Stochastic methods »
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Using random processes and random data for simulation of the real events and processes. This is a very powerful calculation technique, which can do physical modelling for the systems without knowing exact equations.
Pros of Stochastic Methods
Incorporating Uncertainty: Stochastic methods are well-suited for modeling and simulating systems with inherent uncertainty. By considering randomness and variability, these methods provide a more realistic representation of many real-world phenomena.
Flexibility in Complex Systems: Stochastic methods are often more adaptable to complex systems with multiple interacting components and uncertain inputs. They can capture intricate relationships that deterministic models may struggle to represent.
Cons of Stochastic Methods
Computational Intensity: Stochastic simulations can be computationally intensive, especially when a large number of random samples is required for accurate results. This can pose challenges in terms of computational resources and time.
Interpretability: Stochastic models may be less intuitive and harder to interpret compared to deterministic models. The randomness introduced can make it challenging to explain the behaviour of the system, especially to non-experts.
Most popular stochastic methods:
Monte Carlo Simulation: A technique that uses random sampling to obtain numerical results for problems that might be deterministic in principle. It is widely used in finance, engineering, physics, and many other fields.
Markov Chains: A stochastic model describing a sequence of events where the probability of each event depends only on the state attained in the previous event. Markov chains are used in various applications, including modelling systems with memoryless properties.
Stochastic Differential Equations (SDEs): Differential equations where one or more of the terms involve random variables. SDEs are often used in physics, biology, and finance to model systems subject to both deterministic and stochastic influences.
Brownian Motion: A random motion that describes the random movement of particles suspended in a fluid (Brownian motion in physics) or the movement of financial prices in the stock market (geometric Brownian motion in finance).
Agent-Based Modeling: A computational approach that simulates the actions and interactions of agents within a system. Agents follow specific rules and may have stochastic elements, leading to emergent behaviour at the system level.
Queueing Theory: A mathematical theory used to analyze and model the flow of entities (such as customers or data packets) through a system of queues. It is applied in telecommunications, computer networks, and service systems.
Genetic Algorithms: Optimization algorithms inspired by the process of natural selection. They are used for solving optimization and search problems and are employed in machine learning, engineering, and optimization.
Particle Filtering: A recursive Bayesian filter that represents the posterior distribution of a system's state using a set of particles. Particle filtering is commonly used in state estimation problems with non-linear and non-Gaussian dynamics.
Simulated Annealing: An optimization algorithm inspired by the annealing process in metallurgy. It is used to find an approximate solution to an optimization problem, especially in cases where the landscape of the solution space is complex.
Bootstrapping: A resampling method that involves sampling with replacement from the observed data to estimate the distribution of a statistic. Bootstrapping is often used for constructing confidence intervals and assessing the variability of estimators.
I'm not sure that I will tell you about every method, but I'm pretty confident in Monte Carlo Simulations and Simulated Annealing techniques, and I will try to give you some interesting guides about using these techniques.
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