Multiple subtraction using statistically estimated inverse wavelets

Geophysics ◽  
2010 ◽  
Vol 75 (6) ◽  
pp. WB247-WB254 ◽  
Author(s):  
Yike Liu ◽  
Degang Jin ◽  
Xu Chang ◽  
Peng Li ◽  
Hongchuan Sun ◽  
...  
Keyword(s):  
Real Data ◽  
Least Square ◽  
Second Step ◽  
Multiple Events ◽  
Amplitude Distortion ◽  
Computational Costs ◽  
Multiple Elimination

Surface-related multiple elimination (SRME) typically consists of two steps: The first step is prediction and the second step is subtraction. In subtraction, it is important to effectively attenuate multiple events and preserve primary events. When multiples cross with or overlap on primaries, least-square subtraction usually cannot subtract multiples effectively and may also damage the primaries. When multiples overlap with primaries, least-square subtraction cannot always subtract multiples accurately and often damages the primaries. To remedy this problem, we propose to statistically estimate the inverse source wavelet, correct for errors in the estimate of the inverse wavelet, and then use the corrected inverse wavelets for multiple subtraction. Synthetic tests and real data examples show that the proposed method can effectively attenuate multiples, while they also preserve the continuity of reflection events and successfully avoid amplitude distortion. The proposed method is characterized by low computational costs and ease of implementation.

scholarly journals Predictive Analysis for COVID-19 Spread in India by Adaptive Compartmental Model

2020 ◽  
Author(s):  
Sudhansu Sekhar Singh ◽  
Dinakrushna Mohapatra
Keyword(s):  
Compartmental Model ◽  
Real Data ◽  
Least Square ◽  
Time Dependent ◽  
Second Step ◽  
Computational Tool ◽  
Indian States ◽  
Epidemiological Parameters ◽  
Good Agreement

The role of mathematical modelling in predicting spread of an epidemic is of vital importance. The purpose of present study is to develop and apply a computational tool for predicting evolution of different epidemiological variables for COVID-19 in India. We propose a dynamic SIRD (Susceptible-Infected-Recovered-Dead) and SEIRD (Susceptible-Exposed-Infected-Recovered-Dead) model for this purpose. In the dynamic model, time dependent infection rate is assumed for estimating evolution of different variables of the model. Parameter estimation of the model is the first step of the analysis which is performed by least square optimization of priori data. In the second step of the analysis, simulation is carried out by using evaluated parameters for prediction of the outbreak. The computational model has been validated against real data for COVID-19 outbreak in Italy. Time to reach peak, peak infected cases and total reported cases were compared with actual data and found to be in very good agreement. Next the model is applied for the case of India and various Indian states to predict different epidemiological parameters. Priori data was taken from the beginning of nation-wide lockdown on 24 March to 6 July. It was found that peak of the outbreak may reach in the month of August-September with maximum 4-5 lakhs active cases at peak. Total number of reported cases all over India would be in between three to five millions. State wise, Maharashtra, Tamilnadu and Delhi would be worst affected.

Detection of differentially methylated CpG sites between tumor samples with uneven tumor purities

2019 ◽  
Vol 36 (7) ◽  
pp. 2017-2024
Author(s):  
Weiwei Zhang ◽  
Ziyi Li ◽  
Nana Wei ◽  
Hua-Jun Wu ◽  
Xiaoqi Zheng
Keyword(s):  
Real Data ◽  
R Package ◽  
Differential Methylation ◽  
Least Square ◽  
Epigenetic Mechanism ◽  
Supplementary Information ◽  
Cpg Sites ◽  
Tumor Purity ◽  
Different Sources ◽  
Normal Controls

Abstract Motivation Inference of differentially methylated (DM) CpG sites between two groups of tumor samples with different geno- or pheno-types is a critical step to uncover the epigenetic mechanism of tumorigenesis, and identify biomarkers for cancer subtyping. However, as a major source of confounding factor, uneven distributions of tumor purity between two groups of tumor samples will lead to biased discovery of DM sites if not properly accounted for. Results We here propose InfiniumDM, a generalized least square model to adjust tumor purity effect for differential methylation analysis. Our method is applicable to a variety of experimental designs including with or without normal controls, different sources of normal tissue contaminations. We compared our method with conventional methods including minfi, limma and limma corrected by tumor purity using simulated datasets. Our method shows significantly better performance at different levels of differential methylation thresholds, sample sizes, mean purity deviations and so on. We also applied the proposed method to breast cancer samples from TCGA database to further evaluate its performance. Overall, both simulation and real data analyses demonstrate favorable performance over existing methods serving similar purpose. Availability and implementation InfiniumDM is a part of R package InfiniumPurify, which is freely available from GitHub (https://github.com/Xiaoqizheng/InfiniumPurify). Supplementary information Supplementary data are available at Bioinformatics online.

