Chapter 6 Approximate stochastic simulation algorithms
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Saliha Demirbüken
Abstract
Stochastic Simulation Algorithms (SSAs) utilize Monte Carlo methods to precisely model molecular population dynamics in alignment with the chemical master equation (CME). Despite their accuracy, SSAs can be computationally intensive, often requiring extensive simulation of reaction events and thousands of sample paths to accurately characterize probability distributions. These methods are particularly suited for systems with finite molecular populations. To address the computational challenges, approximate SSAs offer a practical alternative, compromising exactness for efficiency. These approximations are grounded in Markov processes and the leap condition, which assumes minimal change in propensity functions over discrete time intervals. The approximate SSAs include the Poisson τ-leap, Langevin τ-leap, estimated midpoint techniques, binomial τ-leap, modified Poisson τ-leap method, and newer approaches such as the τ-selection procedure and approximate Gillespie algorithm. Additionally, advances in statistical analysis, using second and third order truncated Taylor series expansions, enhance the understanding of distribution characteristics by providing insights into variance and covariance, leading to more precise confidence intervals compared to previous studies. This chapter explores the theoretical foundations, practical applications, and computational trade-offs of both exact and approximate SSAs, offering a comprehensive overview for researchers in stochastic process.
Abstract
Stochastic Simulation Algorithms (SSAs) utilize Monte Carlo methods to precisely model molecular population dynamics in alignment with the chemical master equation (CME). Despite their accuracy, SSAs can be computationally intensive, often requiring extensive simulation of reaction events and thousands of sample paths to accurately characterize probability distributions. These methods are particularly suited for systems with finite molecular populations. To address the computational challenges, approximate SSAs offer a practical alternative, compromising exactness for efficiency. These approximations are grounded in Markov processes and the leap condition, which assumes minimal change in propensity functions over discrete time intervals. The approximate SSAs include the Poisson τ-leap, Langevin τ-leap, estimated midpoint techniques, binomial τ-leap, modified Poisson τ-leap method, and newer approaches such as the τ-selection procedure and approximate Gillespie algorithm. Additionally, advances in statistical analysis, using second and third order truncated Taylor series expansions, enhance the understanding of distribution characteristics by providing insights into variance and covariance, leading to more precise confidence intervals compared to previous studies. This chapter explores the theoretical foundations, practical applications, and computational trade-offs of both exact and approximate SSAs, offering a comprehensive overview for researchers in stochastic process.
Chapters in this book
- Frontmatter I
- Contents V
- List of authors VII
- Chapter 1 Use of digital systems in the design system of photovoltaic solar stations 1
- Chapter 2 Potential wind energy in Turkmenistan 21
- Chapter 3 Potential of using biogas technology in Turkmenistan 31
- Chapter 4 Energy efficiency 45
- Chapter 5 Latent renewable energy in Turkmenistan 57
- Chapter 6 Approximate stochastic simulation algorithms 67
- Chapter 7 The role of supply chain management in the construction industry 95
- Chapter 8 Selection of threshold in binary graphs of biological networks 121
- Chapter 9 Model selection criteria with bootstrap algorithms: applications in biological networks 133
- Chapter 10 Technocracy in Governance: new directions in city functioning and urban planning 149
- Chapter 11 Outlier detection in biomedical data: ECG-focused approaches 161
- Chapter 12 Optimization of debt collection strategies for South African banks with machine learning models 183
- Chapter 13 Performance of six turbulence models in predicting two-phase flow on a hydraulic test bench 209
- Index 231
Chapters in this book
- Frontmatter I
- Contents V
- List of authors VII
- Chapter 1 Use of digital systems in the design system of photovoltaic solar stations 1
- Chapter 2 Potential wind energy in Turkmenistan 21
- Chapter 3 Potential of using biogas technology in Turkmenistan 31
- Chapter 4 Energy efficiency 45
- Chapter 5 Latent renewable energy in Turkmenistan 57
- Chapter 6 Approximate stochastic simulation algorithms 67
- Chapter 7 The role of supply chain management in the construction industry 95
- Chapter 8 Selection of threshold in binary graphs of biological networks 121
- Chapter 9 Model selection criteria with bootstrap algorithms: applications in biological networks 133
- Chapter 10 Technocracy in Governance: new directions in city functioning and urban planning 149
- Chapter 11 Outlier detection in biomedical data: ECG-focused approaches 161
- Chapter 12 Optimization of debt collection strategies for South African banks with machine learning models 183
- Chapter 13 Performance of six turbulence models in predicting two-phase flow on a hydraulic test bench 209
- Index 231
