019 ◽  
Author(s):  
Zachary R. McCaw ◽  
Hanna Julienne ◽  
Hugues Aschard
Keyword(s):  
Missing Data ◽  
Mixture Models ◽  
Gaussian Mixture Models ◽  
Model Fitting ◽  
Simulated Data ◽  
R Package ◽  
Gaussian Mixture ◽  
Parameter Estimates ◽  
Cluster Assignment ◽  
Underlying Distribution

AbstractAlthough missing data are prevalent in applications, existing implementations of Gaussian mixture models (GMMs) require complete data. Standard practice is to perform complete case analysis or imputation prior to model fitting. Both approaches have serious drawbacks, potentially resulting in biased and unstable parameter estimates. Here we present MGMM, an R package for fitting GMMs in the presence of missing data. Using three case studies on real and simulated data sets, we demonstrate that, when the underlying distribution is near-to a GMM, MGMM is more effective at recovering the true cluster assignments than state of the art imputation followed by standard GMM. Moreover, MGMM provides an accurate assessment of cluster assignment uncertainty even when the generative distribution is not a GMM. This assessment may be used to identify unassignable observations. MGMM is available as an R package on CRAN: https://CRAN.R-project.org/package=MGMM.

scholarly journals Least Squares Estimations for the General Linear Model Parameters with Epsilon Skew Normal Error Term

2020 ◽  
pp. 636-645
Author(s):  
Hussain Karim Nashoor ◽  
Ebtisam Karim Abdulah
Keyword(s):  
Least Squares ◽  
Linear Model ◽  
Least Squares Method ◽  
General Linear Model ◽  
Ordinary Least Squares ◽  
Skewed Distribution ◽  
General Linear ◽  
Average Error ◽  
Model Parameters ◽  
Skew Normal

Examination of skewness makes academics more aware of the importance of accurate statistical analysis. Undoubtedly, most phenomena contain a certain percentage of skewness which resulted to the appearance of what is -called "asymmetry" and, consequently, the importance of the skew normal family . The epsilon skew normal distribution ESN (μ, σ, ε) is one of the probability distributions which provide a more flexible model because the skewness parameter provides the possibility to fluctuate from normal to skewed distribution. Theoretically, the estimation of linear regression model parameters, with an average error value that is not zero, is considered a major challenge due to having difficulties, as no explicit formula to calculate these estimates can be obtained. Practically, values for these estimates can be obtained only by referring to numerical methods. This research paper is dedicated to estimate parameters of the Epsilon Skew Normal General Linear Model (ESNGLM) using an adaptive least squares method, as along with the employment of the ordinary least squares method for estimating parameters of the General Linear Model (GLM). In addition, the coefficient of determination was used as a criterion to compare the models’ preference. These methods were applied to real data represented by dollar exchange rates. The Matlab software was applied in this work and the results showed that the ESNGLM represents a satisfactory model. 

scholarly journals The identification of a device based on a Peltier element by the least squares method

2020 ◽  
pp. 17-27
Author(s):  
Vladimir Grinkevich ◽  
Keyword(s):  
Mathematical Model ◽  
Least Squares ◽  
Least Squares Method ◽  
Control Object ◽  
Object Identification ◽  
Model Parameters ◽  
Peltier Element ◽  
Transport Delay ◽  
Non Linear ◽  
The Mathematical Model

The evaluation of the mathematical model parameters of a non-linear object with a transport delay is considered in this paper. A temperature controlled stage based on a Peltier element is an identification object in the paper. Several input signal implementations are applied to the input of the identification object. The least squares method is applied for the calculation of the non-linear differential equitation parameters which describe the identification object. The least squares method is used due to its simplicity and the possibility of identification non-linear objects. The parameters values obtained in the process of identification are provided. The plots of temperature changes in the temperature control system with a controller designed based on the mathematical model of the control object obtained as a result of identification are shown. It is found that the mathematical model obtained in the process of identification may be applied to design controllers for non-linear systems, in particular for a temperature stage based on a Peltier element, and for self-tuning controllers. However, the least square method proposed in the paper cannot estimate the transport delay time. Therefore it is required to evaluate the time delay by temperature transient processes. Dynamic object identification is applied when it is required to obtain a mathematical model structure and evaluate the parameters by an input and output control object signal. Also, identification is applied for auto tuning of controllers. A mathematical model of a control object is required to design the controller which is used to provide the required accuracy and stability of control systems. Peltier elements are applied to design low-power and small- size temperature stage . Hot benches based on a Peltier element can provide the desired temperature above and below ambient temperature.

scholarly journals Efficient detection of repeating sites to accelerate phylogenetic likelihood calculations

2016 ◽  
Author(s):  
Kassian Kobert ◽  
Alexandros Stamatakis ◽  
Tomáš Flouri
Keyword(s):  
Evolutionary Biology ◽  
Likelihood Function ◽  
Simulated Data ◽  
Evolutionary Model ◽  
Identical Result ◽  
Model Parameters ◽  
Data Sets ◽  
Efficient Detection ◽  
Novel Method ◽  
Computational Bottleneck

The phylogenetic likelihood function is the major computational bottleneck in several applications of evolutionary biology such as phylogenetic inference, species delimitation, model selection and divergence times estimation. Given the alignment, a tree and the evolutionary model parameters, the likelihood function computes the conditional likelihood vectors for every node of the tree. Vector entries for which all input data are identical result in redundant likelihood operations which, in turn, yield identical conditional values. Such operations can be omitted for improving run-time and, using appropriate data structures, reducing memory usage. We present a fast, novel method for identifying and omitting such redundant operations in phylogenetic likelihood calculations, and assess the performance improvement and memory saving attained by our method. Using empirical and simulated data sets, we show that a prototype implementation of our method yields up to 10-fold speedups and uses up to 78% less memory than one of the fastest and most highly tuned implementations of the phylogenetic likelihood function currently available. Our method is generic and can seamlessly be integrated into any phylogenetic likelihood implementation.

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