Investigating the Number of Monte Carlo Simulations for Statistically Stationary Model Outputs

Zhang, J.; Cui, Shengai

doi:10.3390/axioms12050481

Cited by 2 publications

(2 citation statements)

References 32 publications

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“…The simulations were implemented using R v4.2.2 (a statistical analysis programming language) within the RStudio and a range of specialized packages for Markov chain Monte Carlo (MCMC), the Metropolis-Hasting algorithm, and the Gibbs sampler (see [19,[28][29][30][31]). Statistical simulations were implemented to study the sensitivity of the spatial capture model to the data augmentation parameter L (added number of zeros) by estimating unknown population size N, home range σ, and λ 0 .…”

Section: Resultsmentioning

confidence: 99%

An Enhanced Spatial Capture Model for Population Analysis Using Unidentified Counts through Camera Encounters

Jaber,

Hamad,

Breininger

et al. 2023

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Spatial capture models are broadly used for population analysis in ecological statistics. Spatial capture models for unidentified individuals rely on data augmentation to create a zero-inflated population. The unknown true population size can be considered as the number of successes of a binomial distribution with an unknown number of independent trials and an unknown probability of success. Augmented population size is a realization of the unknown number of trials and is recommended to be much larger than the unknown population size. As a result, the probability of success of binomial distribution, i.e., the unknown probability that a hypothetical individual in the augmented population belongs to the true population, can be obtained by dividing the unknown true population size by the augmented population size. This is an inverse problem as neither the true population size nor the probability of success is known, and the accuracy of their estimates strongly relies on the augmented population size. Therefore, the estimated population size in spatial capture models is very sensitive to the size of a zero-inflated population and in turn to the estimated probability of success. This is an important issue in spatial capture models as a typical count model with censored data (unidentified and/or undetected). Hence, in this research, we investigated the sensitivity and accuracy of the spatial capture model to address this problem with the objective of improving the robustness of the model. We demonstrated that the estimated population size using the proposed enhanced capture model was more accurate in comparison with the previous spatial capture model.

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Section: Resultsmentioning

confidence: 99%

An Enhanced Spatial Capture Model for Population Analysis Using Unidentified Counts through Camera Encounters

Jaber,

Hamad,

Breininger

et al. 2023

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“…The Monte Carlo method is extensively employed to assess the impact of modeling uncertainty on predictions of structural response [9,13]. Through Monte Carlo Simulations, realizations of each random variable are generated.…”

Section: Monte Carlo Simulation Methodsmentioning

confidence: 99%

Probabilistic Assessment of Structural Integrity

Alzbutas,

Dundulis

2024

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A probability-based approach, combining deterministic and probabilistic methods, was developed for analyzing building and component failures, which are especially crucial for complex structures like nuclear power plants. This method links finite element and probabilistic software to assess structural integrity under static and dynamic loads. This study uses NEPTUNE software, which is validated, for a deterministic transient analysis and ProFES software for probabilistic models. In a case study, deterministic analyses with varied random variables were transferred to ProFES for probabilistic analyses of piping failure and wall damage. A Monte Carlo Simulation, First-Order Reliability Method, and combined methods were employed for probabilistic analyses under severe transient loading, focusing on a postulated accident at the Ignalina Nuclear Power Plant. The study considered uncertainties in material properties, component geometry, and loads. The results showed the Monte Carlo Simulation method to be conservative for high failure probabilities but less so for low probabilities. The Response Surface/Monte Carlo Simulation method explored the impact load–failure probability relationship. Given the uncertainties in material properties and loads in complex structures, a deterministic analysis alone is insufficient. Probabilistic analysis is imperative for extreme loading events and credible structural safety evaluations.

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Investigating the Number of Monte Carlo Simulations for Statistically Stationary Model Outputs

Cited by 2 publications

References 32 publications

An Enhanced Spatial Capture Model for Population Analysis Using Unidentified Counts through Camera Encounters

An Enhanced Spatial Capture Model for Population Analysis Using Unidentified Counts through Camera Encounters

Probabilistic Assessment of Structural Integrity

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