Firstly, earthquake sequences are point processes.
Gaussian process
Gaussian distribution or normal distribution
is the mean and is the standard deviation - The moment of a probability density function
the central limit theorem
Under some not-too-strict mathematical conditions, the theorem states that the average of a large number of random variables tends to follow a Gaussian distribution
It is bad practice to estimate qualities of a population using individuals or very small samples.
Bayes theorem
- How often A happens given that B happens?
Markov chain and Markov process
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Hidden Markov Model A statistical Markov model in which the system being modeled is assumed to be a Markov process with unobservable (i.e. hidden) states.
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Particle filter or “sequential Monte Carlo” is used to solve HMM problems.
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Renewal process
- This make sense if earthquake repeats on the same segment according to elastic rebound and never interact or break into other segments.
- The point process analog of Markov Chains.
Declustering
- @Mizrahi2021
Statistical terms
- Independent and identically distributed : iid
See also ETAS