scholarly journals A Phase-Type Distribution for the Sum of Two Concatenated Markov Processes Application to the Analysis Survival in Bladder Cancer

Mathematics ◽  
2020 ◽  
Vol 8 (12) ◽  
pp. 2099
Author(s):  
Belén García-Mora ◽  
Cristina Santamaría ◽  
Gregorio Rubio
Keyword(s):  
Bladder Cancer ◽  
Distribution Function ◽  
Survival Function ◽  
Simulated Data ◽  
Real Data ◽  
Phase Type Distribution ◽  
Cancer Data ◽  
Phase Type ◽  
The Matrix ◽  
Analysis Survival

Stochastic processes are useful and important for modeling the evolution of processes that take different states over time, a situation frequently found in fields such as medical research and engineering. In a previous paper and within this framework, we developed the sum of two independent phase-type (PH)-distributed variables, each of them being associated with a Markovian process of one absorbing state. In that analysis, we computed the distribution function, and its associated survival function, of the sum of both variables, also PH-distributed. In this work, in one more step, we have developed a first approximation of that distribution function in order to avoid the calculation of an inverse matrix for the possibility of a bad conditioning of the matrix, involved in the expression of the distribution function in the previous paper. Next, in a second step, we improve this result, giving a second, more accurate approximation. Two numerical applications, one with simulated data and the other one with bladder cancer data, are used to illustrate the two proposed approaches to the distribution function. We compare and argue the accuracy and precision of each one of them by means of their error bound and the application to real data of bladder cancer.

scholarly journals Mathematical Model For Forwarding Packets In Communication Network

2021 ◽  
Author(s):  
Samaa Adel Ibrahim Hussein ◽  
Fayez Wanis Zaki ◽  
Mohammed Ashour
Keyword(s):  
Data Transfer ◽  
Solution Procedure ◽  
Area Network ◽  
Wide Area Network ◽  
Phase Type Distribution ◽  
Application Performance ◽  
Phase Type ◽  
The Matrix ◽  
Matrix Geometric Solution ◽  
System States

Abstract In recent years, SDN technology has been applied to several networks such as wide area network (WAN). IT provides many benefits, such as: enhancing data transfer, promoting Application performance and reducing deployment costs. Software Defined-WAN networks lack studies and references. This paper introduced a system for SD-WAN network using PH/PH/C queues. It concentrates on the study of algebraic estimates the probability distribution of the system states. The Matrix-Geometric solution procedure of a phase type distribution queue with first-come first-served discipline is used.

scholarly journals A Weibull-Gompertz Makeham Distribution with Properties and Application to Cancer Data

2019 ◽  
pp. 1-17
Author(s):  
Peter O. Koleoso ◽  
Angela U. Chukwu
Keyword(s):  
Bladder Cancer ◽  
Maximum Likelihood ◽  
Order Statistics ◽  
Hazard Function ◽  
Probability Distributions ◽  
Survival Function ◽  
Statistical Properties ◽  
Cancer Data ◽  
Method Of Maximum Likelihood ◽  
Flexible Model

The article presents an extension of the Gompertz Makeham distribution using the Weibull-G family of continuous probability distributions proposed by Tahir et al. (2016a). This new extension generates a more flexible model called Weibull-Gompertz Makeham distribution. Some statistical properties of the distribution which include the moments, survival function, hazard function and distribution of order statistics were derived and discussed. The parameters were estimated by the method of maximum likelihood and the distribution was applied to a bladder cancer data. Weibull-Gompertz Makeham distribution performed best (AIC = -6.8677, CAIC = -6.3759, BIC = 7.3924) when compared with other existing distributions of the same family to model bladder cancer data.

scholarly journals Single-Cell Transcriptome Profiling Simulation Reveals the Impact of Sequencing Parameters and Algorithms on Clustering

Life ◽  
2021 ◽  
Vol 11 (7) ◽  
pp. 716
Author(s):  
Yunhe Liu ◽  
Aoshen Wu ◽  
Xueqing Peng ◽  
Xiaona Liu ◽  
Gang Liu ◽  
...  
Keyword(s):  
Clustering Algorithms ◽  
Simulated Data ◽  
Ground Truth ◽  
Real Data ◽  
Transcriptome Profiling ◽  
Actual Data ◽  
Generation Process ◽  
Data Generation ◽  
The Matrix ◽  
The Impact

Despite the scRNA-seq analytic algorithms developed, their performance for cell clustering cannot be quantified due to the unknown “true” clusters. Referencing the transcriptomic heterogeneity of cell clusters, a “true” mRNA number matrix of cell individuals was defined as ground truth. Based on the matrix and the actual data generation procedure, a simulation program (SSCRNA) for raw data was developed. Subsequently, the consistency between simulated data and real data was evaluated. Furthermore, the impact of sequencing depth and algorithms for analyses on cluster accuracy was quantified. As a result, the simulation result was highly consistent with that of the actual data. Among the clustering algorithms, the Gaussian normalization method was the more recommended. As for the clustering algorithms, the K-means clustering method was more stable than K-means plus Louvain clustering. In conclusion, the scRNA simulation algorithm developed restores the actual data generation process, discovers the impact of parameters on classification, compares the normalization/clustering algorithms, and provides novel insight into scRNA analyses.

