Articles

Point Estimation 🇺🇸

September 13, 2026
Category: Statistics Notes

A parameter is an unknown feature of a population or statistical model, such as a mean $\mu$, variance $\sigma^2$, probability $p$, or regression coefficient $\beta$. A point estimator is a rule or statistic computed from sample data and used to estimate that parameter...

Axioms of Probability 🇺🇸

September 13, 2026
Category: Statistics Notes

Probability theory is built on a small set of principles, called axioms, that define how probability measures behave. These axioms, formalized by the Russian mathematician Andrey Kolmogorov, provide the foundation for the rules used throughout probability theory...

Geometric Probability 🇺🇸

September 13, 2026
Category: Statistics Notes

Geometric probability is a fascinating branch of probability theory where outcomes are associated with geometric figures and their measures—such as lengths, areas, and volumes—rather than discrete numerical outcomes. It often deals with continuous random variables and employs integral calculus to ca...

Total Probability 🇺🇸

September 13, 2026
Category: Statistics Notes

The law of total probability allows for the computation of the probability of an event A based on a set of mutually exclusive and exhaustive events. It's particularly useful when the overall sample space is divided into several distinct scenarios, or partitions, that cover all possible outcomes. The...

Bayes Theorem 🇺🇸

September 13, 2026
Category: Statistics Notes

Bayes' theorem provides a way to update the probability of an event when new evidence becomes available. It connects conditional probabilities and allows us to revise an initial probability, or prior, in light of additional information...

Conditional Probability 🇺🇸

September 13, 2026
Category: Statistics Notes

Conditional Probability is the likelihood of an event occurring given that another event has already occurred. It is denoted as $P(A|B)$, representing the probability of event $A$ happening, assuming event $B$ has already taken place. This concept is crucial in understanding dependent events in prob...

Introduction to Probability 🇺🇸

September 13, 2026
Category: Statistics Notes

Probability theory offers a structured approach to assessing the probability of events, allowing for logical and systematic reasoning about their likelihood...

Probability Tree 🇺🇸

September 13, 2026
Category: Statistics Notes

Probability trees are a visual representation of all possible outcomes of a probabilistic experiment and the paths leading to these outcomes. They are especially helpful in understanding sequences of events, particularly when these events are conditional on previous outcomes...

Descriptive Statistics 🇺🇸

September 13, 2026
Category: Statistics Notes

Descriptive statistics summarize the main characteristics of a dataset or sample. They help us understand data by describing its frequency, center, spread, and overall distribution...

Introduction to Statistics 🇺🇸

September 13, 2026
Category: Statistics Notes

Statistics is the science of learning from data. It provides methods for collecting, summarizing, analyzing, and interpreting observations so that we can describe patterns, quantify uncertainty, and make informed decisions...

F Distribution 🇺🇸

September 13, 2026
Category: Statistics Notes

The F-distribution, also known as the Fisher-Snedecor distribution, is a continuous probability distribution that arises in hypothesis testing when comparing the variances of two normally distributed populations. The F-distribution is denoted as $X \sim F(d_1, d_2)$, where $d_1$ and $d_2$ are the de...

Student T Distribution 🇺🇸

September 13, 2026
Category: Statistics Notes

Student's t-distribution is a continuous probability distribution that arises when a normally distributed quantity is standardized using an estimated standard deviation rather than a known population standard deviation. It has heavier tails than the normal distribution and approaches the normal dist...

Sampling Distributions 🇺🇸

September 13, 2026
Category: Statistics Notes

A statistic is computed from a sample, but before the sample is observed the statistic is itself a random variable. Its probability distribution over hypothetical repeated samples is called its sampling distribution...

Chi Square Distribution 🇺🇸

September 13, 2026
Category: Statistics Notes

A chi-square distribution is a continuous probability distribution of the sum of the squares of k independent standard normal random variables. The chi-square distribution is denoted as $X \sim \chi^2(k)$, where k is the number of degrees of freedom...

Central Limit Theorem 🇺🇸

September 13, 2026
Category: Statistics Notes

The Central Limit Theorem (CLT) is a fundamental result in statistics. It explains why the distribution of sample means often approaches a normal distribution as the sample size increases, even when the population itself is not normally distributed...

Standard Error and Lln 🇺🇸

September 13, 2026
Category: Statistics Notes

Expected Value (E), also known as the mean, is the long-run average of a random variable, representing the value we anticipate on average from repeated random draws from a population...

