A Bayesian View on Detecting Drifts by Nonparametric Methods
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Ansgar Steland
Abstract
We study a nonparametric sequential detection procedure, which aims at detecting the first time point where a drift term appears in a stationary process, from a Bayesian perspective. The approach is based on a nonparametric model for the drift, a nonparametric kernel smoother which is used to define the stopping rule, and a performance measure which determines for each smoothing kernel and each given drift the asymptotic accuracy of the method. We look at this approach by parameterizing the drift and putting a prior distribution on the parameter vector. We are able to identify the optimal prior distribution which minimizes the expected performance measure. Consequently, we can judge whether a certain prior distribution yields good or even optimal asymptotic detection. We consider several important special cases where the optimal prior can be calculated explicitly.
© Heldermann Verlag
Articles in the same Issue
- Determination of Specifications for Tensile Strength of Castings
- Joint Design of Economic Manufacturing Quantity, Sampling Plan and Specification Limits
- Measurement Procedures for the Variance of a Normal Distribution
- A Bayesian View on Detecting Drifts by Nonparametric Methods
- Combining Process and Product Control for Reducing Sampling Costs
- Modelling of Explosives Sensitivity Part 2: The Weibull-Model
- Modified Tightened Three Level Continuous Sampling Plan
- A Note on the Continuous Sampling Plan CSP-V
Articles in the same Issue
- Determination of Specifications for Tensile Strength of Castings
- Joint Design of Economic Manufacturing Quantity, Sampling Plan and Specification Limits
- Measurement Procedures for the Variance of a Normal Distribution
- A Bayesian View on Detecting Drifts by Nonparametric Methods
- Combining Process and Product Control for Reducing Sampling Costs
- Modelling of Explosives Sensitivity Part 2: The Weibull-Model
- Modified Tightened Three Level Continuous Sampling Plan
- A Note on the Continuous Sampling Plan CSP-V
