Sequential Bayesian Experimental Design for Implicit Models via Mutual Information

In this chapter, we provide a general overview on the Bayesian experimental design of various statistical models in the recent years. The Bayesian optimal designs incorporate the prior information and uncertainties of the models by using various utility functions, which describe various aims of the experiments. Although there are difficulties in obtaining the analytical expression of the expected utilities and their corresponding numerical approximations under Bayesian framework, the development of fast computational algorithms will bring wider applications of Bayesian experimental design to more complicated models.

Surrogate-based sequential Bayesian experimental design using non-stationary Gaussian Processes

The sequential optimal experimental design formulated as an information-theoretic sensitivity analysis is applied to the ignition delay problem using real experimental. The optimal design is obtained by maximizing the statistical dependence between the model parameters and observables, which is quantified in this study using mutual information. This is naturally posed in the Bayesian framework. The study shows that by monitoring the information gain after each measurement update, one can design a stopping criteria for the experimental process which gives a minimal set of experiments to efficiently learn the Arrhenius parameters.

Conducting new experiments for biomass gasifiers is expensive and time consuming. Therefore, it is important to select conditions for new experiments so maximum information is obtained. In this study, sequential Bayesian model-based design of experiments (MBDoE) is used to design new experimental runs for a heat-integrated biomass downdraft gasifier. This MBDoE approach is valuable because it accounts for model structure, prior information about plausible parameter values, and previous experimental data in a relatively simple way. Operating conditions selected for each new run are biomass moisture content, water injection rate, and the desired energy demand from the downstream engine. Three types of MBDoE with different objective functions are considered: A-optimal, V-optimal, and a proposed new type of focused V-optimal design. A-optimal design is used to when the goal is to obtain improved parameter estimates, without specifying how the model will be used. Performing two new A-optimal runs reduced the standard deviations for model parameters by 18.4% on average compared to when only old data are available. The three most-improved parameter estimates are activation energies for char gasification reactions involving carbon dioxide, hydrogen, and steam, respectively. The focused V-optimal methodology results in greater improvements in prediction accuracy for tar concentration and outlet temperature, which are key model responses. Using two designed Vf-optimal runs reduces standard deviations for these variables by 59.4%, on average, compared to when only old data are available. New A-optimal and V-optimal runs lead to corresponding improvements of 30.7% and 50%, respectively.

To differentiate between guilty and innocent suspects during a criminal case, investigators often query eyewitness memory with a series of police lineups. Most current research on lineup efficacy, however, focuses almost exclusively on individual lineups—perhaps because the literature lacks analytic tools for the multi-lineup setting. In this article, we develop the first general formalism for evaluating the configurations of series of police lineups, thereby equipping the lineup research community to more fully understand these important cases. To accomplish this, we ground the problem of configuring police lineups in the theory of Bayesian sequential experimental design. Using both synthetic data and publicly available data from human-subjects studies, we find that a well-configured series can yield information greater than the sum of its parts. Evidentiary value increases when lineups are configured in light of what has been learned from past lineups and what might be learned from future lineups. Strikingly, some naive approaches reduce the information gained about the suspect’s guilt or innocence to a degree comparable to losing an entire witness in a multi-witness investigation.

Bayesian optimal experimental design for constitutive model calibration

Optimal experimental design is an important methodology for most efficiently allocating resources in an experiment to best achieve some goal. Bayesian experimental design considers the potential impact that various choices of the controllable variables has on the posterior distribution of the unknowns. Optimal Bayesian design involves optimising an expected utility function, which is an analytically intractable integral over the prior predictive distribution. These integrals are typically estimated via standard Monte Carlo methods. In this paper, we demonstrate that the use of randomised quasi-Monte Carlo can bring significant reductions to the variance of the estimated expected utility. This variance reduction will then lead to a more efficient optimisation algorithm for maximising the expected utility.

Summary When Shannon entropy is used as a criterion in the optimal design of experiments, advantage can be taken of the classical identity representing the joint entropy of parameters and observations as the sum of the marginal entropy of the observations and the preposterior conditional entropy of the parameters. Following previous work in which this idea was used in spatial sampling, the method is applied to standard parameterized Bayesian optimal experimental design. Under suitable conditions, which include non-linear as well as linear regression models, it is shown in a few steps that maximizing the marginal entropy of the sample is equivalent to minimizing the preposterior entropy, the usual Bayesian criterion, thus avoiding the use of conditional distributions. It is shown using this marginal formulation that under normality assumptions every standard model which has a two-point prior distribution on the parameters gives an optimal design supported on a single point. Other results include a new asymptotic formula which applies as the error variance is large and bounds on support size.

Development of a framework for sequential Bayesian design of experiments: Application to a pilot-scale solvent-based CO2 capture process

In this paper, a methodology is developed for sequential design of experiments (SDoE) for process systems and applied to a solvent-based CO2 capture system. In this approach, the prior knowledge of the system is used to prioritize process data collection at specific operating conditions. These data are then incorporated into a Bayesian inference methodology for updating a stochastic model by refining estimations of its underlying parameters, and the updated model is then used to generate the next set of test runs. Thus, the new knowledge obtained from the data is used to guide subsequent iterations of the experimental runs, ensuring that the overall data collection is maximally informative given that most experimental campaigns, especially at pilot or higher-scale plants, are costly, time-consuming, and resource-limited. The test run objective for this work was to minimize the maximum model prediction uncertainty for key output variables, but the methodology is generic and can be readily applied to other test run objectives. This methodology is applied to an aqueous monoethanolamine (MEA) pilot plant campaign at the National Carbon Capture Center (NCCC) in Wilsonville, Alabama, USA. The SDoE framework was utilized for two iterations, while collecting 18 sets of data representing different process conditions, and this resulted in an overall average reduction in uncertainty of approximately 50% in the prediction of CO2 capture percentage. Moreover, 11 additional data sets were obtained with variation of absorber packing height for further model validation. This work shows the capability of the SDoE framework to maximize learning given limited resources, allowing for the reduction of model uncertainty, which is of great importance for many applications including reduction of technical risk associated with scale-up and economic analysis.

