Projection of Mean and Variance Functions for Population Processes with Time-homogeneous Laws of Evolution

1986 ◽  
Vol 3 (1) ◽  
pp. 1-22 ◽  
Author(s):  
GARY T. PICKENS ◽  
CHARLES J. MODE
Keyword(s):  
Variance Functions ◽  
Mean And Variance ◽  
Population Processes

scholarly journals Evolving mtDNA populations within cells

2019 ◽  
Vol 47 (5) ◽  
pp. 1367-1382 ◽  
Author(s):  
Iain G. Johnston ◽  
Joerg P. Burgstaller
Keyword(s):  
Mitochondrial Dna ◽  
Nonlinear Effects ◽  
Eukaryotic Cells ◽  
Change Over Time ◽  
Mean And Variance ◽  
Genetic Makeup ◽  
Population Processes ◽  
The Many ◽  
Cell Functionality ◽  
Over Time

Abstract Mitochondrial DNA (mtDNA) encodes vital respiratory machinery. Populations of mtDNA molecules exist in most eukaryotic cells, subject to replication, degradation, mutation, and other population processes. These processes affect the genetic makeup of cellular mtDNA populations, changing cell-to-cell distributions, means, and variances of mutant mtDNA load over time. As mtDNA mutant load has nonlinear effects on cell functionality, and cell functionality has nonlinear effects on tissue performance, these statistics of cellular mtDNA populations play vital roles in health, disease, and inheritance. This mini review will describe some of the better-known ways in which these populations change over time in different organisms, highlighting the importance of quantitatively understanding both mutant load mean and variance. Due to length constraints, we cannot attempt to be comprehensive but hope to provide useful links to some of the many excellent studies on these topics.

scholarly journals EVALUASI NUMERIK PENDUGA FUNGSI NILAI HARAPAN DAN FUNGSI RAGAM PROSES POISSON MAJEMUK DENGAN INTENSITAS EKSPONENSIAL FUNGSI LINEAR

2018 ◽  
Vol 17 (2) ◽  
pp. 157
Author(s):  
S. UTAMI ◽  
I W. MANGKU ◽  
I G. P. PURNABA
Keyword(s):  
Monte Carlo ◽  
Confidence Intervals ◽  
Observation Interval ◽  
Compound Poisson Process ◽  
Intensity Function ◽  
Significance Level ◽  
Variance Functions ◽  
Mean And Variance ◽  
The Mean ◽  
Strongly Consistent

<em>Performances of estimators for the mean and variance functions of a compound Poisson process having intensity obtained as an exponential of linear function are investigated using Monte Carlo simulations. The intensity function of this process is assumed to be </em>𝑒𝑥𝑝(𝛼+𝛽𝑠) <em>with </em>0&lt;𝛽&lt;<em>∞</em>, <em>where </em>𝛽 <em>is assumed to be known. In [8], estimators of the mean and variance functions of this process have been constructed and have been proved to be unbiased, weakly and strongly consistent. The objectives of this research are to check distributions of these estimators using Monte Carlo simulation and to check the convergence to </em>1−𝛼 <em>of the probabilities that the parameters are contained in the confidence intervals constructed in [11]. Results of the research are as follows. Distribution of estimators for the mean and variance functions are approximately normal. For a given significance level </em>𝛼<em>, the larger the size of observation interval, the closer the probabilities that the parameters are contained in the confidence intervals to </em>1−𝛼<em>.</em>

scholarly journals Semiparametric Smoothing Spline in Joint Mean and Dispersion Models with Responses from the Biparametric Exponential Family: A Bayesian Perspective

2021 ◽  
Vol 9 (2) ◽  
pp. 351-367
Author(s):  
Héctor Zárate ◽  
Edilberto Cepeda
Keyword(s):  
Exponential Family ◽  
Parametric Models ◽  
Efficient Estimation ◽  
Smoothing Methods ◽  
Markov Chain Sampling ◽  
Variance Functions ◽  
Natural Connection ◽  
Mean And Variance ◽  
The Mean ◽  
Two Parameter

This article extends the fusion among various statistical methods to estimate the mean and variance functions in heteroscedastic semiparametric models when the response variable comes from a two-parameter exponential family distribution. We rely on the natural connection among smoothing methods that use basis functions with penalization, mixed models and a Bayesian Markov Chain sampling simulation methodology. The significance and implications of our strategy lies in its potential to contribute to a simple and unified computational methodology that takes into account the factors that affect the variability in the responses, which in turn is important for an efficient estimation and correct inference of mean parameters without the requirement of fully parametric models. An extensive simulation study investigates the performance of the estimates. Finally, an application using the Light Detection and Ranging technique, LIDAR, data highlights the merits of our approach.

scholarly journals Variational Bayesian Learning and Semiparametric Models on the Double Exponential Family

2021 ◽  
Author(s):  
Hector Zarate-Solano ◽  
Edilberto Cepeda-Cuervo
Keyword(s):  
Bayesian Learning ◽  
Linear Models ◽  
Computation Time ◽  
Semiparametric Regression ◽  
Optimization Methods ◽  
Data Models ◽  
Accurate Estimation ◽  
Variational Bayesian ◽  
Variance Functions ◽  
Mean And Variance

In this paper, we focus on variational Bayesian learning deterministic optimization methods for inference in biparametric exponential models where the parameters follow semiparametric regression structures. This combination of data models and algorithms contributes to solving real-world problems and reduces the computation time. This allows both the rapid exploration of many data models and the accurate estimation of the mean and variance functions through the connection between generalized linear models and graph theory. A simulation study was carried out to assess the performance of the deterministic approximation. Finally, herein, we present an application using macroeconomic data to emphasize the benefits of the proposed approach.

Distance Mean and Variance Functions and Sphere Fitting

Statistics ◽  
1994 ◽  
Vol 25 (3) ◽  
pp. 251-266 ◽  
Author(s):  
J. Gates
Keyword(s):  
Variance Functions ◽  
Mean And Variance ◽  
Sphere Fitting
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