Missing data often result in undesirable bias and loss of efficiency. These become substantial problems when the response mechanism is nonignorable, such that the response model depends on unobserved variables. It is necessary to estimate the joint distribution of unobserved variables and response indicators to manage nonignorable nonresponse. However, model misspecification and identification issues prevent robust estimates despite careful estimation of the target joint distribution. In this study, we modelled the distribution of the observed parts and derived sufficient conditions for model identifiability, assuming a logistic regression model as the response mechanism and generalised linear models as the main outcome model of interest. More importantly, the derived sufficient conditions are testable with the observed data and do not require any instrumental variables, which are often assumed to guarantee model identifiability but cannot be practically determined beforehand. To analyse missing data, we propose a new imputation method which incorporates verifiable identifiability using only observed data. Furthermore, we present the performance of the proposed estimators in numerical studies and apply the proposed method to two sets of real data: exit polls for the 19th South Korean election data and public data collected from the Korean Survey of Household Finances and Living Conditions.
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In practice, non-destructive testing (NDT) procedures tend to consider experiments (and their respective models) as distinct, conducted in isolation and associated with independent data. In contrast, this work looks to capture the interdependencies between acoustic emission (AE) experiments (as meta-models) and then use the resulting functions to predict the model hyperparameters for previously unobserved systems. We utilise a Bayesian multilevel approach (similar to deep Gaussian Processes) where a higher level meta-model captures the inter-task relationships. Our key contribution is how knowledge of the experimental campaign can be encoded between tasks as well as within tasks. We present an example of AE time-of-arrival mapping for source localisation, to illustrate how multilevel models naturally lend themselves to representing aggregate systems in engineering. We constrain the meta-model based on domain knowledge, then use the inter-task functions for transfer learning, predicting hyperparameters for models of previously unobserved experiments (for a specific design).
Sequential neural posterior estimation (SNPE) techniques have been recently proposed for dealing with simulation-based models with intractable likelihoods. Unlike approximate Bayesian computation, SNPE techniques learn the posterior from sequential simulation using neural network-based conditional density estimators by minimizing a specific loss function. The SNPE method proposed by Lueckmann et al. (2017) used a calibration kernel to boost the sample weights around the observed data, resulting in a concentrated loss function. However, the use of calibration kernels may increase the variances of both the empirical loss and its gradient, making the training inefficient. To improve the stability of SNPE, this paper proposes to use an adaptive calibration kernel and several variance reduction techniques. The proposed method greatly speeds up the process of training and provides a better approximation of the posterior than the original SNPE method and some existing competitors as confirmed by numerical experiments. We also manage to demonstrate the superiority of the proposed method for a high-dimensional model with real-world dataset.
We consider the problem of sampling a high dimensional multimodal target probability measure. We assume that a good proposal kernel to move only a subset of the degrees of freedoms (also known as collective variables) is known a priori. This proposal kernel can for example be built using normalizing flows. We show how to extend the move from the collective variable space to the full space and how to implement an accept-reject step in order to get a reversible chain with respect to a target probability measure. The accept-reject step does not require to know the marginal of the original measure in the collective variable (namely to know the free energy). The obtained algorithm admits several variants, some of them being very close to methods which have been proposed previously in the literature. We show how the obtained acceptance ratio can be expressed in terms of the work which appears in the Jarzynski-Crooks equality, at least for some variants. Numerical illustrations demonstrate the efficiency of the approach on various simple test cases, and allow us to compare the variants of the algorithm.
In decision-making, maxitive functions are used for worst-case and best-case evaluations. Maxitivity gives rise to a rich structure that is well-studied in the context of the pointwise order. In this article, we investigate maxitivity with respect to general preorders and provide a representation theorem for such functionals. The results are illustrated for different stochastic orders in the literature, including the usual stochastic order, the increasing convex/concave order, and the dispersive order.
We consider linear models with scalar responses and covariates from a separable Hilbert space. The aim is to detect change points in the error distribution, based on sequential residual empirical distribution functions. Expansions for those estimated functions are more challenging in models with infinite-dimensional covariates than in regression models with scalar or vector-valued covariates due to a slower rate of convergence of the parameter estimators. Yet the suggested change point test is asymptotically distribution-free and consistent for one-change point alternatives. In the latter case we also show consistency of a change point estimator.
