Parameters of the Diffusion Leaky Integrate-and-Fire Neuronal Model for a Slowly Fluctuating Signal

Stochastic leaky integrate-and-fire (LIF) neuronal models are common theoretical tools for studying properties of real neuronal systems. Experimental data of frequently sampled membrane potential measurements between spikes show that the assumption of constant parameter values is not realistic and that some (random) fluctuations are occurring. In this article, we extend the stochastic LIF model, allowing a noise source determining slow fluctuations in the signal. This is achieved by adding a random variable to one of the parameters characterizing the neuronal input, considering each interspike interval (ISI) as an independent experimental unit with a different realization of this random variable. In this way, the variation of the neuronal input is split into fast (within-interval) and slow (between-intervals) components. A parameter estimation method is proposed, allowing the parameters to be estimated simultaneously over the entire data set. This increases the statistical power, and the average estimate over all ISIs will be improved in the sense of decreased variance of the estimator compared to previous approaches, where the estimation has been conducted separately on each individual ISI. The results obtained on real data show good agreement with classical regression methods.

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Transformation of circular random variables based on circular distribution functions

Filomat ◽

10.2298/fil1817931m ◽

2018 ◽

Vol 32 (17) ◽

pp. 5931-5947

Author(s):

Hatami Mojtaba ◽

Alamatsaz Hossein

Keyword(s):

Distribution Function ◽

Random Variables ◽

Real Data ◽

Random Variable ◽

Distribution Functions ◽

Likelihood Method ◽

Circular Distribution ◽

Data Set ◽

Trigonometric Moments ◽

Von Mises

In this paper, we propose a new transformation of circular random variables based on circular distribution functions, which we shall call inverse distribution function (id f ) transformation. We show that M?bius transformation is a special case of our id f transformation. Very general results are provided for the properties of the proposed family of id f transformations, including their trigonometric moments, maximum entropy, random variate generation, finite mixture and modality properties. In particular, we shall focus our attention on a subfamily of the general family when id f transformation is based on the cardioid circular distribution function. Modality and shape properties are investigated for this subfamily. In addition, we obtain further statistical properties for the resulting distribution by applying the id f transformation to a random variable following a von Mises distribution. In fact, we shall introduce the Cardioid-von Mises (CvM) distribution and estimate its parameters by the maximum likelihood method. Finally, an application of CvM family and its inferential methods are illustrated using a real data set containing times of gun crimes in Pittsburgh, Pennsylvania.

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A Class of Local Linear Estimators with Functional Data

Journal of Siberian Federal University Mathematics & Physics ◽

10.17516/1997-1397-2019-12-3-379-391 ◽

2019 ◽

pp. 379-391 ◽

Cited By ~ 1

Author(s):

Sara Leulmi ◽

Fatiha Messaci

Keyword(s):

Nonparametric Estimation ◽

Metric Space ◽

Functional Data ◽

Regression Function ◽

Real Data ◽

Random Variable ◽

Data Set ◽

Response Variable ◽

Local Linear ◽

Linear Estimators

We introduce a local linear nonparametric estimation for the generalized regression function of a scalar response variable given a random variable taking values in a semi metric space. We establish a rate of uniform consistency for the proposed estimators. Then, based on a real data set we illustrate the performance of a particular studied estimator with respect to other known estimators

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On Properties of the Bimodal Skew-Normal Distribution and an Application

Mathematics ◽

10.3390/math8050703 ◽

2020 ◽

Vol 8 (5) ◽

pp. 703

Author(s):

David Elal-Olivero ◽

Juan F. Olivares-Pacheco ◽

Osvaldo Venegas ◽

Heleno Bolfarine ◽

Héctor W. Gómez

Keyword(s):

Maximum Likelihood ◽

Normal Distribution ◽

Estimation Method ◽

Likelihood Estimation ◽

Real Data ◽

Skew Normal Distribution ◽

Data Set ◽

Normal Distributions ◽

Stochastic Representations ◽

Skew Normal

The main object of this paper is to develop an alternative construction for the bimodal skew-normal distribution. The construction is based upon a study of the mixture of skew-normal distributions. We study some basic properties of this family, its stochastic representations and expressions for its moments. Parameters are estimated using the maximum likelihood estimation method. A simulation study is carried out to observe the performance of the maximum likelihood estimators. Finally, we compare the efficiency of the new distribution with other distributions in the literature using a real data set. The study shows that the proposed approach presents satisfactory results.

