4,045 research outputs found
Failure Inference and Optimization for Step Stress Model Based on Bivariate Wiener Model
In this paper, we consider the situation under a life test, in which the
failure time of the test units are not related deterministically to an
observable stochastic time varying covariate. In such a case, the joint
distribution of failure time and a marker value would be useful for modeling
the step stress life test. The problem of accelerating such an experiment is
considered as the main aim of this paper. We present a step stress accelerated
model based on a bivariate Wiener process with one component as the latent
(unobservable) degradation process, which determines the failure times and the
other as a marker process, the degradation values of which are recorded at
times of failure. Parametric inference based on the proposed model is discussed
and the optimization procedure for obtaining the optimal time for changing the
stress level is presented. The optimization criterion is to minimize the
approximate variance of the maximum likelihood estimator of a percentile of the
products' lifetime distribution
Hierarchical Stochastic Block Model for Community Detection in Multiplex Networks
Multiplex networks have become increasingly more prevalent in many fields,
and have emerged as a powerful tool for modeling the complexity of real
networks. There is a critical need for developing inference models for
multiplex networks that can take into account potential dependencies across
different layers, particularly when the aim is community detection. We add to a
limited literature by proposing a novel and efficient Bayesian model for
community detection in multiplex networks. A key feature of our approach is the
ability to model varying communities at different network layers. In contrast,
many existing models assume the same communities for all layers. Moreover, our
model automatically picks up the necessary number of communities at each layer
(as validated by real data examples). This is appealing, since deciding the
number of communities is a challenging aspect of community detection, and
especially so in the multiplex setting, if one allows the communities to change
across layers. Borrowing ideas from hierarchical Bayesian modeling, we use a
hierarchical Dirichlet prior to model community labels across layers, allowing
dependency in their structure. Given the community labels, a stochastic block
model (SBM) is assumed for each layer. We develop an efficient slice sampler
for sampling the posterior distribution of the community labels as well as the
link probabilities between communities. In doing so, we address some unique
challenges posed by coupling the complex likelihood of SBM with the
hierarchical nature of the prior on the labels. An extensive empirical
validation is performed on simulated and real data, demonstrating the superior
performance of the model over single-layer alternatives, as well as the ability
to uncover interesting structures in real networks
Bayesian Estimation for Continuous-Time Sparse Stochastic Processes
We consider continuous-time sparse stochastic processes from which we have
only a finite number of noisy/noiseless samples. Our goal is to estimate the
noiseless samples (denoising) and the signal in-between (interpolation
problem).
By relying on tools from the theory of splines, we derive the joint a priori
distribution of the samples and show how this probability density function can
be factorized. The factorization enables us to tractably implement the maximum
a posteriori and minimum mean-square error (MMSE) criteria as two statistical
approaches for estimating the unknowns. We compare the derived statistical
methods with well-known techniques for the recovery of sparse signals, such as
the norm and Log (- relaxation) regularization
methods. The simulation results show that, under certain conditions, the
performance of the regularization techniques can be very close to that of the
MMSE estimator.Comment: To appear in IEEE TS
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