The hottest Probability Substack posts right now

And their main takeaways

Against Learning From Dramatic Events

Astral Codex Ten • 19340 implied HN points • 16 Jan 24

🚌 Education Epistemology Probability

Updating beliefs based on single dramatic events may not be very impactful in the long run.
Predictions can be more valuable than reacting strongly to individual events.
Coordination and response to dramatic events are important, but fundamental beliefs should not change drastically.

There are Complex-Number One-Norm Square-Root of Probability Amplitudes of 0.006 in Which Sam Bankman-Fried Is Happy

Brad DeLong's Grasping Reality • 676 implied HN points • 05 Oct 23

💰 Finance Investing Risk management Probability Psychology Trading

Amplitudes in quantum-mechanical superposition relate to philosophy-of-probability vs. psychology.
Understanding the Kelly Criterion for betting based on win-loss odds and maximizing returns.
Traders use the Kelly Criterion for survival, making positive-value bets, and psychological factors.

Numeracy Injection

moontower: a stoner dad explains options trading to his kids • 98 implied HN points • 24 Jan 24

🚌 Education Math Algebra Probability Learning Teaching

Monty Hall problem can be explained using tree thinking.
Knowing X^2 helps quickly find the product of numbers nearby like (X-1)(X+1).
Using clever polling techniques can help infer true response rates.

Going for Broke

The Better Letter • 275 implied HN points • 06 Oct 23

💰 Finance Investing Behavioral Finance Risk management Financial Markets Probability

In a coin-flipping experiment, even financially savvy individuals struggled with optimal betting strategies.
The world is far more random than we realize, affecting markets and investments unpredictably.
Probabilistic strategies can help in decision-making, especially when human biases lead to suboptimal choices.

Law of Large Numbers and the Gamblers Fallacy[Math Mondays]

Technology Made Simple • 179 implied HN points • 11 Sep 23

🚌 Education Math Probability Theory Computer Science Technology

The Law of Large Numbers states that as the number of trials increase, the average of results will get closer to the expected value.
This law is crucial in scientific fields, allowing predictions on chaotic events, leading to industries like gambling and insurance.
Misunderstanding the Law of Large Numbers can lead to the Gambler's Fallacy, as it deals with the convergence of infinitely many experiments, not individual ones.

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A model of models of probability

Bram’s Thoughts • 78 implied HN points • 23 Nov 23

🔬 Science Probability Models Human behavior

People generally have a simplified internal model of probability with five main categories.
People tend to struggle with accurately gauging differences in expected values within the 40-60% range.
Individuals often display overconfidence in their predictions for probable events and can become overly upset when these predictions fail.

Math Problems

The Better Letter • 157 implied HN points • 17 Mar 23

🔬 Science Mathematics Probability Sports Psychology Economics

Unlikely events happen more often than we realize, influencing outcomes in sports, investments, and life.
Probability plays a significant role in determining outcomes, such as in coin tosses, NCAA brackets, and market predictions.
Randomness, noise, and unpredictability are intrinsic to life, affecting decision-making and the way we perceive events.

Tanks for the memories

Logging the World • 179 implied HN points • 11 Dec 22

🔬 Science Statistics Probability Military History Cybersecurity Data Analysis

In a raffle with a large number of tickets, the biggest number drawn out starts to show some structure as more tickets are selected.
By looking at the maximum value drawn in a raffle, one can estimate the total number of tickets, a concept applied in statistics like the German tank problem.
Sequential numbering schemes can reveal interesting insights, as seen in situations like the Skripal poisonings and Novak Djokovic's COVID test, highlighting the importance of careful numbering practices.

What is Bayesian Statistics? The Beginner Math Guide (Part One)

The Software & Data Spectrum • 78 implied HN points • 13 Apr 23

🔬 Science Statistics Probability Logic Combinatorics

Bayesian Statistics is used in various fields like Machine Learning, Engineering, Data Science, and more.
Bayesian Thinking involves observing data, holding prior beliefs, forming hypotheses, gathering evidence, and comparing hypotheses.
Probability is a way to measure belief strength, and calculating probabilities involves counting outcomes and using ratios of beliefs.

Probability Distributions 101

Olshansky's Newsletter • 67 implied HN points • 20 Feb 23

🔬 Science Mathematics Statistics Probability

Probability is about the likelihood of events happening.
Probability distributions are functions describing random events over a sample space.
Key concepts include random variables, probability mass function, probability density function, cumulative distribution function, Gaussian distribution, and Bernoulli distribution.

The Maximum Likelihood Estimation

The Palindrome • 4 implied HN points • 02 Jan 24

🔬 Science Machine Learning Probability Optimization Data Modeling

Optimizing the loss function by going against its gradient is a key concept in machine learning.
Efficiently computing the gradient and performing matrix operations are foundational for deep learning.
The maximum likelihood estimation is a key statistical method used to estimate parameters in probabilistic models.

