Sequential Shrinkage Estimate for COX Regression Models with Uncertain Number of Effective Variables

In the applications of COX regression models, we always encounter data sets that contain too many variables that only a few of them contribute to the model. Therefore, it will waste much more samples to estimate the “noneffective” variables in the inference. In this paper, we use a sequential procedure for constructing the fixed size confidence set for the “effective” parameters to the model based on an adaptive shrinkage estimate such that the “effective” coefficients can be efficiently identified with the minimum sample size. Fixed design is considered for numerical simulation. The strong consistency, asymptotic distributions and convergence rates of estimates under the fixed design are obtained. In addition, the sequential procedure is shown to be asymptotically optimal in the sense of Chow and Robbins (1965).

A deep Koopman operator-based modelling approach for long-term prediction of dynamics with pixel-level measurements

Although previous studies have made some clear leap in learning latent dynamics from high-dimensional representations,the performances in terms of accuracy and inference time of long-term model prediction still need to be improved.In this study,a deep convolutional network based on the Koopman operator(CKNet)is proposed to model non-linear systems with pixel-level measurements for long-term prediction.CKNet adopts an autoencoder network architecture,consisting of an encoder to generate latent states and a linear dynamical model(i.e.,the Koopman operator)which evolves in the latent state space spanned by the encoder.The decoder is used to recover images from latent states.According to a multi-step ahead prediction loss function,the system matrices for approximating the Koopman operator are trained synchronously with the autoencoder in a mini-batch manner.In this manner,gradients can be synchronously transmitted to both the system matrices and the autoencoder to help the encoder self-adaptively tune the latent state space in the training process,and the resulting model is time-invariant in the latent space.Therefore,the proposed CKNet has the advantages of less inference time and high accuracy for long-term prediction.Experiments are per-formed on OpenAI Gym and Mujoco environments,including two and four non-linear forced dynamical systems with continuous action spaces.The experimental results show that CKNet has strong long-term prediction capabilities with sufficient precision.

Parameter identification of hysteretic model of rubber-bearing based on sequential nonlinear least-square estimation

In order to evaluate the nonlinear performance and the possible damage to rubber-bearings （RBs） during their normal operation or under strong earthquakes, a simplified Bouc-Wen model is used to describe the nonlinear hysteretic behavior of RBs in this paper, which has the advantages of being smooth-varying and physically motivated. Further, based on the results from experimental tests performed by using a particular type of RB （GZN 110） under different excitation scenarios, including white noise and several earthquakes, a new system identification method, referred to as the sequential nonlinear least- square estimation （SNLSE）, is introduced to identify the model parameters. It is shown that the proposed simplified Bouc- Wen model is capable of describing the nonlinear hysteretic behavior of RBs, and that the SNLSE approach is very effective in identifying the model parameters of RBs.

Sequential Parameter Estimation Using Modal Dispersion Curves in Shallow Water

Existing sequential parameter estimation methods use the acoustic pressure of a line array as observations. The modal dispersion curves are employed to estimate the sound speed profile（SSP） and geoacoustic parameters based on the ensemble Kalman filter. The warping transform is implemented to the signals received by a single hydrophone to obtain the dispersion curves. The experimental data are collected at a range-independent shallow water site in the South China Sea. The results indicate that the SSPs are well estimated and the geoacoustic parameters are also well determined. Comparisons of the observed and estimated modal dispersion curves show good agreement.

A Sequential Regression Model for Big Data with Attributive Explanatory Variables

As the applications for modeling of big data and analysis advance in scope,computational efficiency faces greater challenges in terms of storage and speed.In many practical problems,a great amount of historical data is sequentially collected and used for online statistical modeling.For modeling sequential data,we propose a sequential linear regression method that extracts essential information from historical data.This carefully selected information is then utilized to update a model according to a sequential estimation scheme.With this technique,the earlier data no longer needs to be stored,and the sequential updating is computationally efficient in speed and storage.A weighted strategy is introduced on the current model to determine the impact of data from different periods.When compared with estimation methods that use historical data,our numerical experiments demonstrate that our solution increases the speed while decreasing the storage load.

A sequential method for estimating the optical properties of two-layer agro-products from spatially-resolved diffuse reflectance: Simulation

A sequential method for estimating the optical properties of two-layer biological tissues with spatially-resolved diffuse reflectance was proposed and validated using Monte Carlo simulations.The relationship between the penetration depth of detected photons and source-detector separation was first studied.Photons detected at larger source-detector separations generally penetrated deeper into the medium than those detected at small source-detector separations.The effect of each parameter involved in the two-layer diffusion model(i.e.,the absorption and reduced scattering coefficients(μa andμs′)of each layer,and the thickness of top layer)on reflectance was investigated.It was found that the relationship between the optical properties and thickness of top layer was a critical factor in determining whether photons would have sufficient interactions with the top layer and also penetrate into the bottom layer.The constraints for the proposed sequential estimation method were quantitatively determined by the curve fitting procedure coupledwith error contourmap analyses.Results showed that the optical properties of top layer could be determinedwithin 10%error using the semi-infinite diffusion model for reflectance profiles with properly selected start and end points,when the thickness of top layer was larger than two times its mean free path(mfp′).And the optical properties of the bottom layer could be estimatedwithin 10%error by the two-layer diffusion model,when the thickness of top layerwas b16 times its mfp′.The proposed sequential estimation method is promising for improving the estimation of the optical properties of two-layer tissues from the same spatially-resolved reflectance.

Particle flters for probability hypothesis density flter with the presence of unknown measurement noise covariance

In Bayesian multi-target fltering,knowledge of measurement noise variance is very important.Signifcant mismatches in noise parameters will result in biased estimates.In this paper,a new particle flter for a probability hypothesis density（PHD）flter handling unknown measurement noise variances is proposed.The approach is based on marginalizing the unknown parameters out of the posterior distribution by using variational Bayesian（VB）methods.Moreover,the sequential Monte Carlo method is used to approximate the posterior intensity considering non-linear and non-Gaussian conditions.Unlike other particle flters for this challenging class of PHD flters,the proposed method can adaptively learn the unknown and time-varying noise variances while fltering.Simulation results show that the proposed method improves estimation accuracy in terms of both the number of targets and their states.