Git: A free and open source distributed version control system designed to handle everything from small to very large projects with speed and efficiency.
Introduction to git
Initial set up for git:
git config --global user.name "Your Name Comes Here"
Simulation studies are techniques used to imitate a real-world process on a computer, with the objective of understanding or evaluating the statistical properties associated with the process. It serves as a powerful tool for analytical or numerical analysis.
Applications of simulation studies include, but are not limited to:
Evaluating point estimators: Point estimators are used to provide the single "best guess" of a parameter based on observed data.
Assessing confidence intervals: It helps in determining the reliability of estimate intervals through repeated sampling.
Checking the finite-sample statistical properties of estimators and testing procedures that have been motivated through asymptotics. Check the demonstrations in R and Python through the links:
meantest.R and meantest.py
Testing hypotheses: Simulation studies assist in testing the validity of a hypothesis under specific assumptions.
Describing distributions: Helps in understanding and describing the distributions of random variables.
And many others: Including optimizing solutions, predicting outcomes, etc.
Simulation studies are particularly valuable when theoretical derivations are unavailable, difficult, or intractable, offering a practical avenue to gain insights and solutions.
The terms "simulation study" and "Monte Carlo study" are synonymous, both involving statistical simulations to approximate solutions to quantitative problems.
The code find_the_bugs.R and find_the_bugs.py is code for a simulation study to test the effect of an outlier on regression coefficient confidence interval coverage. But it doesn't work. Use these principles too find out why!
Before we delve into the simulations and tests, let's review some important terms:
Size: It refers to the probability of rejecting the null hypothesis when it is true.
Power: This is the probability that a test correctly rejects the null hypothesis when the alternative hypothesis is true.
P-value: This is a function of the observed sample results that is used to decide whether to reject the null hypothesis within the context of a specific statistical model.
Hypothesis Testing and Power Calculation via simulation:
hyp.R: This R script demonstrates the process of hypothesis testing and power calculation through simulation techniques.
hyp.py: This Python script is parallel to the R script and explores hypothesis testing and power calculation using Python.
Permutation Tests:
perm.R and perm.py: This script guides you through the process of conducting permutation tests, a non-parametric method to test the null hypothesis.