57,878 research outputs found
Adaptive mastery testing using the Rasch model and Bayesian sequential decision theory
A version of sequential mastery testing is studied in which response behavior is modeled by an item response theory (IRT) model. First, a general theoretical framework is sketched that is based on a combination of Bayesian sequential decision theory and item response theory. A discussion follows on how IRT based sequential mastery testing can be generalized to adaptive item and testlet selection rules; i.e., to a situation in which the choice of the next item or testlet to be administered is optimized using the information from previous responses. The performance of IRT based sequential and adaptive sequential mastery testing is studied in a number of simulations using the Rasch model. The possibilities and difficulties of application of the approach in the framework of the two-parameter logistic and three-parameter logistic models is also discussed
Sequentiality and Adaptivity Gains in Active Hypothesis Testing
Consider a decision maker who is responsible to collect observations so as to
enhance his information in a speedy manner about an underlying phenomena of
interest. The policies under which the decision maker selects sensing actions
can be categorized based on the following two factors: i) sequential vs.
non-sequential; ii) adaptive vs. non-adaptive. Non-sequential policies collect
a fixed number of observation samples and make the final decision afterwards;
while under sequential policies, the sample size is not known initially and is
determined by the observation outcomes. Under adaptive policies, the decision
maker relies on the previous collected samples to select the next sensing
action; while under non-adaptive policies, the actions are selected independent
of the past observation outcomes.
In this paper, performance bounds are provided for the policies in each
category. Using these bounds, sequentiality gain and adaptivity gain, i.e., the
gains of sequential and adaptive selection of actions are characterized.Comment: 12 double-column pages, 1 figur
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Learning about a Moving Target in Resource Management: Optimal Bayesian Disease Control
Resource managers must often make difficult choices in the face of imperfectly observed and dynamically changing systems (e.g., livestock, fisheries, water, and invasive species). A rich set of techniques exists for identifying optimal choices when that uncertainty is assumed to be understood and irreducible. Standard optimization approaches, however, cannot address situations in which reducible uncertainty applies to either system behavior or environmental states. The adaptive management literature overcomes this limitation with tools for optimal learning, but has been limited to highly simplified models with state and action spaces that are discrete and small. We overcome this problem by using a recently developed extension of the Partially Observable Markov Decision Process (POMDP) framework to allow for learning about a continuous state. We illustrate this methodology by exploring optimal control of bovine tuberculosis in New Zealand cattle. Disease testing—the control variable—serves to identify herds for treatment and provides information on prevalence, which is both imperfectly observed and subject to change due to controllable and uncontrollable factors. We find substantial efficiency losses from both ignoring learning (standard stochastic optimization) and from simplifying system dynamics (to facilitate a typical, simple learning model), though the latter effect dominates in our setting. We also find that under an adaptive management approach, simplifying dynamics can lead to a belief trap in which information gathering ceases, beliefs become increasingly inaccurate, and losses abound
Active Classification: Theory and Application to Underwater Inspection
We discuss the problem in which an autonomous vehicle must classify an object
based on multiple views. We focus on the active classification setting, where
the vehicle controls which views to select to best perform the classification.
The problem is formulated as an extension to Bayesian active learning, and we
show connections to recent theoretical guarantees in this area. We formally
analyze the benefit of acting adaptively as new information becomes available.
The analysis leads to a probabilistic algorithm for determining the best views
to observe based on information theoretic costs. We validate our approach in
two ways, both related to underwater inspection: 3D polyhedra recognition in
synthetic depth maps and ship hull inspection with imaging sonar. These tasks
encompass both the planning and recognition aspects of the active
classification problem. The results demonstrate that actively planning for
informative views can reduce the number of necessary views by up to 80% when
compared to passive methods.Comment: 16 page
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