Adaptive Estimation How To Hit A Moving Target

The procedure is based on a Metropolis algorithm, a Markov chain Monte Carlo method involving an old state, a new state, and a stochastic innovation such that the Markov chain converges to an invariant distribution. The stochastic innovation is partially provided by responses of persons to items, with the Markov chain as a dynamic estimator of ability. Item responses are incorporated in two different places. First, item responses are incorporated as stochastic innovations of the Metropolis candidate distribution, with a discrete Markov chain as an alternative estimate of ability. Second, item responses are used as acceptance variables. A simulation study is provided to demonstrate some properties of these adaptive estimation procedures in monitoring student abilities. Several applications and extensions are discussed.