Robust mixtures of regression models

Doctor of PhilosophyDepartment of StatisticsKun Chen and Weixin YaoThis proposal contains two projects that are related to robust mixture models. In the robust project, we propose a new robust mixture of regression models (Bai et al., 2012). The existing methods for tting mixture regression models assume a normal distribution for error and then estimate the regression param- eters by the maximum likelihood estimate (MLE). In this project, we demonstrate that the MLE, like the least squares estimate, is sensitive to outliers and heavy-tailed error distributions. We propose a robust estimation procedure and an EM-type algorithm to estimate the mixture regression models. Using a Monte Carlo simulation study, we demonstrate that the proposed new estimation method is robust and works much better than the MLE when there are outliers or the error distribution has heavy tails. In addition, the proposed robust method works comparably to the MLE when there are no outliers and the error is normal. In the second project, we propose a new robust mixture of linear mixed-effects models. The traditional mixture model with multiple linear mixed effects, assuming Gaussian distribution for random and error parts, is sensitive to outliers. We will propose a mixture of multiple linear mixed t-distributions to robustify the estimation procedure. An EM algorithm is provided to and the MLE under the assumption of t- distributions for error terms and random mixed effects. Furthermore, we propose to adaptively choose the degrees of freedom for the t-distribution using profile likelihood. In the simulation study, we demonstrate that our proposed model works comparably to the traditional estimation method when there are no outliers and the errors and random mixed effects are normally distributed, but works much better if there are outliers or the distributions of the errors and random mixed effects have heavy tails

Biomimetic lubricant-infused titania nanoparticle surfaces via layer-by-layer deposition to control biofouling

Lubricant-infused surfaces have attracted a lot of attention in antifouling applications. Previously, lubricant-infused surfaces fabricated by a layer-by-layer process involved two or more polyelectrolytes and needed post-treatments to generate pores. Here, the paper proposes a layer-by-layer sol-gel process to prepare a lubricant-infused surface. This process only involves a single material and without any post-treatment. The nanostructured titania layers were layer-by-layer assembled onto 316L stainless steel substrates by immersing the substrates into a titanium (IV) butoxide ethanol solution. The titania layers were subsequently surface-functionalized by fluorinated silanes and infiltrated with fluorinated lubricant to form lubricant-infused nanoparticle surfaces. The physicochemical properties of the lubricant-infused nanoparticle surfaces dominated the antifouling performance. These results give some insight into the construction of lubricant-infused nanoparticle surfaces with desirable liquid repellency and antifouling properties via a layer-by-layer sol-gel process

Functional Disconnection and Compensation in Mild Cognitive Impairment: Evidence from DLPFC Connectivity Using Resting-State fMRI

The known regional abnormality of the dorsolateral prefrontal cortex (DLPFC) and its role in various neural circuits in mild cognitive impairment (MCI) has given prominence to its importance in studies on the disconnection associated with MCI. The purpose of the current study was to examine the DLPFC functional connectivity patterns during rest in MCI patients and the impact of regional grey matter (GM) atrophy on the functional results. Structural and functional MRI data were collected from 14 MCI patients and 14 age, gender-matched healthy controls. We found that both the bilateral DLPFC showed reduced functional connectivity with the inferior parietal lobule (IPL), superior/medial frontal gyrus and sub-cortical regions (e.g., thalamus, putamen) in MCI patients when compared with healthy controls. Moreover, the DLPFC connectivity with the IPL and thalamus significantly correlated with the cognitive performance of patients as measured by mini-mental state examination (MMSE), clock drawing test (CDT), and California verbal learning test (CVLT) scores. When taking GM atrophy as covariates, these results were approximately consistent with those without correction, although there may be a decrease in the statistical power. These results suggest that the DLPFC disconnections may be the substrates of cognitive impairments in MCI patients. In addition, we also found enhanced functional connectivity between the left DLPFC and the right prefrontal cortex in MCI patients. This is consistent with previous findings of MCI-related increased activation during cognitive tasks, and may represent a compensatory mechanism in MCI patients. Together, the present study demonstrated the coexistence of functional disconnection and compensation in MCI patients using DLPFC functional connectivity analysis, and thus might provide insights into biological mechanism of the disease

