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Probability Theory

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Model Perspective
Model Perspective
Aug 16, 2023 · Fundamentals

Understanding the Beta Distribution: A Key to Bayesian Inference

This article explores the Beta distribution’s role in Bayesian statistics, detailing its definition, properties, conjugate prior relationship, and practical examples such as coin flips and bus arrivals, illustrating how it simplifies probability updates and supports intuitive belief revision.

Bayesian inferenceProbability Theorybeta distribution
0 likes · 10 min read
Understanding the Beta Distribution: A Key to Bayesian Inference
Model Perspective
Model Perspective
Nov 9, 2022 · Fundamentals

Why Monte Carlo Converges Slowly: Insights from the Law of Large Numbers and Central Limit Theorem

This article explains how the law of large numbers and the central limit theorem underpin Monte Carlo methods, revealing why their convergence rate is low, how significance and confidence levels are defined, and why variance reduction is crucial for efficient simulations.

Law of Large NumbersProbability TheoryVariance Reduction
0 likes · 5 min read
Why Monte Carlo Converges Slowly: Insights from the Law of Large Numbers and Central Limit Theorem
Model Perspective
Model Perspective
Sep 28, 2022 · Fundamentals

Understanding the Beta Distribution: PDF, CDF, and Real‑World Applications

This article explains the Beta distribution’s definition, its probability density and cumulative distribution functions, key statistical properties such as mode, mean, variance, skewness and kurtosis, and illustrates its practical use in modeling relative humidity in atmospheric studies.

Probability Theorybeta distributioncumulative distribution function
0 likes · 4 min read
Understanding the Beta Distribution: PDF, CDF, and Real‑World Applications
Model Perspective
Model Perspective
Sep 27, 2022 · Fundamentals

Understanding the Gamma and Inverse Gamma Distributions: Definitions, Properties, and Connections

This article explains the Gamma distribution and its inverse, detailing their probability density functions, expectations, variances, special cases, and how the Gamma distribution relates to Poisson and exponential distributions, providing concise mathematical insights and reference sources.

Gamma distributionProbability Theoryinverse Gamma
0 likes · 2 min read
Understanding the Gamma and Inverse Gamma Distributions: Definitions, Properties, and Connections
Model Perspective
Model Perspective
Sep 8, 2022 · Fundamentals

Why Monte Carlo Converges Slowly: Law of Large Numbers & Central Limit Theorem Explained

This article explains how the law of large numbers and the central limit theorem underpin Monte Carlo methods, illustrating their convergence rate, the role of variance reduction, and the practical steps for applying Monte Carlo to both stochastic and deterministic problems.

Law of Large NumbersProbability TheoryVariance Reduction
0 likes · 4 min read
Why Monte Carlo Converges Slowly: Law of Large Numbers & Central Limit Theorem Explained
Architects' Tech Alliance
Architects' Tech Alliance
Feb 17, 2019 · Operations

Modeling SSD Garbage Collection as a Gambler's Ruin Problem: Probabilistic Analysis and Control Strategies

By drawing analogies between casino gambling and SSD garbage collection, the article uses probability theory, Brownian motion, and stochastic processes to model victim block selection, resource depletion, and I/O bandwidth fluctuations, proposing control strategies that balance performance stability and resource safety.

Probability TheorySSDStochastic Processes
0 likes · 21 min read
Modeling SSD Garbage Collection as a Gambler's Ruin Problem: Probabilistic Analysis and Control Strategies