Optimum Design of Experiments

Atkinson, Anthony C.; Федоров, В. В.

doi:10.1002/0471667196.ess3056

Cited by 6 publications

(5 citation statements)

References 27 publications

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“…He later incorporated these ideas into the more general theory of Bayesian experimental design outlined above, first described in his influential 1972 review of Bayesian statistics [17]. Although non-Bayesian methods for optimal design predate Lindley's work (standard references are [1,2,3]), the Bayesian approach provides a more fundamental rationale for many earlier methods, and unifies and generalizes them (see [4] for discussion of the relationships between Bayesian and non-Bayesian design).…”

Section: Design Stagementioning

confidence: 99%

“…The idea that use of partial knowledge can improve the design of experiments has long been recognized in statistics; there are well-developed theories of experimental design using both the frequentist and Bayesian approaches to statistics (good entry points to the large literature are [1,2,3] for frequentist design, and [4,5] for Bayesian design). Unfortunately, practice has lagged theory, largely due to the complicated calculations required for rigorous experimental design, particularly in adaptive settings where many designs must be calculated.…”

Section: Introductionmentioning

confidence: 99%

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Bayesian Adaptive Exploration

Loredo

2004

AIP Conference Proceedings

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I describe a framework for adaptive scientific exploration based on iterating an Observation--Inference--Design cycle that allows adjustment of hypotheses and observing protocols in response to the results of observation on-the-fly, as data are gathered. The framework uses a unified Bayesian methodology for the inference and design stages: Bayesian inference to quantify what we have learned from the available data and predict future data, and Bayesian decision theory to identify which new observations would teach us the most. When the goal of the experiment is simply to make inferences, the framework identifies a computationally efficient iterative ``maximum entropy sampling'' strategy as the optimal strategy in settings where the noise statistics are independent of signal properties. Results of applying the method to two ``toy'' problems with simulated data--measuring the orbit of an extrasolar planet, and locating a hidden one-dimensional object--show the approach can significantly improve observational efficiency in settings that have well-defined nonlinear models. I conclude with a list of open issues that must be addressed to make Bayesian adaptive exploration a practical and reliable tool for optimizing scientific exploration.Comment: 17 pages, 5 figure

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Section: Design Stagementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Bayesian Adaptive Exploration

Loredo

2004

AIP Conference Proceedings

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“…The optimal design of experiments is a long‐standing area of research in statistics (e.g. see reviews in Atkinson & Federov 1988; Federov & Hackl 1997). In the environmental and ecological sciences, there has also been a strong research emphasis on network design for monitoring spatial processes (e.g.…”

Section: General Methodologymentioning

confidence: 99%

Optimal spatio‐temporal hybrid sampling designs for ecological monitoring

Hooten

Wikle

Sheriff

et al. 2009

J Vegetation Science

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Question: Static sampling designs for collecting spatial data efficiently are being readily utilized by ecologists, however, most ecological systems involve a multivariate spatial process that evolves dynamically over time. Efficient monitoring of such spatio‐temporal systems can be achieved by modeling the dynamic system and reducing the uncertainty associated with the effect of design choice at future observation times. However, can we combine traditional techniques with dynamic methods to find optimal dynamic sampling designs for monitoring the succession of a herbaceous community? Location: Lower Hamburg Bend Conservation Area, Missouri, USA (40°34′42″ lat. 95°45′38″ long.). Methods: The dynamic nature of the system under study is modeled in such a way that uncertainty in the measurements and temporal process can both be accounted for. Both fixed and roving monitoring locations were used in conjunction with a spatio‐temporal statistical model to efficiently determine optimal locations of roving monitors over time based on the reduction of uncertainty in predictions. Results: During the first 3 years of the study, roving monitors where held at fixed locations to allow for statistical parameter estimation from which to make predictions. Optimal monitoring locations for the remaining 2 years were selected based on the overall reduction in prediction uncertainty. Conclusions: The dynamic and adaptive vegetation monitoring scheme allowed for the efficient collection of data that will be utilized for many future ecological studies. By optimally placing an additional set of monitoring locations, we were able to utilize information about the system dynamics when informing the data collection process.

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“…Federov and Müller, 1989;Haas, 1992;Guttorp et al, 1993;Cox et al, 1996;Oehlert, 1996;Nychka and Saltzman, 1998;Bueso et al, 1998;Sansó and Müller, 1998;Müller and Pázman, 2003). For comprehensive overviews of optimal spatial design see Atkinson and Federov (1988), Federov and Hackl (1997) and Müller (2000). Given that most environmental and ecological processes are dynamic in the sense that the underlying process evolves in space and time, static designs based on spatial correlation only may not be as efficient as designs that consider the joint spatio-temporal dependence.…”

Section: Non-gaussian Space-time Dynamic Designmentioning

confidence: 99%

“…Such algorithms are widely used in practice and many variations on the basic theme exist (e.g. see Cook and Nachtsheim, 1980;Atkinson and Federov, 1988;Nychka and Saltzman, 1998). Although these algorithms can be 'greedy' and may converge to local optima, for relatively small problems they typically find either the true optimum or 'good' designs that are close to the optimum.…”

Section: Simulation Based Dynamic Designmentioning

confidence: 99%

Dynamic design of ecological monitoring networks for non‐Gaussian spatio‐temporal data

Wikle

Royle

2005

Environmetrics

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SUMMARYMany ecological processes exhibit spatial structure that changes over time in a coherent, dynamical fashion. This dynamical component is often ignored in the design of spatial monitoring networks. Furthermore, ecological variables related to processes such as habitat are often non-Gaussian (e.g. Poisson or log-normal). We demonstrate that a simulation-based design approach can be used in settings where the data distribution is from a spatiotemporal exponential family. The key random component in the conditional mean function from this distribution is then a spatio-temporal dynamic process. Given the computational burden of estimating the expected utility of various designs in this setting, we utilize an extended Kalman filter approximation to facilitate implementation. The approach is motivated by, and demonstrated on, the problem of selecting sampling locations to estimate July brood counts in the prairie pothole region of the U.S.

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Optimum Design of Experiments

Cited by 6 publications

References 27 publications

Bayesian Adaptive Exploration

Bayesian Adaptive Exploration

Optimal spatio‐temporal hybrid sampling designs for ecological monitoring

Dynamic design of ecological monitoring networks for non‐Gaussian spatio‐temporal data

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