scholarly journals Sources of Artifacts in SLODR Detection

2021 ◽  
Vol 14 (1) ◽  
pp. 86-100
Author(s):  
Aleksei A. Korneev ◽  
Anatoly N. Krichevets ◽  
Konstantin V. Sugonyaev ◽  
Dmitriy V. Ushakov ◽  
Alexander G. Vinogradov ◽  
...  
Keyword(s):  
Correlation Matrix ◽  
Simulated Data ◽  
Real Data ◽  
False Identification ◽  
Data Set ◽  
The Third ◽  
Intellectual Abilities ◽  
The Matrix ◽  
Simulation Parameters ◽  
Selection Of

Background. Spearman’s law of diminishing returns (SLODR) states that intercorrelations between scores on tests of intellectual abilities were higher when the data set was comprised of subjects with lower intellectual abilities and vice versa. After almost a hundred years of research, this trend has only been detected on average. Objective. To determine whether the very different results were obtained due to variations in scaling and the selection of subjects. Design. We used three methods for SLODR detection based on moderated factor analysis (MFCA) to test real data and three sets of simulated data. Of the latter group, the first one simulated a real SLODR effect. The second one simulated the case of a different density of tasks of varying difficulty; it did not have a real SLODR effect. The third one simulated a skewed selection of respondents with different abilities and also did not have a real SLODR effect. We selected the simulation parameters so that the correlation matrix of the simulated data was similar to the matrix created from the real data, and all distributions had similar skewness parameters (about -0.3). Results. The results of MFCA are contradictory and we cannot clearly distinguish by this method the dataset with real SLODR from datasets with similar correlation structure and skewness, but without a real SLODR effect. Theresults allow us to conclude that when effects like SLODR are very subtle and can be identified only with a large sample, then features of the psychometric scale become very important, because small variations of scale metrics may lead either to masking of real SLODR or to false identification of SLODR.

Concentrated matrix exponential distributions with real eigenvalues

2021 ◽  
pp. 1-17
Author(s):  
András Mészáros ◽  
Miklós Telek
Keyword(s):  
Stochastic Models ◽  
Laplace Transformation ◽  
Matrix Exponential ◽  
Phase Type Distribution ◽  
Exponential Distributions ◽  
Inverse Laplace Transformation ◽  
Complex Eigenvalues ◽  
Phase Type ◽  
The Matrix ◽  
The Laplace Transform

Abstract Concentrated random variables are frequently used in representing deterministic delays in stochastic models. The squared coefficient of variation ( $\mathrm {SCV}$ ) of the most concentrated phase-type distribution of order $N$ is $1/N$ . To further reduce the $\mathrm {SCV}$ , concentrated matrix exponential (CME) distributions with complex eigenvalues were investigated recently. It was obtained that the $\mathrm {SCV}$ of an order $N$ CME distribution can be less than $n^{-2.1}$ for odd $N=2n+1$ orders, and the matrix exponential distribution, which exhibits such a low $\mathrm {SCV}$ has complex eigenvalues. In this paper, we consider CME distributions with real eigenvalues (CME-R). We present efficient numerical methods for identifying a CME-R distribution with smallest SCV for a given order $n$ . Our investigations show that the $\mathrm {SCV}$ of the most concentrated CME-R of order $N=2n+1$ is less than $n^{-1.85}$ . We also discuss how CME-R can be used for numerical inverse Laplace transformation, which is beneficial when the Laplace transform function is impossible to evaluate at complex points.

scholarly journals A Bayesian Inference Approach for Bivariate Weibull Distributions Derived from Roy and Morgenstern Methods

2021 ◽  
Vol 9 (3) ◽  
pp. 529-554
Author(s):  
Ricardo Puziol de Oliveira ◽  
Marcos Vinicius de Oliveira Peres ◽  
Milene Regina dos Santos ◽  
Edson Zangiacomi Martinez ◽  
Jorge Aberto Achcar
Keyword(s):  
Survival Function ◽  
Factorial Moment ◽  
Simulated Data ◽  
Real Data ◽  
Rate Function ◽  
Strength Parameter ◽  
Numerical Application ◽  
Lifetime Distributions ◽  
Proposed Model ◽  
Joint Survival Function

Bivariate lifetime distributions are of great importance in studies related to interdependent components, especially in engineering applications. In this paper, we introduce two bivariate lifetime assuming three- parameter Weibull marginal distributions. Some characteristics of the proposed distributions as the joint survival function, hazard rate function, cross factorial moment and stress-strength parameter are also derived. The inferences for the parameters or even functions of the parameters of the models are obtained under a Bayesian approach. An extensive numerical application using simulated data is carried out to evaluate the accuracy of the obtained estimators to illustrate the usefulness of the proposed methodology. To illustrate the usefulness of the proposed model, we also include an example with real data from which it is possible to see that the proposed model leads to good fits to the data.

