How to Write a Proof in a paper
Reviewers are not required to read supplementary materials, but many do. Therefore, making your proof easy to read is important. General Guidelines: Example: Theorem 1: Let and be real numbers. If , then . The…
Example of using derivatives to find optimal drug dosage
Dosage Optimization: Pharmacologists use derivatives to find the optimal drug dosage that maximizes therapeutic effects while minimizing side effects. The concentration of the drug in the bloodstream is modeled as a function of time, and…
Example of using derivatives to optimize the material cost
Optimization of Material Usage: Engineers use derivatives to minimize the cost of materials while maintaining structural integrity. For example, determining the optimal dimensions of a container to minimize surface area for a given volume. Example:…
Examples of using the derivative tests for finding maximum/minimum
Problem 2: Find the minimum distance from the point (2, 3) to the line . Solution: More examples:
Combining datasets to increase sample size
Detailed information can be found in Combining datasets to improve model fitting or its presentation slide. Summary: The key points of the paper titled “Combining Datasets to Improve Model Fitting” are as follows: Problem and…
Calculus can hurt
Supplementary contents for section “Calculus can hurt” in the KSML app: Limit: Derivatives Integral
Expectation Maximization (EM) & implementation
Expectation Maximization (EM) is an iterative algorithm used for finding maximum likelihood estimates of parameters in statistical models, particularly when the model involves latent variables (variables that are not directly observed). The algorithm is commonly…
A comic guide to denoising noisy data
Handling noisy data is a crucial step in data preprocessing and analysis. In general, here are some common approaches to manage noisy data: 1. Data Cleaning 2. Data Transformation 3. Statistical Techniques 4. Machine Learning…
Writing the paragraph detailing the contribution of your paper
After you introduce the motivation of your work, it’s time to write a paragraph detailing the contribution of your work for a paper. In that paragraph, consider the following structure and key elements: Significance and…
A comical guide to Missing Not At Random (MNAR)
Recall that Missing Not At Random (MNAR) is a type of missing data mechanism where the probability of missingness is related to the unobserved data itself. Here are some more examples of MNAR: In each…
What’s Missing at Random (MAR)?
Missing at Random (MAR) is a statistical term indicating that the likelihood of data being missing is related to some of the observed data but not to the missing data itself. This means that the…
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…