Estimate the Performance of Multi-Model Estimation Algorithms

2013 ◽  
Vol 427-429 ◽  
pp. 1506-1509
Author(s):  
Yong Yan Yu
Keyword(s):  
Estimation Procedure ◽  
Model Parameters ◽  
Data Sets ◽  
Model Estimation ◽  
Multiple Model ◽  
Estimation Algorithms ◽  
Performance Metric ◽  
Testing Dataset ◽  
Correctness Criterion ◽  
Line Fitting

A robust estimation procedure is necessary to estimate the true model parameters in computer vision. Evaluating the multiple-model in the presence of outliers-robust is a fundamentally different task than the single-model problem.Despite there are many diversity multi-model estimation algorithms, it is difficult to pick an effective and advisably approach.So we present a novel quantitative evaluation of multi-model estimation algorithms, efficiency may be evaluated by either examining the asymptotic efficiency of the algorithms or by running them for a series of data sets of increasing size.Thus we create a specifical testing dataset,and introduce a performance metric, Strongest-Intersection.and using the model-aware correctness criterion. Finally, well show the validity of estimation strategy by the Experimention of line-fitting.

scholarly journals View on a mechanistic model of Chlorella vulgaris in incubated shake flasks

2021 ◽  
Author(s):  
Fabian Kuhfuß ◽  
Veronika Gassenmeier ◽  
Sahar Deppe ◽  
George Ifrim ◽  
Tanja Hernández Rodríguez ◽  
...  
Keyword(s):  
Chlorella Vulgaris ◽  
Growth Models ◽  
Mechanistic Model ◽  
Estimation Procedure ◽  
Model Parameters ◽  
Data Sets ◽  
Related Model ◽  
Kinetic Growth ◽  
Light Intensities ◽  
Shake Flasks

Abstract Kinetic growth models are a useful tool for a better understanding of microalgal cultivation and for optimizing cultivation conditions. The evaluation of such models requires experimental data that is laborious to generate in bioreactor settings. The experimental shake flask setting used in this study allows to run 12 experiments at the same time, with 6 individual light intensities and light durations. This way, 54 biomass data sets were generated for the cultivation of the microalgae Chlorella vulgaris. To identify the model parameters, a stepwise parameter estimation procedure was applied. First, light-associated model parameters were estimated using additional measurements of local light intensities at differ heights within medium at different biomass concentrations. Next, substrate related model parameters were estimated, using experiments for which biomass and nitrate data were provided. Afterwards, growth-related model parameters were estimated by application of an extensive cross validation procedure. Graphic abstract

Development of Distress Progression Models Using Panel Data Sets of In-Service Pavements

1998 ◽  
Vol 1643 (1) ◽  
pp. 20-24 ◽  
Author(s):  
Samer Madanat ◽  
Hee Cheol Shin
Keyword(s):  
Panel Data ◽  
Unobserved Heterogeneity ◽  
Continuous Model ◽  
Model Parameters ◽  
Data Sets ◽  
Model Estimation ◽  
Data Set ◽  
Pavement Distress ◽  
Progression Model ◽  
Design Characteristics

Pavement distress progression models predict the extent of a distress on pavement sections as a function of age, design characteristics, traffic loads and environmental factors. These models are usually developed using data from in-service facilities to calibrate the parameters of mechanistic deterioration models. The data used for the statistical estimation of such models consist of observations of pavements for which the distress has already appeared. Unfortunately, common statistical methods, when applied to such data sets, produce biased and inconsistent model parameters. This type of bias is known as selectivity bias, and it results from the fact that less durable pavement sections are over-represented in the sample used for model estimation. A joint pavement distress initiation and progression model, consisting of a discrete model of distress initiation and a continuous model of pavement progression is presented. This approach explicitly accounts for the self-selected nature of the sample used in developing the progression model, through the use of appropriate correction terms. Moreover, previous research is extended by accounting for the potential presence of unobserved heterogeneity in the model, which is related to the use of a panel data set for model estimation. This is achieved by using a random effects specification for both the discrete and continuous models. An empirical case study demonstrates the application of this approach for highway pavement cracking models.

