Jiayang Sun

Bayesian Model Selection in Finite Mixtures by Marginal Density Decompositions

We consider the problem of estimating the number of components d and the unknown mixing distribution in a finite mixture model, in which d is bounded by some fixed finite number N. Our approach relies on the use of a prior over the space of mixing distributions with at most N components. By decomposing the resulting marginal density under this prior, we discover a weighted Bayes factor method for consistently estimating d that can be implemented by an iid generalized weighted Chinese restaurant (GWCR) Monte Carlo algorithm. We also discuss a Gibbs sampling method (the blocked Gibbs sampler) for estimating d and also the mixing distribution. We show that our resulting posterior is consistent and achieves the frequentist optimal Op (n−1/4) rate of estimation. We compare the performance of the new GWCR model selection procedure with that of the Akaike information criterion and the Bayes information criterion implemented through an EM algorithm. Applications of our methods to five real datasets and simulations are considered.

Functional corticomuscular connection during reaching is weakened following stroke

OBJECTIVE To investigate the functional connection between motor cortex and muscles, we measured electroencephalogram-electromyogram (EEG-EMG) coherence of stroke patients and controls. METHODS Eight healthy controls and 21 patients with shoulder and elbow coordination deficits were enrolled. All subjects performed a reaching task involving shoulder flexion and elbow extension. EMG of the anterior deltoid (AD) and brachii muscles (BB, TB) and 64-channel scalp EEG were recorded during the task. Time-frequency coherence was calculated using the bivariate autoregressive model. RESULTS Stroke patients had significantly lower corticomuscular coherence compared with healthy controls for the AD and BB muscles at both the beta (20-30 Hz) and lower gamma (30-40 Hz) bands during the movement. BH procedure (FDR) identified a reduced corticomuscular coherence for stroke patients in 11 of 15 scalp area-muscle combinations. There was no statistically significant difference between stroke patients and control subjects according to coherence in other frequency bands. CONCLUSION Poorly recovered stroke survivors with persistent upper-limb motor deficits exhibited significantly lower gamma-band corticomuscular coherence in performing a reaching task. SIGNIFICANCE The study suggests poor brain-muscle communication or poor integration of the EEG and EMG signals in higher frequency band during reaching task may reflect an underlying mechanism producing movement deficits post-stroke.

Fatigue induces greater brain signal reduction during sustained than preparation phase of maximal voluntary contraction

Animal studies have shown that there are cell populations only discharging phasically before a motor task and others only active tonically during holding phase of the task. How muscle fatigue influences these two types of cell populations, however, is unknown. Because the phasic neurons are only active briefly before the task but the tonic ones are active continuously throughout the task, we hypothesized that fatigue would have a less effect on cortical signals during the preparation phase (representing phasic discharge) than that during the sustained phase (representing tonic discharge). Eight participants performed 200 handgrip maximal voluntary contractions (MVCs) with simultaneous recordings of scalp electroencephalographic (EEG), handgrip force, and finger flexor surface electromyographic (EMG) signals. Power spectrograms of the EEG during the preparation and sustained phases were analyzed in each of the five 40-trial blocks, with data from the first block representing a condition of moderate fatigue and the last, severe fatigue. Movement-related cortical potential (MRCP) was derived by trigger-averaging 40 EEG epochs in each block. The power of all EEG frequencies did not alter significantly during the preparation phase but decreased significantly during the sustained phase of the contraction. The MRCP negative potential (NP) related to motor task preparation only showed minimal changes. These results suggest that MVC-induced fatigue has differential effects on cortical signals during motor task preparation compared to its execution and maintenance. The signals of the two phases may represent activities of the two cortical cell populations previously found by animal studies.

