BIC criterion is widely used by the neural-network community for model selection tasks, although its convergence properties are not always theoretically established. In this paper we will focus on estimating the number of components in a mixture of multilayer perceptrons and proving the convergence of the BIC criterion in this frame. The penalized marginal-likelihood for mixture models and hidd...

Determining when a numerical simulation is fully converged is important in getting accurate and reliable results. In this study a new convergence criterion based on extracting the energetic modes of a numerical solution, based on the Proper Orthogonal Decomposition method, is suggested. The POD convergence criterion is tested and applied to flow over a bluff body which has been solved numerical...

We study systems of simple point processes that admit stochastic intensities. represent these as thinnings Poisson measures and are interested in a convergence result such systems. This states that, if the intensities limit independent underlying measures, distribution Skorohod topology implies same for processes.

Iterative data-based controller tuning consists of iterative adjustment of the controller parameters towards the parameter values which minimize an H2 performance criterion. The convergence to the global minimum of the performance criterion depends on the initial controller parameters and on the step size of each iteration. This paper presents convergence properties of iterative algorithms when...

This work concerns controlled Markov chains with denumerable state space, (possibly) unbounded cost function, and an expected average cost criterion. Under a Lyapunov function condition, together with mild continuity-compactness assumptions, a simple necessary and sufficient criterion is given so that the relative value functions and differential costs produced by the value iteration scheme con...

In this study, we introduce the notion of pointwise and uniform statistical convergence of double sequences of real-valued functions. We also give the relations between these convergences and pointwise,uniform convergence. Furthermore, we introduce the concept of statistically Cauchy sequence and study statistical analogue of convergence and Cauchy criterion for double sequences of real-valued ...

We characterize sequences of numbers (an) such that ∑ n≥1 anΦn converges a.e. for any orthonormal system (Φn) in any L2-space. In our criterion, we use the set B = { ∑ m≥n |am| ;n ≥ 1} and its information function hB(t) = − log3(β − α) for t ∈ (α, β], [α, β] ∩B = {α, β}.

We give a criterion for H-convergence of conductivity matrices in terms of ordinary weak convergence of the factors in certain quotient representations of the matrices.