Inferential models (IMs) are data-dependent, imprecise-probabilistic structures designed to quantify uncertainty about unknowns. As the name suggests, the focus has been on uncertainty quantification for inference and on its reliability properties in that context. Focusing on a likelihood-based possibilistic IM formulation, the present paper develops a corresponding framework for decision making, and investigates the decision-theoretic implications of the IM’s reliability guarantees. Here we show that the possibilistic IM’s assessment of an action’s quality, defined by a simple Choquet integral, tends not be too optimistic compared to that of an oracle. This ensures that the IM tends not to favor actions that the oracle doesn’t also favor, hence the IM is also reliable for decision making. We also establish a complementary, large-sample efficiency result that says the IM’s reliability isn’t achieved by being grossly conservative. In the special case of equivariant statistical models, further connections can be made between the IM’s and Bayesian’s recommended actions, from which certain optimality conclusions can be drawn.

Inferential models (IMs) offer provably reliable, data-driven, possibilistic statistical inference. But despite the IM framework's theoretical and foundational advantages, efficient computation is a challenge. This paper presents a simple yet powerful numerical strategy for approximating the IM's possibility contour, or at least its α -cut for a specified α ∈ ( 0 , 1 ) . Our proposal starts with the specification of a parametric family that, in a certain sense, approximately covers the credal set associated with the IM's possibility measure. Akin to variational inference, we then propose to tune the parameters of that parametric family so that its 100 ( 1 − α ) % credible set roughly matches the IM contour's α -cut. This parametric α -cut matching strategy implies a full approximation to the IM's possibility contour at a fraction of the computational cost associated with previous strategies. • This paper introduces an effective numerical strategy for approximating the computation of Inferential Models (IMs). • The key idea is to specify a parametric family that approximately covers the IM's associated credal set. • This framework makes previously infeasible computations, due to their high computational cost, now practically achievable.

In this paper we adopt the familiar sparse, high-dimensional linear regression model and focus on the important but often overlooked task of prediction. In particular, we consider a new empirical Bayes framework that incorporates data in the prior in two ways: one is to center the prior for the non-zero regression coefficients and the other is to provide some additional regularization. We show that, in certain settings, the asymptotic concentration of the proposed empirical Bayes posterior predictive distribution is very fast, and we establish a Bernstein--von Mises theorem which ensures that the derived empirical Bayes prediction intervals achieve the targeted frequentist coverage probability. The empirical prior has a convenient conjugate form, so posterior computations are relatively simple and fast. Finally, our numerical results demonstrate the proposed method's strong finite-sample performance in terms of prediction accuracy, uncertainty quantification, and computation time compared to existing Bayesian methods.

We discuss the application of indirect learning methods in zero-sum and identical payoff learning automata games. We propose a novel decentralized version of the well-known pursuit learning algorithm. Such a decentralized algorithm has significant computational advantages over its centralized counterpart. The theoretical study of such a decentralized algorithm requires the analysis to be carried out in a nonstationary environment. We use a novel bootstrapping argument to prove the convergence of the algorithm. To our knowledge, this is the first time that such analysis has been carried out for zero-sum and identical payoff games. Extensive simulation studies are reported, which demonstrate the proposed algorithm's fast and accurate convergence in a variety of game scenarios. We also introduce the framework of partial communication in the context of identical payoff games of learning automata. In such games, the automata may not communicate with each other or may communicate selectively. This comprehensive framework has the capability to model both centralized and decentralized games discussed in this paper.

This article offers a newly design and built industrial automation technique for compressor testing procedures for their final tests of assembled compressors. Sequential total test procedure activities for a model of twin screw compressor tests have been developed. In this particular project it is developed how some of the activities can be automated using ADAM programmable data communication module communicating with a PC. For data listening such as pressure and temperature values of a compressor a pressure transducer of model Energair T-16 and a temperature sensor of model OMEGA TAC 80 B-K, respectively, have been successfully used at the experimental stage. The output derivatives were displayed using GUI on a computer screen for visualization as well as recorded in the computer memory for further uses. The GUI screen was developed using Java programming technique. The results of the research based experimental project could be valuable information and technology usable in compressor manufacturing industries as well as for compressor using industries.