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.
Buonaguidi, B., Bayesian change-point detection for a Brownian motion with a total miss criterion, Contributed paper, in Book of the Short Papers - SIS 2022, (Caserta, 22-24 June 2022), Pearson, Milano 2022: 1197-1202 [https://hdl.handle.net/10807/228210]
Bayesian change-point detection for a Brownian motion with a total miss criterion
Buonaguidi, Bruno
Primo
2022
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.