A stochastic Expectation–Maximisation (EM) algorithm for construction of mortality tables

2017 ◽  
Vol 12 (1) ◽  
pp. 1-22
Author(s):  
Luz Judith R. Esparza ◽  
Fernando Baltazar-Larios
Keyword(s):  
Real Data ◽  
Jump Process ◽  
Ageing Process ◽  
Physiological Age ◽  
Phase Type Distribution ◽  
Markov Jump ◽  
Death Time ◽  
Intensity Matrix ◽  
Expectation Maximisation ◽  
Phase Type

AbstractIn this paper, we present an extension of the model proposed by Lin & Liu that uses the concept of physiological age to model the ageing process by using phase-type distributions to calculate the probability of death. We propose a finite-state Markov jump process to model the hypothetical ageing process in which it is possible the transition rates between non-consecutive physiological ages. Since the Markov process has only a single absorbing state, the death time follows a phase-type distribution. Thus, to build a mortality table the challenge is to estimate this matrix based on the records of the ageing process. Considering the nature of the data, we consider two cases: having continuous time information of the ageing process, and the more interesting and realistic case, having reports of the process just in determined times. If the ageing process is only observed at discrete time points we have a missing data problem, thus, we use a stochastic Expectation–Maximisation (SEM) algorithm to find the maximum likelihood estimator of the intensity matrix. And in order to do that, we build Markov bridges which are sampled using the Bisection method. The theory is illustrated by a simulation study and used to fit real data.

scholarly journals Separation of Chromatographic Co-Eluted Compounds by Clustering and by Functional Data Analysis

Metabolites ◽  
2021 ◽  
Vol 11 (4) ◽  
pp. 214
Author(s):  
Aneta Sawikowska ◽  
Anna Piasecka ◽  
Piotr Kachlicki ◽  
Paweł Krajewski
Keyword(s):  
Simulated Data ◽  
Principal Component ◽  
Real Data ◽  
Functional Principal Component Analysis ◽  
Additional Advantage ◽  
Time Alignment ◽  
Peak Separation ◽  
Biological Mixtures ◽  
Overlapping Peaks ◽  
Retention Time Alignment

Peak overlapping is a common problem in chromatography, mainly in the case of complex biological mixtures, i.e., metabolites. Due to the existence of the phenomenon of co-elution of different compounds with similar chromatographic properties, peak separation becomes challenging. In this paper, two computational methods of separating peaks, applied, for the first time, to large chromatographic datasets, are described, compared, and experimentally validated. The methods lead from raw observations to data that can form inputs for statistical analysis. First, in both methods, data are normalized by the mass of sample, the baseline is removed, retention time alignment is conducted, and detection of peaks is performed. Then, in the first method, clustering is used to separate overlapping peaks, whereas in the second method, functional principal component analysis (FPCA) is applied for the same purpose. Simulated data and experimental results are used as examples to present both methods and to compare them. Real data were obtained in a study of metabolomic changes in barley (Hordeum vulgare) leaves under drought stress. The results suggest that both methods are suitable for separation of overlapping peaks, but the additional advantage of the FPCA is the possibility to assess the variability of individual compounds present within the same peaks of different chromatograms.

scholarly journals A Closed-Form Solution to Planar Feature-Based Registration of LiDAR Point Clouds

2021 ◽  
Vol 10 (7) ◽  
pp. 435
Author(s):  
Yongbo Wang ◽  
Nanshan Zheng ◽  
Zhengfu Bian
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Simulated Data ◽  
Real Data ◽  
Point Clouds ◽  
Form Solution ◽  
Spatial Transformation ◽  
Dual Quaternions ◽  
Feature Based ◽  
Planar Feature

Since pairwise registration is a necessary step for the seamless fusion of point clouds from neighboring stations, a closed-form solution to planar feature-based registration of LiDAR (Light Detection and Ranging) point clouds is proposed in this paper. Based on the Plücker coordinate-based representation of linear features in three-dimensional space, a quad tuple-based representation of planar features is introduced, which makes it possible to directly determine the difference between any two planar features. Dual quaternions are employed to represent spatial transformation and operations between dual quaternions and the quad tuple-based representation of planar features are given, with which an error norm is constructed. Based on L2-norm-minimization, detailed derivations of the proposed solution are explained step by step. Two experiments were designed in which simulated data and real data were both used to verify the correctness and the feasibility of the proposed solution. With the simulated data, the calculated registration results were consistent with the pre-established parameters, which verifies the correctness of the presented solution. With the real data, the calculated registration results were consistent with the results calculated by iterative methods. Conclusions can be drawn from the two experiments: (1) The proposed solution does not require any initial estimates of the unknown parameters in advance, which assures the stability and robustness of the solution; (2) Using dual quaternions to represent spatial transformation greatly reduces the additional constraints in the estimation process.

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