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Stochastic dynamics thus stands in sharp contrast to deterministic dynamics.
The results demonstrate that our stochastic approach provides different model decisions compared to the traditional deterministic approach.
Whereas the stochastic models work in situations where chance dominates, for example when the number of cells is small, or under random mutations, the deterministic models are more important for large-scale, normal hematopoiesis.
Results show that stochastic modelling considerably increases the uncertainty of parameter estimates, but ensures their consistency between separate trainings, whereas deterministic models are less robust and offer a less reliable forecasting.
Therefore, in some circumstances deterministic modelling may offer water resource managers a pragmatic alternative to stochastic modelling, but its usefulness as a surrogate will depend upon the level of uncertainty in the model parameters.
It is shown that when the system of interest is stochastic the expected variability of a stochastic parameter is biased when a deterministic model is employed for parameter estimation.
Our results provide support for the contention that stochastic modeling in economics should be more than a mere extension of the deterministic realm.
The stochastic model implemented into the deterministic model results in almost similar predictions with the deterministic model in 50% (best guess) probability.
We show that the dynamics of the system are influenced by both stochastic and deterministic processes.
We show that the stochastic model predicts the deterministic behavior on a reasonable time scale, which can be consistently obtained from both models.
Prediction accuracies, as well as the results of a test for the existence of determinism point to the conclusion that many of the seemingly stochastic series considered were deterministic.
These studies demonstrate that results from the deterministic analysis method are realizable in the stochastic analysis method.
These significant differences between the stochastic and the deterministic model results can serve to confirm the shortfalls of deterministic design.
This analysis has shown close correspondence between the stochastic and deterministic modelling results.
Open accessJournal ArticleDOI
Sandor Csorgo, Jan Mielniczuk 
01 Apr 1999-Bernoulli
56 Citations
The main results contrast with previous findings for deterministic-design regression.

Related Questions

Where regression analysis is used?4 answersRegression analysis is used in a variety of fields and industries. It is commonly applied in engineering and various industries to describe the association between variables and predict one variable based on others. In the insurance industry, regression analysis is used to predict the risk associated with a policy based on available information. Regression models are also widely used in communication networks, the internet of things, and data-driven statistical machine learning tasks to establish a parametric relationship between input variables and the output. In the field of randomized clinical trials, regression analysis is used to estimate and infer treatment effects, even when the regression model is misspecified. Regression analysis has also become central to quantitative analysis in International Relations, contributing to description, inference, and causal analysis. Additionally, regression analysis is applied in biomedical studies for prediction, feature selection, and dimensionality reduction.
What is regression analysis?5 answersRegression analysis is a mathematical and statistical method used to analyze experimental data and fit mathematical models to the data by estimating unknown parameters. It is commonly used in engineering, science, social sciences, business, medicine, and data analytics. Regression analysis can be linear or nonlinear, and it can involve single or multiple variables and sets of experimental data. The goal of regression analysis is to design optimal regression models, interpret the results accurately, and avoid common pitfalls and biases. It is a powerful technique for synthesizing information, measuring the mean and variance of the conditional distribution, and predicting continuous variables based on multivariate input variables. Regression analysis is also used for describing associations between variables and predicting outcomes in various industries, such as insurance, where risk assessment is crucial.
What are the assumptions of a regression model?5 answersRegression models rely on certain assumptions. These assumptions include linearity, reliability of measurement, homoscedasticity, and normality. It is important to test these assumptions because when they are violated, the results may not be trustworthy, leading to errors or biased estimates. Misconceptions about these assumptions are widespread, leading to inappropriate use of linear regression and less powerful alternative procedures. In the field of cardiothoracic surgery, regression models such as linear, logistic, and Cox proportional hazards regression are commonly used, but they also rely on assumptions that need to be checked. Additionally, there are cases where the assumptions of standard regression approaches are not appropriate, and more general approaches, such as fully nonparametric regression models, are needed. Overall, assessing assumptions in regression models is crucial for reliable and generalizable results.
Why is there an increasing necessity for stochastic intervention compared to deterministic approaches?5 answersThere is an increasing necessity for stochastic intervention compared to deterministic approaches due to several reasons. Firstly, stochastic interventions provide a promising solution to the theoretical and practical problems faced in evaluating the effects of inflexible static interventions. Secondly, stochastic simulations allow for the study of systems with uncertainties arising in natural processes and engineering applications, which are often ignored in deterministic approaches. Additionally, stochastic models can capture the transmission dynamics of diseases more accurately, such as in the case of investigating cryptosporidiosis transmission dynamics in humans and cattle. Moreover, stochastic interventions enable the estimation of causal effects in study designs subject to real-world limitations, such as outcome-dependent two-phase sampling. Lastly, stochastic approaches, such as Bayesian inversion, yield more robust estimations and provide posterior probabilistic distribution functions, enhancing the evaluation of inversion results.
How to determine if a regression model can be developed?7 answers
What could be the objectives behind fitting a regression model?16 answers

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