Understanding Confidence Intervals: A spelled out guide to clarify misconceptions
A clear guide to confidence intervals, what they really mean, common misconceptions, how to calculate them, and why they matter in statistical...
Statistics and Math
Every Statistics and Math tutorial on Machine Learning Plus in one place: Statistics, Probability, Linear Algebra and Time Series. 59 guides with code you can read, copy and run.
Statistics 25
Ridge Regression as MAP Estimation – Supporting notes
Explore the elegant connection between Ridge Regression and MAP estimation. Step-by-step derivation showing why the L2 penalty equals a Gaussian...
Maximum A Posteriori (MAP) Estimation – Clearly Explained
Maximum A Posteriori (MAP) estimation is a Bayesian method for finding the most likely parameter values given observed data and prior knowledge...
F Statistic Formula – Explained
The F statistic is used in statistical hypothesis testing to determine if there are significant differences between group means. It is most commonly...
Correlation – Connecting the Dots, the Role of Correlation in Data Analysis
Understand intricacies of correlation with our concise guide. Explore its importance, applications, and visual insights in data analysis.
Hypothesis Testing – A Deep Dive into Hypothesis Testing, The Backbone of Statistical Inference
Explore the intricacies of hypothesis testing, a cornerstone of statistical analysis. Dive into methods, interpretations, and applications for making...
Sampling and Sampling Distributions – A Comprehensive Guide on Sampling and Sampling Distributions
Explore the fundamentals of sampling and sampling distributions in statistics. Dive deep into various sampling methods, from simple random to...
Law of Large Numbers – A Deep Dive into the World of Statistics
Understanding the Law of Large Numbers: Explore how bigger sample sizes give more accurate results and why it matters in statistics and real life.
Central Limit Theorem – A Deep Dive into Central Limit Theorem and its Significance in Statistics
Explore the Central Limit Theorem's essence in this comprehensive guide. Dive deep into its significance in statistics, understand its assumptions...
Skewness and Kurtosis – Peaks and Tails, Understanding Data Through Skewness and Kurtosis”
Unravel the secrets of data distributions with skewness and kurtosis. A concise guide to understanding data asymmetry and tail behaviors
Quantiles and Percentiles – Understanding Quantiles and Percentiles, A Deep Dive with Python Examples
Dive into quantiles vs. percentiles: their key differences, applications, and tips for data analysis. Master data segmentation in this concise guide
Measures of Dispersion – Unlocking the Variability Diving Deep into Measures of Dispersion
Dive deep into the world of statistics and measures of dispersion, from understanding its essence to its practical application using Python.
Measures of Central Tendency – A Clear Guide with Examples on Measures of Central Tendency
Uncover the essentials of Measures of Central Tendency: mean, median, and mode. A concise guide for data enthusiasts and statisticians.
Types of Data in Statistics – A Comprehensive Guide
Explore the diverse world of statistics as we break down the various types of data. From qualitative to quantitative, nominal to ratio, this...
Descriptive and Inferential Statistics – Deep Dive into Descriptive and Inferential Statistics
In statistics understanding the difference between descriptive and inferential statistics is crucial for anyone looking to make sense of data...
Partial Correlation
Partial correlation is used to find the correlation between two variables with the effect of other influencing variables being controlled.
Chi-Square test – How to test statistical significance for categorical data?
Chi-square test is used to determine whether there is a statistically significant difference between the observed frequency and the expected...
Brier Score – How to measure accuracy of probablistic predictions
Brier score is a evaluation metric that is used to check the goodness of a predicted probability score. This is very similar to the mean squared...
One Sample T Test – Clearly Explained with Examples | ML+
One sample T-Test tests if the mean of a given sample is statistically different from a known value (a hypothesized population mean). If it is found...
Standard Error in Statistics – Understanding the concept, formula and how to calculate
Standard error allows you to build a relationship between a sample statistic (computed from a smaller sample of the population and the population's...
Confidence Interval in Statistics – Formula and Mathematical Calculation
Confidence interval is a measure to quantify the uncertainty in an estimated statisic (like the mean) when the true population parameter is unknown.
T Test (Students T Test) – Understanding the math and how it works
T Test (Students T Test) is one of the foundational statistical tests. It is used to compare the means of two groups and determine if the difference...
What is P-Value? – Understanding the meaning, math and methods
The p-value is a probability score used in statistical tests to establish the significance of an observed effect. Its meaning is often unclear even...
Mahalanobis Distance – Understanding the math with examples (python)
Mahalanobis distance is an effective multivariate distance metric that measures the distance between a point and a distribution. It is an extremely...
How to implement common statistical significance tests and find the p value?
Learn the purpose, when to use and how to implement statistical significance tests (hypothesis testing) with example codes in R. How to interpret P...
Probability 13
Difference between Joint probability and Conditional probability
Joint probability and conditional probability are two concepts in probability theory that deal with the likelihood of events, but they are used in...
