An Empirical Bayes Approach for Estimating the Mean of N Stationary Time Series

1977 ◽  
Vol 72 (358) ◽  
pp. 397 ◽  
Author(s):  
Aroona S. Borpujari
Keyword(s):  
Time Series ◽  
Empirical Bayes ◽  
Stationary Time Series ◽  
Stationary Time ◽  
The Mean ◽  
Empirical Bayes Approach ◽  
Bayes Approach

Estimation of the mean of a stationary time series by sampling

1973 ◽  
Vol 10 (02) ◽  
pp. 419-431 ◽  
Author(s):  
David R. Brillinger
Keyword(s):  
Time Series ◽  
Asymptotic Distribution ◽  
Stationary Point ◽  
Limit Theorems ◽  
Stationary Time Series ◽  
Stationary Time ◽  
Stationary Point Process ◽  
The Mean ◽  
The Times ◽  
Sampling Times

LetX(t), – ∞ <t< ∞, be a stationary time series with meancx. Let 0 <τ1<τ2 < … <τN≦Tdenote A given sampling times in the interval (0,T]. We determine the asymptotic distribution of the estimate [X(τ1) + … +X(τN)]/Nofcxwhen the sampling times are fixed, satisfying a form of generalised harmonic analysis requirement, and when the sampling times are the times of events of a stationary point process independent of the seriesX(t). The results obtained may be viewed as non-standard central limit theorems.

Estimation of the mean of a stationary time series by sampling

1973 ◽  
Vol 10 (2) ◽  
pp. 419-431 ◽  
Author(s):  
David R. Brillinger
Keyword(s):  
Time Series ◽  
Asymptotic Distribution ◽  
Stationary Point ◽  
Limit Theorems ◽  
Stationary Time Series ◽  
Stationary Time ◽  
Stationary Point Process ◽  
The Mean ◽  
The Times ◽  
Sampling Times

Let X(t), – ∞ < t < ∞, be a stationary time series with mean cx. Let 0 < τ1 < τ2 < … < τN ≦ T denote A given sampling times in the interval (0, T]. We determine the asymptotic distribution of the estimate [X(τ1) + … + X(τN)]/N of cx when the sampling times are fixed, satisfying a form of generalised harmonic analysis requirement, and when the sampling times are the times of events of a stationary point process independent of the series X(t). The results obtained may be viewed as non-standard central limit theorems.

scholarly journals An Empirical Bayes approach for the identification of long-range chromosomal interaction from Hi-C data

2021 ◽  
Vol 20 (1) ◽  
pp. 1-15
Author(s):  
Qi Zhang ◽  
Zheng Xu ◽  
Yutong Lai
Keyword(s):  
Long Range ◽  
Latent Variables ◽  
Empirical Bayes ◽  
Genome Structure ◽  
Peak Detection ◽  
Data Matrix ◽  
Dispersion Modeling ◽  
Empirical Bayes Approach ◽  
Over Dispersion ◽  
Bayes Approach

Abstract Hi-C experiments have become very popular for studying the 3D genome structure in recent years. Identification of long-range chromosomal interaction, i.e., peak detection, is crucial for Hi-C data analysis. But it remains a challenging task due to the inherent high dimensionality, sparsity and the over-dispersion of the Hi-C count data matrix. We propose EBHiC, an empirical Bayes approach for peak detection from Hi-C data. The proposed framework provides flexible over-dispersion modeling by explicitly including the “true” interaction intensities as latent variables. To implement the proposed peak identification method (via the empirical Bayes test), we estimate the overall distributions of the observed counts semiparametrically using a Smoothed Expectation Maximization algorithm, and the empirical null based on the zero assumption. We conducted extensive simulations to validate and evaluate the performance of our proposed approach and applied it to real datasets. Our results suggest that EBHiC can identify better peaks in terms of accuracy, biological interpretability, and the consistency across biological replicates. The source code is available on Github (https://github.com/QiZhangStat/EBHiC).

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