<div class="htmlview paragraph">The search for improvements in fuel economy, specific power, exhaust emissions and refinement leads to an increasing number of experimental variables and flexibility in their operating strategy. This makes identification of optimum settings and robust solutions more demanding. New test and analysis techniques are required to identify underlying trends and sensitivities in order to determine, with some confidence, the technical and commercial benefits of changes to one or more parameters. Greater emphasis on experimental design will therefore be essential for any engine research and development programme.</div> <div class="htmlview paragraph">Design of experiments (DoE) techniques have been widely used for identifying optimum settings. Traditional experimental designs can be improved by including engineering knowledge more directly into the design process and by providing information on a continuous basis during the test programme.</div> <div class="htmlview paragraph">This paper explores the potential of Bayesian methods in engine Research and Development testing. By employing Bayesian methods, it is possible to define a prior model and update the model as test data become available. This makes it possible to build and interrogate the model earlier in the test programme. The model can then be used to identify the best settings and plan further test work.</div> <div class="htmlview paragraph">Examples are given to illustrate ways for collecting and using the required engineering knowledge, alternative criteria for selecting the test points and some Bayesian analysis tools.</div>

SummaryMany animals communicate using sequences of discrete acoustic elements which can be complex, vary in their degree of stereotypy, and are potentially open‐ended. Variation in sequences can provide important ecological, behavioural or evolutionary information about the structure and connectivity of populations, mechanisms for vocal cultural evolution and the underlying drivers responsible for these processes. Various mathematical techniques have been used to form a realistic approximation of sequence similarity for such tasks.Here, we use both simulated and empirical data sets from animal vocal sequences (rock hyrax,Procavia capensis; humpback whale,Megaptera novaeangliae; bottlenose dolphin,Tursiops truncatus; andCarolina chickadee,Poecile carolinensis) to test which of eight sequence analysis metrics are more likely to reconstruct the information encoded in the sequences, and to test the fidelity of estimation of model parameters, when the sequences are assumed to conform to particular statistical models.Results from the simulated data indicated that multiple metrics were equally successful in reconstructing the information encoded in the sequences of simulated individuals (Markov chains,n‐gram models, repeat distribution and edit distance) and data generated by different stochastic processes (entropy rate andn‐grams). However, the string edit (Levenshtein) distance performed consistently and significantly better than all other tested metrics (including entropy,Markov chains,n‐grams, mutual information) for all empirical data sets, despite being less commonly used in the field of animal acoustic communication.TheLevenshtein distance metric provides a robust analytical approach that should be considered in the comparison of animal acoustic sequences in preference to other commonly employed techniques (such asMarkov chains, hiddenMarkov models orShannon entropy). The recent discovery that non‐Markovian vocal sequences may be more common in animal communication than previously thought provides a rich area for future research that requires non‐Markovian‐based analysis techniques to investigate animal grammars and potentially the origin of human language.

A method of model discrimination and parameter estimation in enzyme kinetics is proposed. The experimental design and analysis of the model are carried out simultaneously and the stopping rule for experimentation is deduced by the experimenter when the probabilities a posteriori indicate that one model is clearly superior to the rest. A FORTRAN77 program specifically developed for joint designs is given. The method is very powerful, as indicated by its usefulness in the discrimination between models. For example, it has been successfully applied to three cases of enzyme kinetics (a single-substrate Michaelian reaction with product inhibition, a single-substrate complex reaction and a two-substrate reaction). By using this method the most probable model and the estimates of the parameters can be obtained in one experimental session. The FORTRAN77 program is deposited as Supplementary Publication SUP 50134 (19 pages) at the British Library (Lending Division), Boston Spa, Wetherby, West Yorkshire LS23 7BQ, U.K., from whom copies can be obtained on the terms indicated in Biochem. J. (1986) 233, 5.

A mathematical model was developed to simulate the emulsion copolymerization of acrylonitrile/butadiene, otherwise known as nitrile rubber. Our goal was to develop a practical tool to predict polymer production rate and product quality on an industrial scale. Model predictions include the polymerization rate, the polymer composition, the number- and weight-average molecular weights, branching averages, and the number and average size of the polymer latex particles. The prediction of conversion was compared to a limited amount of industrial pilot-plant data and was found to be adequate. The model is currently being applied in two ways. The first application involves the testing of nonlinear model-based control schemes for an industrial nitrile rubber reactor. The second application involves using the model as a storehouse of prior knowledge for the implementation of a Bayesian sequential design of emulsion terpolymerization experiments as part of a larger, systematic study of multicomponent polymerization ...

The Kilombero Valley floodplain in Tanzania is a major agricultural area. Government initiatives and projects supported by international funding have long sought to boost productivity. Due to increasing population pressure, smallholder farmers are forced to increase their output. Nevertheless, the level of intensification is still lower than what is considered necessary to increase production and support smallholder livelihoods significantly. This article aims to better understand farmers’ intensification choices and their interdependent determinants. We propose a novel modeling approach for identifying determinants of intensification and their interrelationships by combining a Bayesian belief network (BBN), experimental design, and multivariate regression trees. Our approach complements existing lower‐dimensional statistical models by considering uncertainty and providing an easily updatable model structure. The BBN is constructed and calibrated using data from a survey of 304 farm households. Our findings show how the data‐driven BBN approach can be used to identify variables that influence farmers’ decision to choose one technique over another. Furthermore, the most important drivers vary widely, depending on the intensification options being considered.