Comparison of two different types of fractional-order COVID-19 distributed time-delay models with real data application

2021 ◽  
pp. 2150219
Author(s):  
Liangli Yang ◽  
Yongmei Su ◽  
Xinjian Zhuo
Keyword(s):  
Time Delay ◽  
Fractional Order ◽  
Distributed Delay ◽  
Real Data ◽  
Least Square ◽  
Order Model ◽  
The Real ◽  
Fractional Order Model ◽  
Different Types ◽  
Distributed Time Delay

The outbreak of COVID-19 has a great impact on the world. Considering that there are different infection delays among different populations, which can be expressed as distributed delay, and the distributed time-delay is rarely used in fractional-order model to simulate the real data, here we establish two different types of fractional order (Caputo and Caputo–Fabrizio) COVID-19 models with distributed time-delay. Parameters are estimated by the least-square method according to the report data of China and other 12 countries. The results of Caputo and Caputo–Fabrizio model with distributed time-delay and without delay, the integer-order model with distributed delay are compared. These show that the fractional-order model can be better in fitting the real data. Moreover, Caputo order is better in short-term time fitting, Caputo–Fabrizio order is better in long-term fitting and prediction. Finally, the influence of several parameters is simulated in Caputo order model, which further verifies the importance of taking strict quarantine measures and paying close attention to the incubation period population.

scholarly journals Using WSR-88D Polarimetric Data to Identify Bird-Contaminated Doppler Velocities

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Yuan Jiang ◽  
Qin Xu ◽  
Pengfei Zhang ◽  
Kang Nai ◽  
Liping Liu
Keyword(s):  
Fuzzy Logic ◽  
Real Data ◽  
Radar Data ◽  
Second Step ◽  
Doppler Velocity ◽  
Data Quality Control ◽  
Fuzzy Logic Method ◽  
Automated Technique ◽  
Migrating Birds ◽  
Logic Method

As an important part of Doppler velocity data quality control for radar data assimilation and other quantitative applications, an automated technique is developed to identify and remove contaminated velocities by birds, especially migrating birds. This technique builds upon the existing hydrometeor classification algorithm (HCA) for dual-polarimetric WSR-88D radars developed at the National Severe Storms Laboratory, and it performs two steps. In the first step, the fuzzy-logic method in the HCA is simplified and used to identify biological echoes (mainly from birds and insects). In the second step, another simple fuzzy logic method is developed to detect bird echoes among the biological echoes identified in the first step and thus remove bird-contaminated velocities. The membership functions used by the fuzzy logic method in the second step are extracted from normalized histograms of differential reflectivity and differential phase for birds and insects, respectively, while the normalized histograms are constructed by polarimetric data collected during the 2012 fall migrating season and sorted for bird and insects, respectively. The performance and effectiveness of the technique are demonstrated by real-data examples.

scholarly journals Characteristics and Application of the NHPP Log-Logistic Reliability Model

2018 ◽  
Vol 8 (1) ◽  
pp. 44
Author(s):  
Lutfiah Ismail Al turk
Keyword(s):  
Evaluation Criteria ◽  
Real Data ◽  
Least Square ◽  
Estimation Methods ◽  
Data Sets ◽  
Reliability Model ◽  
Reliability Engineering ◽  
Reliability Models ◽  
Time Domain Data ◽  
Linear Least Square

In this paper, a Nonhomogeneous Poisson Process (NHPP) reliability model based on the two-parameter Log-Logistic (LL) distribution is considered. The essential model’s characteristics are derived and represented graphically. The parameters of the model are estimated by the Maximum Likelihood (ML) and Non-linear Least Square (NLS) estimation methods for the case of time domain data. An application to show the flexibility of the considered model are conducted based on five real data sets and using three evaluation criteria. We hope this model will help as an alternative model to other useful reliability models for describing real data in reliability engineering area.

scholarly journals New Lindley Half Cauchy Distribution: Theory and Applications

2020 ◽  
Vol 9 (4) ◽  
pp. 1-7
Keyword(s):  
Maximum Likelihood ◽  
Real Data ◽  
Cauchy Distribution ◽  
Least Square ◽  
Cumulative Distribution ◽  
Likelihood Method ◽  
Estimation Methods ◽  
Model Parameters ◽  
Data Set ◽  
Von Mises

In this paper, we have defined a new two-parameter new Lindley half Cauchy (NLHC) distribution using Lindley-G family of distribution which accommodates increasing, decreasing and a variety of monotone failure rates. The statistical properties of the proposed distribution such as probability density function, cumulative distribution function, quantile, the measure of skewness and kurtosis are presented. We have briefly described the three well-known estimation methods namely maximum likelihood estimators (MLE), least-square (LSE) and Cramer-Von-Mises (CVM) methods. All the computations are performed in R software. By using the maximum likelihood method, we have constructed the asymptotic confidence interval for the model parameters. We verify empirically the potentiality of the new distribution in modeling a real data set.