Robust mixtures of regressions models

Master of ScienceDepartment of StatisticsWeixin YaoIn the fitting of mixtures of linear regression models, the normal assumption has been traditionally used for the error term and then the regression parameters are estimated by the maximum likelihood estimate (MLE) using the EM algorithm. Under the normal assumption, the M step of the EM algorithm uses a weighted least squares estimate (LSE) for the regression parameters. It is well known that the LSE is sensitive to outliers or heavy tailed error distributions. In this report, we propose a robust mixture of linear regression model, which replaces the least square criterion with some robust criteria in the M step of the EM algorithm. In addition, we will use a simulation study to demonstrate how sensitive the traditional mixture regression estimation method is to outliers or heavy tailed error distributions and compare it with our proposed robust mixture regression estimation method. Based on our empirical studies, our proposed robust estimation method works comparably to the traditional estimation method when there are no outliers and the error is normally distributed but is much better if there are outliers or the error has heavy tails (such as t-distribution). A real data set application is also provided to illustrate the effectiveness of our proposed methodology

Robust fitting of mixture regression models

The existing methods for tting mixture regression models assume a normal dis- tribution for error and then estimate the regression parameters by the maximum likelihood estimate (MLE). In this article, we demonstrate that the MLE, like the least squares estimate, is sensitive to outliers and heavy-tailed error distributions. We propose a robust estimation procedure and an EM-type algorithm to estimate the mixture regression models. Using a Monte Carlo simulation study, we demon-strate that the proposed new estimation method is robust and works much better than the MLE when there are outliers or the error distribution has heavy tails. In addition, the proposed robust method works comparably to the MLE when there are no outliers and the error is normal. A real data application is used to illustrate the success of the proposed robust estimation procedure

Insight into tribological problems of green ship and corresponding research progresses

Abstract The so-called “green ship” is being regarded as a potential solution to the problems that the shipping industry faces, such as energy conservation and environmental protection. Some new features, such as integrated renewable energy application, biomimetic materials, and antifriction and wear resistant coating have been accepted as the typical characteristics of a green ship, but the tribology problems involved in these domains have not been precisely redefined yet. Further, the related research work is generally focused on the technology or material itself, but not on the integration of the applicable object or green ship, marine environment, and tribological systematical analysis from the viewpoint of the energy efficiency design index (EEDI) and ship energy efficiency management plan (SEEMP) improvements. Aiming at the tribology problems of the green ship, this paper reviews the research status of this issue from three specific domains, which are the tribology problems of the renewable energy system, tribological research for hull resistance reduction, and energy efficiency enhancement. Some typical tribological problems in the sail‐auxiliary system are discussed, along with the solar photovoltaic system and hull drag reduction in traditional marine mechanical equipment. Correspondingly, four domains that should be further considered for the future development target of the green ship are prospected

Effect of corrosion on cavitation erosion behavior of HVOF sprayed cobalt-based coatings

Cobalt-based coatings have been widely applied to provide guidance to cavitation erosion (CE) and corrosion resistance since the coatings possessing superior mechanical and anti-corrosion properties. In this study, we prepared cobalt-based alloy (Stellite 21) coating and WC-17Co coating on 1Cr18Ni9Ti by HVOF. The CE resistances were evaluated in deionized water and 3.5 wt% NaCl solution (NaCl solution), and the anti-corrosion properties were studied using polarization tests. Results show that the WC-17Co coating had superior CE resistance than cobalt-based alloy coating in deionized water because of superior microhardness and fracture toughness characteristics. The WC-17Co coating presented much loose corrosion products (W/Co-oxides) in NaCl solution, which prone to be removed by the mechanical effect of the CE and accelerated the coating damage. On the contrary, the compact Cr oxides formed on cobalt-based alloy coating surface in NaCl solution could seal the pores, preventing to formation of erosion pits, and mitigate the damage of CE. Therefore, the cobalt-based alloy coating exhibited the best CE resistance in NaCl solution and had the potential to prevent CE in seawater