Abstract #302210

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JSM 2003 Abstract #302210
Activity Number: 378
Type: Contributed
Date/Time: Wednesday, August 6, 2003 : 12:00 PM to 1:50 PM
Sponsor: General Methodology
Abstract - #302210
Title: Bootstrap Confidence Intervals for the Probability of Correctly Predicting the Next State of a Finite-State Markov Chain With a Point Predictor or a Prediction Region
Author(s): Clyde Sugahara*+
Companies: California State University, Hayward
Address: 27 Entrada Ave., Oakland, CA, 94611-4311,
Keywords: bootstrap ; Markov chain ; prediction
Abstract:

Consider predicting the next state of an irreducible, aperiodic, finite-state Markov chain with unknown transition matrix, given the present state and the empirical transition matrix based on the past states of the chain. A natural point predictor is the mode of the row of the empirical transition matrix corresponding to the present state. The bootstrap method is used to construct a confidence interval for the conditional probability that this point predictor will predict the next state correctly given the current state and the empirical transition matrix. A prediction region for the next state is also considered and the bootstrap method is used to construct a confidence interval for the conditional probability that the prediction region will contain the next state.

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