Tips & Tricks for research newbies
Coding and managing projects Using AI to better code, debug and manage projects How to export an R dataframe to LaTeX Paper writing: Analyze experiment results faster with ChatGPT How to write in Latex faster…
Check Plagiarism by grammarly
Plagiarism is the act of using someone else’s work, ideas, words, or intellectual property without proper acknowledgment or permission, and presenting it as your own. Even reusing your own previously published work or parts of…
Multiple regression analysis: waiting time to log in to Windows
Multiple regression analysis can be used to understand the relationship between the waiting time to log in to Windows (dependent variable) and several independent variables. Let’s assume we have the following independent variables: Suppose that…
Using AI to better code, debug and manage projects
1. Code Completion and Suggestions AI-powered code completion tools can predict and suggest the next lines of code based on the context of your current coding. Examples include: Copilot: Uses OpenAI’s Codex to provide code…
Analyze experiment results faster with ChatGPT
I have experiment and I want to put the best result in bold in Latex, but it takes time to compare values and identify the smallest values in each row. So, I can ask ChatGPT…
The success rates of Cupid’s arrows
I advised a master’s student to use the binomial probability formula to determine the likelihood of attracting the affection of 15 girls, with Cupid’s success rate at 0.7. The analysis shows that the highest probability of success occurs when 10 girls reciprocate love, with a probability of 0.33.
Grazing the maze of probability
Supplementary materials for section Grazing the maze of probability & A random variable mood in the KSML app: Basic rules of probability: Mutually exclusive events Conditional probability for medical testing in a forestThe conditional probability…
How to write in Latex faster with ChatGPT
Type into ChatGPT: And you may see something like this So, you basically typed something really simple, and ask ChatGPT to do the annoying math formatting for you ?.
Tricks for remembering elementary matrix operations
Connecting matrices to systems of linear equations can indeed help in better understanding and remembering the properties of matrices. By visualizing how matrix operations correspond to operations on systems of equations, abstract matrix properties become…
Estimating the sparse inverse covariance matrix (precision matrix) by Graphical Lasso (with Python implementation)
Graphical Lasso, also known as GLasso, is a statistical technique used for estimating the sparse inverse covariance matrix (precision matrix) of a multivariate Gaussian distribution. Here, Sparsity means that many elements of the matrix are…
Generating missing data and evaluating missing data analysis in Python
Generating missing values Generating missing values with a given percentage of missingness for a dataframe or numpy array: Generating missing values with a given missing rate for a time series list: Calculating MSE ignoring missing…
The conditional probability of Tom finding Jerry
My all time favourite catch is “JERRY catching TOM!” ? Little Jerry is so smart, and do you know that he knows probability as well? One day, Jerry was thinking, “Hmm, every time Tom chases…
Introduction to Principal Component Analysis (PCA) and implementation in R and Python
Principal Component Analysis (PCA) is a statistical technique used for dimensionality reduction, which simplifies the complexity in high-dimensional data while retaining important infomation. The basic idea of this method is to transform a large set…
Bayes theorem in finance of a magical forest
Here, we denote by the event NOT . Example 1: Magical Investment Returns In the magical forest, gnomes invest in enchanted acorns, which sometimes turn into golden trees. A gnome named Glim invests in an…
Conditional probability
Here, we denote by the event NOT . Example 1: Squirrel Flu Testing In a forest, a group of squirrels is concerned about a new illness called “Squirrel Flu.” It’s more dangerous than the ordinary…
Tricks for remembering formulas & properties of multivariate normal distribution
First, it’s easier to understand & remember the keys properties of multivariate normal distribution by understanding the Mahalanobis distance. So, to start, recall that the Mahalanobis distance is a measure of the distance between a…
Tricks for remembering integral rules
Understanding the relationship between derivatives and antiderivatives can significantly help in remembering and applying the rules for finding antiderivatives (also known as integrals). Here’s how this relationship aids in comprehension and recall: 1. Fundamental Theorem…
Permutation
A permutation refers to the arrangement of objects in a specific order. The order of arrangement is important in permutation. A permutation let us know how many different ways a set or number of things…
Examples of combinations
Previous: Combinations definition and quizzes
Examples of Exponential distribution
The exponential distribution is commonly used to model the time between events in a Poisson process. It is defined by a single parameter, , which is the rate parameter. The probability density function (PDF) of…
Finding the derivative of a composite function with chain rule
The chain rule is a fundamental technique in calculus for finding the derivative of a composite function. Here are some examples that illustrate its use: Example 1: Simple Composite Function Let’s find the derivative of…
examples of limit computations
Here are a few more examples of limit computations involving various techniques: Example 1: Basic Limit Find the limit: Solution: This is a basic limit where we can directly substitute : Example 2: Limit Involving…
Mathematical functions
A function in mathematics and computer science is a relation between a set of inputs and a set of permissible outputs. It assigns each input exactly one output. Functions can be simple or complex, depending…
denoising via dimension reduction in python
Dimension reduction methods like Principal Component Analysis (PCA) or Singular Value Decomposition (SVD) can be used for denoising data because they work by retaining the most important features (or dimensions) that capture the majority of…
why we can & probably should use missing at random imputation methods for data that’s not missing at random?
Missing At Random (MAR) imputation methods are based on the assumption that the chance of missing data is not related to the missing data itself, but might be related to some of the observed data.…
Missing data analysis: where’s your missing piece?
Why missing data occurs can be attributed to various reasons, including human error, malfunctioning equipment, or even intentional omission. It is important to handle missing data because it can significantly impact the reliability and accuracy…
Imputation using SoftImpute in python
SoftImpute is a matrix completion algorithm in Python that allows you to fill in missing data in your dataset. This method is based on Singular Value Decomposition (SVD) and Iterative Soft Thresholding. Here’s a basic…
Multiple Imputation with Chained Equations method & Python codes
MICE (Multiple Imputation by Chained Equations) is a statistical method used for handling missing data by creating multiple imputations or “guesses” for the missing values. It works by using a set of regression models to…
K-Nearest Neighbors (KNN) imputation in sklearn
K-Nearest Neighbors (KNN) imputation is another method to handle missing data. It uses the ‘k’ closest instances (rows) to each instance that contains any missing values to fill in those values. In sklearn, you can…
A comic guide to mean/median/mode imputation & Python codes
Handling missing data is a common preprocessing task in machine learning. In scikit-learn, you can handle missing data by using imputation techniques provided by the SimpleImputer class or by employing other strategies like dropping rows/columns with missing…
SVD for dimension reduction
Singular Value Decomposition (SVD) is a powerful matrix decomposition technique that generalizes the concept of eigenvalue decomposition to non-square matrices. Eigenvalue decomposition specifically decomposes a square matrix into its constituent eigenvalues and eigenvectors. This decomposition…
test for outliers in multivariate data in Python
To test for outliers in multivariate data in Python, you can use several libraries like numpy, scipy, pandas, sklearn, etc. Here’s how you can do it: Mahalanobis distance using Scipy library The Mahalanobis distance is a statistical measure used…