Abstract
We study the following problem of sequential analysis: we observe a Brownian motion which has a zero drift initially; at a an unknown and random time θ, known as change-point, the Brownian motion takes a non-zero drift. Since the Brownian motion is observed in real time, we want to estimate θ optimally by means of a stopping time which minimizes a total miss criterion, namely the linear combination between the expected advance in detecting θ wrongly and expected delay of a late detection. This problem is solved in the Bayesian formulation, where θ is assumed to follow an exponential prior distribution.
| Original language | English |
|---|---|
| Title of host publication | Book of the Short Papers - SIS 2022 |
| Pages | 1197-1202 |
| Number of pages | 6 |
| Publication status | Published - 2022 |
| Event | SIS 2022, 51st Scientific Meeting of the Italian Statistical Society - Caserta Duration: 22 Jun 2022 → 24 Jun 2022 |
Conference
| Conference | SIS 2022, 51st Scientific Meeting of the Italian Statistical Society |
|---|---|
| City | Caserta |
| Period | 22/6/22 → 24/6/22 |
Keywords
- Brownian motion
- change-point/disorder problem
- optimal stopping
- sequential analysis
- total miss criterion
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