Bayesian wavefield separation by transform-domain sparsity promotion

Geophysics ◽  
2008 ◽  
Vol 73 (5) ◽  
pp. A33-A38 ◽  
Author(s):  
Deli Wang ◽  
Rayan Saab ◽  
Özgür Yilmaz ◽  
Felix J. Herrmann
Keyword(s):  
Bayesian Approach ◽  
Real Data ◽  
Transform Domain ◽  
Coherent Noise ◽  
Noise Sources ◽  
Wavefield Separation ◽  
Ground Roll ◽  
Successful Removal ◽  
Multiple Elimination ◽  
Made In

Successful removal of coherent-noise sources greatly determines seismic imaging quality. Major advances have been made in this direction, e.g., surface-related multiple elimination (SRME) and interferometric ground-roll removal. Still, moderate phase, timing, amplitude errors, and clutter in predicted signal components can be detrimental. Adopting a Bayesian approach, along with assuming approximate curvelet-domain independence of the to-be-separated signal components, we construct an iterative algorithm that takes predictions produced by, for example, SRME as input and separates these components in a robust manner. In addition, the proposed algorithm controls the energy mismatch between separated and predicted components. Such a control, lacking in earlier curvelet-domain formulations, improves results for primary-multiple separation on synthetic and real data.

scholarly journals Obtaining the Correspondence Between Bayesian and Neural Networks

1998 ◽  
Vol 12 (07) ◽  
pp. 901-920 ◽  
Author(s):  
A. Stassopoulou ◽  
M. Petrou
Keyword(s):  
Neural Network ◽  
Bayesian Network ◽  
Full Range ◽  
Closed Form Solution ◽  
Real Data ◽  
Form Solution ◽  
Least Square ◽  
Novel Method ◽  
Probability Matrices ◽  
Desertification Assessment

We present in this paper a novel method for eliciting the conditional probability matrices needed for a Bayesian network with the help of a neural network. We demonstrate how we can obtain a correspondence between the two networks by deriving a closed-form solution so that the outputs of the two networks are similar in the least square error sense, not only when determining the discriminant function, but for the full range of their outputs. For this purpose we take into consideration the probability density functions of the independent variables of the problem when we compute the least square error approximation. Our methodoloy is demonstrated with the help of some real data concerning the problem of risk of desertification assessment for some burned forests in Attica, Greece where the parameters of the Bayesian network constructed for this task are successfully estimated given a neural network trained with a set of data.

Mathematical properties of the Kumaraswamy-Lindley distribution and its applications

2017 ◽  
Vol 5 (1) ◽  
pp. 17
Author(s):  
Hamdy Salem ◽  
Abd-Elwahab Hagag
Keyword(s):  
Hazard Function ◽  
Likelihood Estimation ◽  
Real Data ◽  
Quantile Function ◽  
Moment Generating Function ◽  
Least Square ◽  
Estimation Of Parameters ◽  
Least Square Estimation ◽  
Mathematical Properties ◽  
Composite Distribution

In this paper, a composite distribution of Kumaraswamy and Lindley distributions namely, Kumaraswamy-Lindley Kum-L distribution is introduced and studied. The Kum-L distribution generalizes sub-models for some widely known distributions. Some mathematical properties of the Kum-L such as hazard function, quantile function, moments, moment generating function and order statistics are obtained. Estimation of parameters for the Kum-L using maximum likelihood estimation and least square estimation techniques are provided. To illustrate the usefulness of the proposed distribution, simulation study and real data example are used.

scholarly journals Model-based leak detection and location in water distribution networks considering an extended-horizon analysis of pressure sensitivities

2013 ◽  
Vol 16 (3) ◽  
pp. 649-670 ◽  
Author(s):  
Myrna V. Casillas Ponce ◽  
Luis E. Garza Castañón ◽  
Vicenç Puig Cayuela
Keyword(s):  
Water Distribution ◽  
Real Data ◽  
Leak Detection ◽  
Distribution Networks ◽  
Optimization Method ◽  
Least Square ◽  
Water Distribution Networks ◽  
Sensitivity Matrix ◽  
Model Based ◽  
Leak Detection And Location

In this paper, we propose a new approach for model-based leak detection and location in water distribution networks (WDN), which considers an extended time-horizon analysis of pressure sensitivities. Five different ways of using the leak sensitivity matrix to isolate the leaks are described and compared. The first method is based on the binarization approach. The second, third and fourth methods are based on the comparison of the measured pressure vectors with the leak sensitivity matrix using different metrics: correlation, angle between vectors and Euclidean distance, respectively. The fifth method is based on the least square optimization method. The performance of these methods is compared when applied to two academic small networks (Hanoi and Quebra) widely used in the literature. Finally, the three methods with better performance are applied to a district metering area of the Barcelona WDN using real data.

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