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.
2022
Inglese
Book of the Short Papers - SIS 2022
SIS 2022, 51st Scientific Meeting of the Italian Statistical Society
Caserta
Contributed paper
22-giu-2022
24-giu-2022
9788891932310
Pearson
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]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10807/228210
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