Bayesian vs Frequentist 🇺🇸

September 13, 2026
Category: Statistics Notes

Bayesian and frequentist statistics are two major approaches to statistical inference. Both use sample data to learn about an underlying population or data-generating process, but they differ in how they interpret probability, represent uncertainty, and draw conclusions about unknown parameters...

Multiple Regression 🇺🇸

September 13, 2026
Category: Statistics Notes

Multiple linear regression is a statistical technique used to model the relationship between a single dependent variable and two or more independent variables. It extends the concept of simple linear regression by incorporating multiple predictors to explain the variability in the dependent variable...

Logistic Regression 🇺🇸

September 13, 2026
Category: Statistics Notes

Logistic regression is a statistical method used for modeling the probability of a binary outcome based on one or more predictor variables. It is widely used in various fields such as medicine, social sciences, and machine learning for classification problems where the dependent variable is dichotom...

Simple Linear Regression 🇺🇸

September 13, 2026
Category: Statistics Notes

Simple linear regression is a statistical method used to model the relationship between a single dependent variable and one independent variable. It aims to find the best-fitting straight line through the data points, which can be used to predict the dependent variable based on the independent varia...

Analysis of Variance 🇺🇸

September 13, 2026
Category: Statistics Notes

Does peer assessment enhance student learning...

Statistical Moments 🇺🇸

September 13, 2026
Category: Statistics Notes

In both statistics and mechanics the word moment measures how much "leverage" the values of a quantity exert about a chosen reference point. In statistics the leverage is exerted by probability mass, in mechanics by physical mass, but the mathematics is identical: take a distance from the reference ...

Normal Curve and z Score 🇺🇸

September 13, 2026
Category: Statistics Notes

A normal distribution (often referred to as the normal curve or Gaussian distribution) is a continuous probability distribution that is symmetric about the mean, where most of the observations cluster around the central peak and taper off symmetrically towards both ends. Many real-world datasets suc...

Introduction to Distributions 🇺🇸

September 13, 2026
Category: Statistics Notes

A distribution is a function that describes the probability of a random variable. It helps to understand the underlying patterns and characteristics of a dataset. Distributions are widely used in statistics, data analysis, and machine learning for tasks such as hypothesis testing, confidence interva...

Validation and Model Selection 🇺🇸

September 13, 2026
Category: Statistics Notes

A fitted model is optimized using observed data. Model assessment asks a different question: how well will the modeling procedure perform on new data generated under comparable conditions...

Metrics 🇺🇸

September 13, 2026
Category: Statistics Notes

Evaluation metrics are essential tools for assessing the performance of statistical and machine learning models. They provide quantitative measures that help us understand how well a model is performing and where improvements can be made. In both classification and regression tasks, selecting approp...

Resampling 🇺🇸

September 13, 2026
Category: Statistics Notes

Statistical inference often involves estimating population parameters and constructing confidence intervals based on sample data. Traditional methods rely on assumptions about the sampling distribution of estimators, such as normality and known standard errors. However, these assumptions may not hol...

Geostatistics 🇺🇸

September 13, 2026
Category: Statistics Notes

Geostatistics is used when observations are tied to locations and nearby values may be more similar than distant values...

Spatial Weights 🇺🇸

September 13, 2026
Category: Statistics Notes

A spatial weights matrix turns a qualitative statement such as...

Point Processes 🇺🇸

September 13, 2026
Category: Statistics Notes

A spatial point process is used when the observed data are the event locations themselves...

Spatial Autocorrelation 🇺🇸

September 13, 2026
Category: Statistics Notes

Spatial autocorrelation asks whether values attached to locations show a systematic spatial pattern...

Kriging 🇺🇸

September 13, 2026
Category: Statistics Notes

Kriging is a method for predicting a spatial variable at unsampled locations using a model of spatial dependence...

Spatial Data and Distance 🇺🇸

September 13, 2026
Category: Statistics Notes

Spatial analysis begins before any spatial statistic is calculated...

Spatial Regression 🇺🇸

September 13, 2026
Category: Statistics Notes

Regression models the mean relationship between an outcome and its predictors...

Spatial Validation 🇺🇸

September 13, 2026
Category: Statistics Notes

Spatial model performance depends not only on which observations are held out, but also on where those observations are located relative to the training data...