bayesian-probability

Angela Carollo from the Laboratory of Fertility and Well-Being at the Max Planck Institute for Demographic Research (MPIDR), successfully defended her doctoral thesis, “Statistical Analysis of Time-to-Event Data with Multiple Time Scales“, at Leiden University. In her thesis she introduces a statistical model that addresses an important gap in the literature on statistical models for time-to-even…

Researchers at Binghamton University have applied a 70-year-old theory of information to the viral word game Wordle, revealing how a carefully chosen first guess can dramatically improve a player’s chances of solving the puzzle. The post Scientists Use Math to Solve Viral Word Game ‘Wordle’ with 99% Success Rate appeared first on Sci.News: Breaking Science News .

In probability theory an event of probability 1 is said to happen almost surely. That is, A statement about outcomes is said to be true almost surely, or with probability 1, if and . Where is a point in the sample space , a -algebra? on , and a probability measure on , . (Williams 1991) In measure theory, such subsets are also known as full subsets. Their complements are known as null subsets or …

There are two prisoners and a warden. The warder offers the following challenge to the prisoners: The two prisoners will be put in separate rooms. Then, each prisoner will be given either a white or ...

Every day, millions of people play Wordle, the popular New York Times game that challenges users to guess a secret five-letter word. Using information theory, a team of researchers at Binghamton University, State University of New York, has developed a method to solve the game with a 99% success rate.

Basically the title, I am looking for interesting applications of Egoroff's theorem. Recall that if $(X,\mathcal{M},\mu)$ is a finite measure space and $(f_n)$ is a sequence of measurable functions ...

Some mathematicians have predicted when humanity’s downfall might occur—though the circumstances are unspecified

A single model hands you a single answer and no sense of how much it hinges on the dozens of choices buried inside it. The post I Built 11 Models to Predict the 2026 World Cup. They Crown Four Different Champions. appeared first on Towards Data Science .

Let $X$ be a random variable in $\mathbb{R}^d$ with law $\mu$. We denote by $\mathcal{P}(\mathbb{R}^d)$ the set of all Borel probability measures on $\mathbb{R}^d$. Assume that $\mu \in ...

Let's practice data science thinking through a probability problem The post Solving the 3Blue1Brown String Probability Problem (Without AI) appeared first on Towards Data Science .

Introduction Concepts of correlation and regression may be applied not only to ordinary one-dimensional variates but also to variates of two or more dimensions. This is the first sentence from the paper “Relations Between Two Sets of Variates” (Hotelling 1936) by statistician and economist Harold Hotelling. This paper introduced Canonical Correlation Analysis (CCA). In modern terminology, “CCA is…

Below is an open problem, an approachable problem, one perhaps you will be the one to solve! We send a bit over a noisy grid, starting from the origin and propagating out as a wave. Can we recover the original bit when looking at just the wavefront? This is easy to solve for 1D, mostly solved in 2D, and still open in 3D and above. Here is the lecture that introduced the problem to me, as well as …

There are a number of approaches to apply category theory to probability and related fields, such as statistics, information theory and dynamical systems. On one hand, one can study the existing structures in traditional probability theory (such as probability spaces, integration, and so on) using a categorical lens. For instance, the Giry monad models the formation of spaces of probability measu…

A stochastic process describes a dynamical system evolving over a linearly ordered set (“time”), typically taken to be the (positive) integers or real numbers, whose dynamical laws of motion are morphisms in the Kleisli category of the Giry monad (or any other probability monad). By working in the larger category of algebras of that monad, a characterization of a stochastic processes can be model…

Here’s a probability puzzle from a TED-Ed video called Can you solve the frog riddle? by Derek Abbott. It came up recently in this Reddit thread: You’re stranded in a rainforest after accidentally eating a poisonous mushroom. To survive the poison, you need to lick a certain species of frog. Only female frogs produce the antidote. Male and female frogs occur in equal numbers and look identical, b…

Two players start 1 meter away from a target. They simultaneously begin moving towards the target at a same constant speed. If the left player shoots when he is X meters from the target, his shot hit with a probability 1-X... Read more

Question: Let $K$ be a compact Hausdorff space. Is there always a strictly positive Borel probability measure? Thoughts: If $K$ is metrizable it contains a dense countable subset, so the sum over all ...

How large would the following number be? The minimum number of digits of $b^{1/b}$ in base $b$ that are necessary for each number from $0$ to $b$ to occur the same number of times. For example in base ...

Nature, Published online: 01 June 2026; doi:10.1038/d41586-026-00821-4 An experiment with 2,520 participants backs Richard Feynman’s answer to every diner’s dilemma: do I want to try something new?

Physicist Richard Feynman turned a lunch dilemma into a math problem. Researchers finally cracked his notes and found people approximate his solution on their own.