Everything about Bernoulli process
Random process of binary (boolean) random variables
In probability and statistics, a Bernoulli process is a finite or infinite sequence of binary random variables, so it is a discrete-time stochastic process that takes only two values, canonically 0 and 1. The component Bernoulli variables Xi are identically distributed and independent. Prosaically, a Bernoulli process is a repeated coin flipping, possibly with an unfair coin. Every variable Xi in the sequence is associated with a Bernoulli trial or experiment. They all have the same Bernoulli distribution. Much of what can be said about the Bernoulli process can also be generalized to more than two outcomes ; this generalization is known as the Bernoulli scheme. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Bernoulli processA 5-minute orientation
- Skim a recent paper: Student’s t-Based Robust Poisson Multi-Bernoulli Mixture Filter under Heavy-Tailed Process and Measurement NoisesInfluential work since 2022
- Pick up a classic book: Resolving Markov chains onto Bernoulli shifts via positive polynomialsThe most-reprinted book on the subject
- Read the landmark paper: Inference for a Bernoulli Process (a Bayesian View)Cited 110 times
- Go sideways: De Finetti's theoremA closely related topic
- Go sideways: Entropy (information theory)A closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🏆 Landmark papers (most cited)
Inference for a Bernoulli Process (a Bayesian View)
Asymptotics and Criticality for a Correlated Bernoulli Process
Markov modulated Bernoulli process
On the rate of Poisson process approximation to a Bernoulli process
Bayesian Interpretation of Frequentist Procedures for a Bernoulli Process
Methodology for traffic modeling using two-state Markov-modulated Bernoulli process
A relation between moments of Liu process and Bernoulli numbers
Generalized Bernoulli process with long-range dependence and fractional binomial distribution
🆕 Influential since 2022
Student’s t-Based Robust Poisson Multi-Bernoulli Mixture Filter under Heavy-Tailed Process and Measurement Noises
A New Framework for Evaluating Random Early Detection Using Markov Modulate Bernoulli Process Stationary Distribution
Monitoring and diagnosis of complex production process based on free energy of Gaussian–Bernoulli restricted Boltzmann machine
Generalized Bernoulli process and fractional Poisson process
On relativistic hydrodynamics: bernoulli process equations
📚 Books worth reading
Resolving Markov chains onto Bernoulli shifts via positive polynomialsBrian Marcus, Selim Tuncel · 2001- 📕Densities and dependence for point processesMarie M. Franzosa · 1988
- 📕Resolving Markov chains onto Bernoulli shifts via positive polynomialsBrian Marcus · 2001
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
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