farming simulation
traffic simulation
flood simulation
swimming simulation
simulation of posterior distribution
Dr. Richard Gran
Source: https://www.youtube.com/watch?v=OCMafswcNkY
A model is a conceptual representation of a relationship, a system or an aspect of a real world
Example: When you are buying a second-hand car, the car travelled a longer distance cost more.
Most of the distribution can be approximated by simulating data from a uniform distribution and manipulating the values.
runif(1000, min = 0, max = 1)
rchisq(1000, df = 2)
rnorm(mean = 0, sd = 1)
rgamma(1000, shape = 2)
rcauchy(1000, scale = 1.5)
rbeta(1000, 1.3, 2.4)
In most software, we can draw random samples from a different distribution.
Random sample to solve problems that might be deterministic
Used in Optimization, Numerical Integration, Drawing samples from a probability distribution, etc
source: http://tiny.cc/eistcz
simrel
simulator
simTools
simglm, ...
simpy
pysimrel
numpy
stata
SAS
Proper use of experimental design makes the simulation more effective. Consider a model,
Proper use of experimental design makes the simulation more effective. Consider a model,
DOI: 10.1016/j.chemolab.2019.05.004: Comparison of multi-response prediction methods
DOI: 10.1080/00401706.2013.872700: Simultaneous Envelopes for Multivariate Linear Regression
DOI: 10.1111/j.1467-9469.2011.00770.x: Near Optimal Prediction from Relevant Components
Following are some of these studies:
- Patrick Landscape
Ripley, B. D. (2009). Stochastic simulation (Vol. 316). John Wiley & Sons.
Jones, O., Maillardet, R., & Robinson, A. (2014). Introduction to scientific programming and simulation using R. Chapman and Hall/CRC.
Morris, T. P., White, I. R., & Crowther, M. J. (2019). Using simulation studies to evaluate statistical methods. Statistics in medicine, 38(11), 2074-2102.
Ross, S. M. (2014). Introduction to probability models. Academic press.
Ripley, B. D. (1988). Uses and abuses of statistical simulation. Mathematical Programming, 42(1-3), 53-68.
Knežo, D., & Vagaská, A. (2019). Monte Carlo Method Application and Generation of Random Numbers by Usage of Numerical Methods. In Models and Theories in Social Systems (pp. 197-207). Springer, Cham.
Birta Louis, G., & Gilbert, A. (2007). Modelling and Simulation: Exploring Dynamic System Behaviour. Ottawa: School of information technology and engineering.
Sigal, M. J., & Chalmers, R. P. (2016). Play it again: Teaching statistics with Monte Carlo simulation. Journal of Statistics Education, 24(3), 136-156.
Sæbø, S., Almøy, T., & Helland, I. S. (2015). simrel—A versatile tool for linear model data simulation based on the concept of a relevant subspace and relevant predictors. Chemometrics and Intelligent Laboratory Systems, 146, 128-135.