Probability frequency distribution – A Comprehensive guide on probability frequency distribution with Examples
Probability frequency distribution - A Comprehensive guide on probability frequency distribution with Examples
Expected Value – Understanding Expected Value in Probability and Its Real-Time Applications in Machine Learning
Expected Value - Understanding Expected Value in Probability and Its Real-Time Applications in Machine Learning
Discrete Frequency Distributions – Decoding Discrete Frequency Distributions and Probability Mass Functions (PMFs) with Real-World Scenarios
Discrete Frequency Distributions - Decoding Discrete Frequency Distributions and Probability Mass Functions (PMFs) with Real-World Scenarios
Continuous Frequency Distributions – Understanding Continuous Frequency Distributions and the Probability Density Function (PDF)
Continuous Frequency Distributions - Understanding Continuous Frequency Distributions and the Probability Density Function (PDF)
Conditional Probability – Understanding Conditional Probability with Examples
Conditional Probability - Understanding Conditional Probability with Examples
Bayes’ Theorem – Bayes’ Theorem and Bayesian Inference Unraveling the Mysteries of Probability
Bayes' Theorem - Bayes' Theorem and Bayesian Inference Unraveling the Mysteries of Probability
Odds and Odds Ratios – Understanding Odds and Odds Ratios in the World of Data Science
Odds and Odds Ratios - Understanding Odds and Odds Ratios in the World of Data Science
Mutually Exclusive Events – Understanding Mutually Exclusive Events in Probability with Examples
Mutually Exclusive Events - Understanding Mutually Exclusive Events in Probability
Joint Probability – A Comprehensive Guide with Examples
Joint Probability - A Comprehensive Guide with Examples
Introduction to Probability – A Glimpse into Chance and Statistics
Introduction to Probability - A Glimpse into Chance and Statistic
Independent and Dependent Events – Understanding Independent and Dependent Events in Probability
Independent and Dependent Events - Understanding Independent and Dependent Events in Probability
Gentle Introduction to Markov Chain
Markov Chains are probabilistic graphical models of dynamic processes: they describe how the state of a process changes with time. Learn what a...
Linear Algebra 14
Vectors Linear Algebra – A Comprehensive Guide on Basis, Orthogonal, and Orthonormal Vectors with examples
Vectors Linear Algebra - A Comprehensive Guide on Basis, Orthogonal, and Orthonormal Vectors with examples
Vectors – Vector Transposition, Norms, and Unit Vectors: A Comprehensive Guide
Vectors - Vector Transposition, Norms, and Unit Vectors: A Comprehensive Guide
Types of Tensors – A Comprehensive Guide in Exploring the Different Types of Tensors
A Comprehensive Guide in Exploring the Different Types of Tensors
System of Equations – Understanding Linear Algebra System of Equations and Plotting
Understanding Linear Algebra System of Equations and Plotting
Singular Value Decomposition – A Comprehensive guide on Singular Value Decomposition
Singular Value Decomposition - A Comprehensive guide on Singular Value Decomposition
Scalars – Understanding Scalars (Zero-Order Tensors)
Understand scalars, the zero-order tensors of linear algebra: what they are, why they matter, how they interact with vectors and matrices, and how...
Principal Component Analysis – A Deep Dive into Principal Component Analysis and its Linear Algebra Foundations
A Deep Dive into Principal Component Analysis and its Linear Algebra Foundations
Orthogonal Matrix – Detailed Understanding on Orthogonal and Orthonormal Second Order Matrices
Orthogonal Matrix - Detailed Understanding on Orthogonal and Orthonormal Second Order Matrices
Matrix Types – Understanding Second Order Matrix Types with Examples
Matrix Types - Understanding Second Order Matrix Types with Examples
Matrix Operations – A Comprehensive Guide on Matrix Tensors and its operations with Examples
Matrix Operations - A Comprehensive Guide on Matrix Tensors and its operations with Examples
Linear Regression Algorithm – Applications and Concepts of Linear Algebra Using the Linear Regression Algorithm
Applications and Concepts of Linear Algebra Using the Linear Regression Algorithm
Eigenvectors and Eigenvalues – Detailed Explanation on Eigenvectors and Eigenvalues
Eigenvectors and Eigenvalues - Detailed Explanation on Eigenvectors and Eigenvalues
Affine Transformation – A Comprehensive Guide on Affine Transformation in Linear Algebra
Affine Transformation - A Comprehensive Guide on Affine Transformation in Linear Algebra
Introduction to Linear Algebra for Data Science
Introduction to Linear Algebra for Data Scientist - Dive into the Core Concepts with Examples & Illustrations
Time Series 7
Granger Causality Test in Python
Granger Causality test is a statistical test that is used to determine if a given time series and it's lags is helpful in explaining the value of...
Granger Causality Test
Granger causality test is a statistical test that is used to determine of a particular time series is helpful in forecasting another series
ARIMA Model – Complete Guide to Time Series Forecasting in Python
Using ARIMA model, you can forecast a time series using the series past values. In this post, we build an optimal ARIMA model from scratch and extend...
KPSS Test for Stationarity
The KPSS test checks whether a series is stationary around a deterministic trend. Like the ADF test it is widely used, but it differs in function and...
Augmented Dickey Fuller Test (ADF Test) – Must Read Guide
Augmented Dickey Fuller test (ADF Test) is a common statistical test used to test whether a given Time series is stationary or not. It is one of the...
Vector Autoregression (VAR) – Comprehensive Guide with Examples in Python
Learn Vector Autoregression (VAR) for multivariate time series forecasting. Covers the intuition, math, model training, diagnostics, and forecasting...
Time Series Analysis in Python – A Comprehensive Guide with Examples
Time series is a sequence of observations recorded at regular time intervals. This guide walks you through the process of analysing the...