scholarly journals The Exponentiated Burr XII Power Series Distribution: Properties and Applications

Stats ◽  
2018 ◽  
Vol 2 (1) ◽  
pp. 15-31
Author(s):  
Arslan Nasir ◽  
Haitham Yousof ◽  
Farrukh Jamal ◽  
Mustafa Korkmaz
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Power Series ◽  
Likelihood Estimation ◽  
Real Data ◽  
Estimation Procedure ◽  
Model Parameters ◽  
Data Sets ◽  
Power Series Distributions ◽  
New Distribution

In this work, we introduce a new Burr XII power series class of distributions, which is obtained by compounding exponentiated Burr XII and power series distributions and has a strong physical motivation. The new distribution contains several important lifetime models. We derive explicit expressions for the ordinary and incomplete moments and generating functions. We discuss the maximum likelihood estimation of the model parameters. The maximum likelihood estimation procedure is presented. We assess the performance of the maximum likelihood estimators in terms of biases, standard deviations, and mean square of errors by means of two simulation studies. The usefulness of the new model is illustrated by means of three real data sets. The new proposed models provide consistently better fits than other competitive models for these data sets.

scholarly journals Theory and Applications of the Unit Gamma/Gompertz Distribution

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1850
Author(s):  
Rashad A. R. Bantan ◽  
Farrukh Jamal ◽  
Christophe Chesneau ◽  
Mohammed Elgarhy
Keyword(s):  
Stochastic Ordering ◽  
Real Data ◽  
Rate Function ◽  
The Other ◽  
Likelihood Method ◽  
Model Parameters ◽  
Data Sets ◽  
Gompertz Distribution ◽  
Probability And Statistics ◽  
Analytical Behavior

Unit distributions are commonly used in probability and statistics to describe useful quantities with values between 0 and 1, such as proportions, probabilities, and percentages. Some unit distributions are defined in a natural analytical manner, and the others are derived through the transformation of an existing distribution defined in a greater domain. In this article, we introduce the unit gamma/Gompertz distribution, founded on the inverse-exponential scheme and the gamma/Gompertz distribution. The gamma/Gompertz distribution is known to be a very flexible three-parameter lifetime distribution, and we aim to transpose this flexibility to the unit interval. First, we check this aspect with the analytical behavior of the primary functions. It is shown that the probability density function can be increasing, decreasing, “increasing-decreasing” and “decreasing-increasing”, with pliant asymmetric properties. On the other hand, the hazard rate function has monotonically increasing, decreasing, or constant shapes. We complete the theoretical part with some propositions on stochastic ordering, moments, quantiles, and the reliability coefficient. Practically, to estimate the model parameters from unit data, the maximum likelihood method is used. We present some simulation results to evaluate this method. Two applications using real data sets, one on trade shares and the other on flood levels, demonstrate the importance of the new model when compared to other unit models.

scholarly journals Bayesian Inference of Species Trees using Diffusion Models

2020 ◽  
Vol 70 (1) ◽  
pp. 145-161 ◽  
Author(s):  
Marnus Stoltz ◽  
Boris Baeumer ◽  
Remco Bouckaert ◽  
Colin Fox ◽  
Gordon Hiscott ◽  
...  
Keyword(s):  
Bayesian Inference ◽  
Numerical Algorithms ◽  
Diffusion Models ◽  
Model Parameters ◽  
Data Sets ◽  
Species Trees ◽  
Computationally Efficient ◽  
Data Set ◽  
Snp Data ◽  
Binary Markers

Abstract We describe a new and computationally efficient Bayesian methodology for inferring species trees and demographics from unlinked binary markers. Likelihood calculations are carried out using diffusion models of allele frequency dynamics combined with novel numerical algorithms. The diffusion approach allows for analysis of data sets containing hundreds or thousands of individuals. The method, which we call Snapper, has been implemented as part of the BEAST2 package. We conducted simulation experiments to assess numerical error, computational requirements, and accuracy recovering known model parameters. A reanalysis of soybean SNP data demonstrates that the models implemented in Snapp and Snapper can be difficult to distinguish in practice, a characteristic which we tested with further simulations. We demonstrate the scale of analysis possible using a SNP data set sampled from 399 fresh water turtles in 41 populations. [Bayesian inference; diffusion models; multi-species coalescent; SNP data; species trees; spectral methods.]

