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Register a new userSequential Bayesian experimental design for estimation of extreme-event probability in stochastic dynamical systems
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We consider a dynamical system with two sources of uncertainties: (1) parameterized input with a known probability distribution and (2) stochastic input-to-response (ItR) function with heteroscedastic randomness. Our purpose is to efficiently quantify the extreme response probability when the ItR function is expensive to evaluate. The problem setup arises often in physics and engineering problems, with randomness in ItR coming from either intrinsic uncertainties (say, as a solution to a stochastic equation) or additional (critical) uncertainties that are not incorporated in the input parameter space. To reduce the required sampling numbers, we develop a sequential Bayesian experimental design method leveraging the variational heteroscedastic Gaussian process regression (VHGPR) to account for the stochastic ItR, along with a new criterion to select the next-best samples sequentially. The validity of our new method is first tested in two synthetic problems with the stochastic ItR functions defined artificially. Finally, we demonstrate the application of our method to an engineering problem of estimating the extreme ship motion probability in ensemble of wave groups, where the uncertainty in ItR naturally originates from the uncertain initial condition of ship motion in each wave group.
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We introduce Deep Adaptive Design (DAD), a method for amortizing the cost of adaptive Bayesian experimental design that allows experiments to be run in real-time. Traditional sequential Bayesian optimal experimental design approaches require substantial computation at each stage of the experiment. This makes them unsuitable for most real-world applications, where decisions must typically be made quickly. DAD addresses this restriction by learning an amortized design network upfront and then using this to rapidly run (multiple) adaptive experiments at deployment time. This network represents a design policy which takes as input the data from previous steps, and outputs the next design using a single forward pass; these design decisions can be made in milliseconds during the live experiment. To train the network, we introduce contrastive information bounds that are suitable objectives for the sequential setting, and propose a customized network architecture that exploits key symmetries. We demonstrate that DAD successfully amortizes the process of experimental design, outperforming alternative strategies on a number of problems.
Inference on unknown quantities in dynamical systems via observational data is essential for providing meaningful insight, furnishing accurate predictions, enabling robust control, and establishing appropriate designs for future experiments. Merging mathematical theory with empirical measurements in a statistically coherent way is critical and challenges abound, e.g.,: ill-posedness of the parameter estimation problem, proper regularization and incorporation of prior knowledge, and computational limitations on full uncertainty qualification. To address these issues, we propose a new method for learning parameterized dynamical systems from data. In many ways, our proposal turns the canonical framework on its head. We first fit a surrogate stochastic process to observational data, enforcing prior knowledge (e.g., smoothness), and coping with challenging data features like heteroskedasticity, heavy tails and censoring. Then, samples of the stochastic process are used as surrogate data and point estimates are computed via ordinary point estimation methods in a modular fashion. An attractive feature of this approach is that it is fully Bayesian and simultaneously parallelizable. We demonstrate the advantages of our new approach on a predator prey simulation study and on a real world application involving within-host influenza virus infection data paired with a viral kinetic model.
Inferring the causal structure of a system typically requires interventional data, rather than just observational data. Since interventional experiments can be costly, it is preferable to select interventions that yield the maximum amount of information about a system. We propose a novel Bayesian method for optimal experimental design by sequentially selecting interventions that minimize the expected posterior entropy as rapidly as possible. A key feature is that the method can be implemented by computing simple summaries of the current posterior, avoiding the computationally burdensome task of repeatedly performing posterior inference on hypothetical future datasets drawn from the posterior predictive. After deriving the method in a general setting, we apply it to the problem of inferring causal networks. We present a series of simulation studies in which we find that the proposed method performs favorably compared to existing alternative methods. Finally, we apply the method to real and simulated data from a protein-signaling network.
In this paper we develop a nonparametric maximum likelihood estimate of the mixing distribution of the parameters of a linear stochastic dynamical system. This includes, for example, pharmacokinetic population models with process and measurement noise that are linear in the state vector, input vector and the process and measurement noise vectors. Most research in mixing distributions only considers measurement noise. The advantages of the models with process noise are that, in addition to the measurements errors, the uncertainties in the model itself are taken into the account. For example, for deterministic pharmacokinetic models, errors in dose amounts, administration times, and timing of blood samples are typically not included. For linear stochastic models, we use linear Kalman-Bucy filtering to calculate the likelihood of the observations and then employ a nonparametric adaptive grid algorithm to find the nonparametric maximum likelihood estimate of the mixing distribution. We then use the directional derivatives of the estimated mixing distribution to show that the result found attains a global maximum. A simple example using a one compartment pharmacokinetic linear stochastic model is given. In addition to population pharmacokinetics, this research also applies to empirical Bayes estimation.
Bayesian optimization (BO) is an approach to globally optimizing black-box objective functions that are expensive to evaluate. BO-powered experimental design has found wide application in materials science, chemistry, experimental physics, drug development, etc. This work aims to bring attention to the benefits of applying BO in designing experiments and to provide a BO manual, covering both methodology and software, for the convenience of anyone who wants to apply or learn BO. In particular, we briefly explain the BO technique, review all the applications of BO in additive manufacturing, compare and exemplify the features of different open BO libraries, unlock new potential applications of BO to other types of data (e.g., preferential output). This article is aimed at readers with some understanding of Bayesian methods, but not necessarily with knowledge of additive manufacturing; the software performance overview and implementation instructions are instrumental for any experimental-design practitioner. Moreover, our review in the field of additive manufacturing highlights the current knowledge and technological trends of BO.
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