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The KM-Algorithm Identifies Regulated Genes in Time Series Expression Data

Advances in Bioinformatics ◽

10.1155/2009/284251 ◽

2009 ◽

Vol 2009 ◽

pp. 1-10

Author(s):

Martina Bremer ◽

R. W. Doerge

Keyword(s):

Gene Expression ◽

Time Series ◽

Statistical Power ◽

Regulatory Networks ◽

Real Data ◽

Model Parameters ◽

Expression Data ◽

Data Set ◽

Gene Expression Time Series ◽

Expression Time

We present a statistical method to rank observed genes in gene expression time series experiments according to their degree of regulation in a biological process. The ranking may be used to focus on specific genes or to select meaningful subsets of genes from which gene regulatory networks can be built. Our approach is based on a state space model that incorporates hidden regulators of gene expression. Kalman (K) smoothing and maximum (M) likelihood estimation techniques are used to derive optimal estimates of the model parameters upon which a proposed regulation criterion is based. The statistical power of the proposed algorithm is investigated, and a real data set is analyzed for the purpose of identifying regulated genes in time dependent gene expression data. This statistical approach supports the concept that meaningful biological conclusions can be drawn from gene expression time series experiments by focusing on strong regulation rather than large expression values.

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Clustering Based on a Novel Density Estimation Method

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.748.590 ◽

2013 ◽

Vol 748 ◽

pp. 590-594

Author(s):

Li Liao ◽

Yong Gang Lu ◽

Xu Rong Chen

Keyword(s):

Density Estimation ◽

Nearest Neighbor ◽

Mean Shift ◽

Estimation Method ◽

Synthetic Data ◽

Real Data ◽

Data Sets ◽

Clustering Methods ◽

K Nearest Neighbor ◽

Data Set

We propose a novel density estimation method using both the k-nearest neighbor (KNN) graph and the potential field of the data points to capture the local and global data distribution information respectively. The clustering is performed based on the computed density values. A forest of trees is built using each data point as the tree node. And the clusters are formed according to the trees in the forest. The new clustering method is evaluated by comparing with three popular clustering methods, K-means++, Mean Shift and DBSCAN. Experiments on two synthetic data sets and one real data set show that our approach can effectively improve the clustering results.

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Negative binomial improved second degree lindley distribution and its application

Advances in Mathematics: Scientific Journal ◽

10.37418/amsj.9.2.5 ◽

2020 ◽

pp. 569-581

Author(s):

R. Ashly ◽

C. S. Rajitha

Keyword(s):

Negative Binomial Distribution ◽

Binomial Distribution ◽

Negative Binomial ◽

Estimation Method ◽

Likelihood Estimation ◽

Real Data ◽

Data Set ◽

Factorial Moments ◽

Lindley Distribution ◽

Second Degree

The objective of this paper is to introduce a new two parameter mixed negative binomial distribution, namely negative binomial-improved second degree Lindley(NB-ISL) distribution. This distribution is obtained by mixing the negative binomial distribution with the improved second degree Lindley distribution. Many mixed distributions have been used in the literature for modeling the over dispersed count data, which provide a better fit compared to the Poisson and negative binomial distribution. In addition, we present the basic statistical properties of the new distribution such as factorial moments, mean and variance and the behavior of mean, variance and coefficient of variation are also discussed. Parameter estimation is implemented by using maximum likelihood estimation method. The performance of the NB-ISL distribution is shown in practice by applying it on real data set and compare it with some well-known count distributions. The result shows that the negative binomial-improved second degree Lindley distribution provides a better fit compared to Poisson, negative binomial and negative binomial-Lindley distributions.

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Signatures Extraction of Ship Radiated Noise Based on Passive Sonar

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.568-570.233 ◽

2014 ◽

Vol 568-570 ◽

pp. 233-237 ◽

Cited By ~ 1

Author(s):

Hong Ji Wang ◽

Ri Jie Yang ◽

Jian Hui Han

Keyword(s):

Feature Extraction ◽

Shallow Water ◽

Kalman Filtering ◽

Estimation Method ◽

Likelihood Estimation ◽

Real Data ◽

Underwater Noise ◽

Data Set ◽

Radiated Noise ◽

Extraction Algorithm

By combining likelihood estimation method and Kalman filtering tracking approach, feature extraction algorithm was developed in this paper to extract the harmonic feature from the underwater noise radiated by different kinds of ships. The ability of harmonic features extrication algorithm is demonstrated by simulation and real shallow water data set comprised of a number of ships. The processing results of real data set also show that he harmonics of different kinds of ships can be used to separate from each other.