scholarly journals The seven sisters DANCe

2018 ◽  
Vol 612 ◽  
pp. A70 ◽  
Author(s):  
J. Olivares ◽  
E. Moraux ◽  
L. M. Sarro ◽  
H. Bouy ◽  
A. Berihuete ◽  
...  
Keyword(s):  
Spatial Distribution ◽  
Model Comparison ◽  
Precise Determination ◽  
Model Parameters ◽  
Data Sets ◽  
Adequate Model ◽  
Comparison Results ◽  
Bayesian Evidence ◽  
Mass Segregation

Context. Membership analyses of the DANCe and Tycho + DANCe data sets provide the largest and least contaminated sample of Pleiades candidate members to date. Aims. We aim at reassessing the different proposals for the number surface density of the Pleiades in the light of the new and most complete list of candidate members, and inferring the parameters of the most adequate model. Methods. We compute the Bayesian evidence and Bayes Factors for variations of the classical radial models. These include elliptical symmetry, and luminosity segregation. As a by-product of the model comparison, we obtain posterior distributions for each set of model parameters. Results. We find that the model comparison results depend on the spatial extent of the region used for the analysis. For a circle of 11.5 parsecs around the cluster centre (the most homogeneous and complete region), we find no compelling reason to abandon King’s model, although the Generalised King model introduced here has slightly better fitting properties. Furthermore, we find strong evidence against radially symmetric models when compared to the elliptic extensions. Finally, we find that including mass segregation in the form of luminosity segregation in the J band is strongly supported in all our models. Conclusions. We have put the question of the projected spatial distribution of the Pleiades cluster on a solid probabilistic framework, and inferred its properties using the most exhaustive and least contaminated list of Pleiades candidate members available to date. Our results suggest however that this sample may still lack about 20% of the expected number of cluster members. Therefore, this study should be revised when the completeness and homogeneity of the data can be extended beyond the 11.5 parsecs limit. Such a study will allow for more precise determination of the Pleiades spatial distribution, its tidal radius, ellipticity, number of objects and total mass.

scholarly journals Bayesian Analysis of Interleaved Learning and Response Bias in Behavioral Experiments

2007 ◽  
Vol 97 (3) ◽  
pp. 2516-2524 ◽  
Author(s):  
Anne C. Smith ◽  
Sylvia Wirth ◽  
Wendy A. Suzuki ◽  
Emery N. Brown
Keyword(s):  
Bayesian Analysis ◽  
State Space ◽  
State Space Model ◽  
Estimation Procedure ◽  
Ideal Observer ◽  
Model Parameters ◽  
Behavioral Experiments ◽  
Actual Object ◽  
Space Model ◽  
Multiple Tasks

Accurate characterizations of behavior during learning experiments are essential for understanding the neural bases of learning. Whereas learning experiments often give subjects multiple tasks to learn simultaneously, most analyze subject performance separately on each individual task. This analysis strategy ignores the true interleaved presentation order of the tasks and cannot distinguish learning behavior from response preferences that may represent a subject's biases or strategies. We present a Bayesian analysis of a state-space model for characterizing simultaneous learning of multiple tasks and for assessing behavioral biases in learning experiments with interleaved task presentations. Under the Bayesian analysis the posterior probability densities of the model parameters and the learning state are computed using Monte Carlo Markov Chain methods. Measures of learning, including the learning curve, the ideal observer curve, and the learning trial translate directly from our previous likelihood-based state-space model analyses. We compare the Bayesian and current likelihood–based approaches in the analysis of a simulated conditioned T-maze task and of an actual object–place association task. Modeling the interleaved learning feature of the experiments along with the animal's response sequences allows us to disambiguate actual learning from response biases. The implementation of the Bayesian analysis using the WinBUGS software provides an efficient way to test different models without developing a new algorithm for each model. The new state-space model and the Bayesian estimation procedure suggest an improved, computationally efficient approach for accurately characterizing learning in behavioral experiments.

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