## Bayesian Analysis

### Bayesian Multiple Changepoint Detection for Stochastic Models in Continuous Time

Lu Shaochuan

#### Abstract

A multiple changepoint model in continuous time is formulated as a continuous-time hidden Markov model, defined on a countable infinite state space. The new formulation of the multiple changepoint model allows the model complexities, i.e. the number of changepoints, to accrue unboundedly upon the arrivals of new data. Inference on the number of changepoints and their locations is based on a collapsed Gibbs sampler. We suggest a new version of forward-filtering backward-sampling (FFBS) algorithm in continuous time for simulating the full trajectory of the latent Markov chain, i.e. the changepoints. The FFBS algorithm is based on a randomized time-discretization for the latent Markov chain through uniformization schemes, combined with a discrete-time version of FFBS algorithm. It is shown that, desirably, both the computational cost and the memory cost of the FFBS algorithm are only quadratic to the number of changepoints. The new formulation of the multiple changepoint models allows varying scale of run lengths of changepoints to be characterized. We demonstrate the methods through simulations and a real data example for earthquakes.

#### Article information

Source
Bayesian Anal., Advance publication (2020), 24 pages.

Dates
First available in Project Euclid: 16 June 2020

https://projecteuclid.org/euclid.ba/1592272905

Digital Object Identifier
doi:10.1214/20-BA1218

#### Citation

Shaochuan, Lu. Bayesian Multiple Changepoint Detection for Stochastic Models in Continuous Time. Bayesian Anal., advance publication, 16 June 2020. doi:10.1214/20-BA1218. https://projecteuclid.org/euclid.ba/1592272905

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