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Estimation for Entropy and Parameters of Generalized Bilal Distribution under Adaptive Type II Progressive Hybrid Censoring Scheme

Entropy ◽

10.3390/e23020206 ◽

2021 ◽

Vol 23 (2) ◽

pp. 206

Author(s):

Xiaolin Shi ◽

Yimin Shi ◽

Kuang Zhou

Keyword(s):

Monte Carlo ◽

Likelihood Estimation ◽

Real Data ◽

Random Variable ◽

Credible Interval ◽

Mcmc Methods ◽

Type Ii ◽

Data Set ◽

Lindley’S Approximation ◽

Bayesian Estimations

Entropy measures the uncertainty associated with a random variable. It has important applications in cybernetics, probability theory, astrophysics, life sciences and other fields. Recently, many authors focused on the estimation of entropy with different life distributions. However, the estimation of entropy for the generalized Bilal (GB) distribution has not yet been involved. In this paper, we consider the estimation of the entropy and the parameters with GB distribution based on adaptive Type-II progressive hybrid censored data. Maximum likelihood estimation of the entropy and the parameters are obtained using the Newton–Raphson iteration method. Bayesian estimations under different loss functions are provided with the help of Lindley’s approximation. The approximate confidence interval and the Bayesian credible interval of the parameters and entropy are obtained by using the delta and Markov chain Monte Carlo (MCMC) methods, respectively. Monte Carlo simulation studies are carried out to observe the performances of the different point and interval estimations. Finally, a real data set has been analyzed for illustrative purposes.

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ON THE MUTH DISTRIBUTION

Mathematical Modelling and Analysis ◽

10.3846/13926292.2015.1048540 ◽

2015 ◽

Vol 20 (3) ◽

pp. 291-310 ◽

Cited By ~ 6

Author(s):

Pedro Jodra ◽

Maria Dolores Jimenez-Gamero ◽

Maria Virtudes Alba-Fernandez

Keyword(s):

Least Squares ◽

Weighted Least Squares ◽

Golden Ratio ◽

Natural Extension ◽

Real Data ◽

Random Variable ◽

Quantile Function ◽

Lambert W Function ◽

Data Set ◽

Monte Carlo Simulation Study

The Muth distribution is a continuous random variable introduced in the context of reliability theory. In this paper, some mathematical properties of the model are derived, including analytical expressions for the moment generating function, moments, mode, quantile function and moments of the order statistics. In this regard, the generalized integro-exponential function, the Lambert W function and the golden ratio arise in a natural way. The parameter estimation of the model is performed by the methods of maximum likelihood, least squares, weighted least squares and moments, which are compared via a Monte Carlo simulation study. A natural extension of the model is considered as well as an application to a real data set.

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dearseq: a variance component score test for RNA-seq differential analysis that effectively controls the false discovery rate

NAR Genomics and Bioinformatics ◽

10.1093/nargab/lqaa093 ◽

2020 ◽

Vol 2 (4) ◽

Author(s):

Marine Gauthier ◽

Denis Agniel ◽

Rodolphe Thiébaut ◽

Boris P Hejblum

Keyword(s):

False Discovery Rate ◽

Statistical Power ◽

Differential Expression Analysis ◽

Score Test ◽

Real Data ◽

Differential Analysis ◽

Rna Seq ◽

Data Set ◽

Mathematical Proofs ◽

False Discovery

Abstract RNA-seq studies are growing in size and popularity. We provide evidence that the most commonly used methods for differential expression analysis (DEA) may yield too many false positive results in some situations. We present dearseq, a new method for DEA that controls the false discovery rate (FDR) without making any assumption about the true distribution of RNA-seq data. We show that dearseq controls the FDR while maintaining strong statistical power compared to the most popular methods. We demonstrate this behavior with mathematical proofs, simulations and a real data set from a study of tuberculosis, where our method produces fewer apparent false positives.

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