Logistic regression

The Palindrome • 3 implied HN points • 17 Jan 24

🔬 Science Machine Learning Algorithms Probability

Classification problems are prevalent and play a significant role in machine learning.
Logistic regression is a binary classification algorithm that estimates probabilities.
The logistic regression model involves a sigmoid function to predict outcomes based on coefficients.

Statistics for the Working Mathematician

From AI to ZI • 19 implied HN points • 25 May 23

🚌 Education Statistics Mathematics Probability

Probability and statistics differ in given information and desired outcomes
Statistical analysis involves hypothesis testing, parameter estimation, and confidence intervals
Bayesian statistics combines prior beliefs with evidence to reach posterior probabilities

The most important assumption in statistics- IID [Math Mondays]

Technology Made Simple • 39 implied HN points • 01 Aug 22

🔬 Science Statistics Probability Machine Learning

The most important assumption in statistics is IID, which stands for Independently and Identically Distributed
IID assumption is crucial for statistical analysis - it helps in making accurate deductions and avoiding mistakes, like the gambler's fallacy
Understanding IID involves recognizing independent and identical distributions in data samples, which are essential for various statistical techniques

How large that number in the Law of Large Numbers is?

The Palindrome • 4 implied HN points • 04 Sep 23

🔬 Science Probability

The term 'large' is relative and depends on what you are comparing it to.
The Law of Large Numbers states that sample averages converge to the true expected value as the number of samples increases.
The speed of convergence in the Law of Large Numbers depends on the variance of the sample, with higher variance leading to slower convergence.

Do half of AI researchers believe that there's a 10% chance AI will kill us all?

AI: A Guide for Thinking Humans • 4 HN points • 23 Apr 23

🕹 Technology AI Research Ethics Survey Probability

Half of AI researchers do not necessarily believe there's a 10% chance AI will kill us all.
The claim is based on a survey with 162 respondents from specific conferences.
Possible issues include vague question, small sample size, response bias, and level of expertise of the respondents.

Machine learning is not just statistics

The Palindrome • 2 implied HN points • 09 Aug 23

🔬 Science Machine Learning Statistics Probability Mathematics Data science

Machine learning heavily utilizes statistics, but it is not just applied statistics.
Probability enables reasoning about uncertainty, while statistics quantifies and explains it.
Probability theory provides tools to deal with missing information and formulate models with likelihood measures.

What is Bayesian Statistics? The Beginner Math Guide (Part Three)

The Software & Data Spectrum • 1 HN point • 20 Apr 23

🔬 Science Statistics Mathematics Probability Data Analysis Experiments

Normal distribution helps determine the probability of an estimate compared to others.
Use probability density function to estimate parameters like conversion rates.
Bayesian A/B testing uses Monte Carlo simulation to compare different variants.

Bayesian A/B Testing

Boris Again • 1 HN point • 18 Apr 23

🔬 Science Statistics Data Analysis Inference Probability

A/B testing compares two treatments to measure impact.
Frequentist A/B testing involves hypothesis formulation, experiment design, and statistical testing.
Bayesian A/B testing incorporates prior beliefs to estimate probabilities directly.

Entropic emanations

Simplicity is SOTA • 1 HN point • 13 Mar 23

🔬 Science Statistics Machine Learning Probability

Log loss is a proper scoring function that incentivizes honest prediction and has intrinsic meaning.
Cross entropy in multiclass problems is based on log loss, which compares predictions to outcomes on a log scale.
Modifying cross entropy to consider negative classes in loss functions may impact gradient calculation simplicity and model fitting.

Basics of Probability and Stats - The inequalities that lead to LLN and CLT - PS01

Arkid’s Newsletter • 0 implied HN points • 09 May 23

🚌 Education Mathematics Statistics Machine Learning Artificial Intelligence Probability

The Markov Inequality helps predict unlikely extreme events based on distribution info
The Chebyshev Inequality shows that a small variance means a random variable is close to the mean
The Weak Law of Large Numbers and Central Limit Theorem are essential for understanding probability and statistics in ML

Simple Kelly betting in prediction markets

Unstabler Ontology • 0 implied HN points • 06 Mar 24

💰 Finance Betting Prediction Markets Probability

Kelly betting is a strategy in gambling that maximizes money growth by betting a fixed fraction of one's income each round.
In prediction markets, the optimal Kelly betting strategy involves spending a portion of money on contracts based on the subjective probabilities of outcomes.
The simple Kelly betting rule can be equivalent to the original Kelly rule in cases with two outcomes, providing a more intuitive understanding of betting strategies.