In the present work, strong approximation errors are analyzed for both the spatial semi-discretization and the spatio-temporal fully discretization of stochastic wave equations (SWEs) with cubic polynomial nonlinearities and additive noises. The fully discretization is achieved by the standard Galerkin ffnite element method in space and a novel exponential time integrator combined with the averaged vector ffeld approach. The newly proposed scheme is proved to exactly satisfy a trace formula based on an energy functional. Recovering the convergence rates of the scheme, however, meets essential difffculties, due to the lack of the global monotonicity condition. To overcome this issue, we derive the exponential integrability property of the considered numerical approximations, by the energy functional. Armed with these properties, we obtain the strong convergence rates of the approximations in both spatial and temporal direction. Finally, numerical results are presented to verify the previously theoretical findings.
Many proposals for the identification of causal effects require an instrumental variable that satisfies strong, untestable unconfoundedness and exclusion restriction assumptions. In this paper, we show how one can potentially identify causal effects under violations of these assumptions by harnessing a negative control population or outcome. This strategy allows one to leverage sup-populations for whom the exposure is degenerate, and requires that the instrument-outcome association satisfies a certain parallel trend condition. We develop the semiparametric efficiency theory for a general instrumental variable model, and obtain a multiply robust, locally efficient estimator of the average treatment effect in the treated. The utility of the estimators is demonstrated in simulation studies and an analysis of the Life Span Study.
We develop both first and second order numerical optimization methods to solve non-smooth optimization problems featuring a shared sparsity penalty, constrained by differential equations with uncertainty. To alleviate the curse of dimensionality we use tensor product approximations. To handle the non-smoothness of the objective function we introduce a smoothed version of the shared sparsity objective. We consider both a benchmark elliptic PDE constraint, and a more realistic topology optimization problem. We demonstrate that the error converges linearly in iterations and the smoothing parameter, and faster than algebraically in the number of degrees of freedom, consisting of the number of quadrature points in one variable and tensor ranks. Moreover, in the topology optimization problem, the smoothed shared sparsity penalty actually reduces the tensor ranks compared to the unpenalised solution. This enables us to find a sparse high-resolution design under a high-dimensional uncertainty.
We propose a novel, highly efficient, second-order accurate, long-time unconditionally stable numerical scheme for a class of finite-dimensional nonlinear models that are of importance in geophysical fluid dynamics. The scheme is highly efficient in the sense that only a (fixed) symmetric positive definite linear problem (with varying right hand sides) is involved at each time-step. The solutions to the scheme are uniformly bounded for all time. We show that the scheme is able to capture the long-time dynamics of the underlying geophysical model, with the global attractors as well as the invariant measures of the scheme converge to those of the original model as the step size approaches zero. In our numerical experiments, we take an indirect approach, using long-term statistics to approximate the invariant measures. Our results suggest that the convergence rate of the long-term statistics, as a function of terminal time, is approximately first order using the Jensen-Shannon metric and half-order using the L1 metric. This implies that very long time simulation is needed in order to capture a few significant digits of long time statistics (climate) correct. Nevertheless, the second order scheme's performance remains superior to that of the first order one, requiring significantly less time to reach a small neighborhood of statistical equilibrium for a given step size.
Gate-defined quantum dots are a promising candidate system for realizing scalable, coupled qubit systems and serving as a fundamental building block for quantum computers. However, present-day quantum dot devices suffer from imperfections that must be accounted for, which hinders the characterization, tuning, and operation process. Moreover, with an increasing number of quantum dot qubits, the relevant parameter space grows sufficiently to make heuristic control infeasible. Thus, it is imperative that reliable and scalable autonomous tuning approaches are developed. This meeting report outlines current challenges in automating quantum dot device tuning and operation with a particular focus on datasets, benchmarking, and standardization. We also present insights and ideas put forward by the quantum dot community on how to overcome them. We aim to provide guidance and inspiration to researchers invested in automation efforts.
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