New technique for real-time interface pressure analysis: Getting more out of large image data sets

Recent technological improvements have led to increasing clinical use of interface pressure mapping for seating pressure evaluation, which often requires repeated assessments. However, clinical conditions cannot be controlled as closely as research settings, thereby creating challenges to statistical analysis of data. A multistage longitudinal analysis and self-registration (LASR) technique is introduced that emphasizes real-time interface pressure image analysis in three dimensions. Suitable for use in clinical settings, LASR is composed of several modern statistical components, including a segmentation method. The robustness of our segmentation method is also shown. Application of LASR to analysis of data from neuromuscular electrical stimulation (NMES) experiments confirms that NMES improves static seating pressure distributions in the sacral-ischial region over time. Dynamic NMES also improves weight-shifting over time. These changes may reduce the risk of pressure ulcer development.

Crowdsourcing Awareness: Exploration of the Ovarian Cancer Knowledge Gap through Amazon Mechanical Turk

Background Ovarian cancer is the most lethal gynecologic disease in the United States, with more women dying from this cancer than all gynecological cancers combined. Ovarian cancer has been termed the “silent killer” because some patients do not show clear symptoms at an early stage. Currently, there is a lack of approved and effective early diagnostic tools for ovarian cancer. There is also an apparent severe knowledge gap of ovarian cancer in general and of its indicative symptoms among both public and many health professionals. These factors have significantly contributed to the late stage diagnosis of most ovarian cancer patients (63% are diagnosed at Stage III or above), where the 5-year survival rate is less than 30%. The paucity of knowledge concerning ovarian cancer in the United States is unknown. Methods The present investigation examined current public awareness and knowledge about ovarian cancer. The study implemented design strategies to develop an unbiased survey with quality control measures, including the modern application of multiple statistical analyses. The survey assessed a reasonable proxy of the US population by crowdsourcing participants through the online task marketplace Amazon Mechanical Turk, at a highly condensed rate of cost and time compared to traditional recruitment methods. Conclusion Knowledge of ovarian cancer was compared to that of breast cancer using repeated measures, bias control and other quality control measures in the survey design. Analyses included multinomial logistic regression and categorical data analysis procedures such as correspondence analysis, among other statistics. We confirmed the relatively poor public knowledge of ovarian cancer among the US population. The simple, yet novel design should set an example for designing surveys to obtain quality data via Amazon Mechanical Turk with the associated analyses.

Simultaneous Confidence Bands for Linear Regression with Heteroscedastic Errors

Abstract The Scheffe method may be used to construct simultaneous confidence bands for a regression surface for the whole predictor space. When the bands need only hold for a subset of that space, previous authors have described how the bands can be appropriately narrowed while still maintaining the desired level of confidence. Data with heteroscedastic errors occur often, and unless some transformation is feasible, there is no obvious way to construct bands using the current methods. This article shows how to construct approximate simultaneous confidence bands when the errors are heteroscedastic and symmetric. The method works when the weights are known or unknown and have to be estimated. The region in which the bands must hold can be quite general and will work for any linear unbiased estimate of the regression surface. The method can even be extended to linear estimates with a small amount of bias such as nonparametric kernel regression smoothers.

Adaptive smoothing for a penalized NPMLE of a non-increasing density

Abstract A penalized version of the well-known non-parametric maximum likelihood estimator of a non-increasing density f has been developed recently. The penalized version depends on a smoothing parameter, as well as the data. Here some adaptive choices of the smoothing parameter are considered. The asymptotically optimal smoothing parameter depends on f through β = − 1 2 f(0) f′(0) . In the adaptive procedures, estimates of β are used to determine the smoothing parameter. Two such procedures are shown to be theoretically correct and practically viable.

A semi-local paradigm for wavelet denoising

Wavelet denoising methods have been proven useful for many one- and two-dimensional problems. Most existing methods can in principle be carried over to three-dimensional problems, such as the denoising of volumetric positron emission tomography (PET) images, but they may not be sufficiently flexible in allowing some regions of an image to be denoised more aggressively than others. In this paper, we propose a semi-local paradigm for wavelet denoising. The semi-local paradigm involves the division of an image into suitable blocks, which are then individually denoised. To denoise the blocks, we use our modification of the generalized cross validation (GCV) technique of Jansen and Bultheel to choose thresholding parameters; we also present risk estimators to guide some of the other choices involved in the implementation. Experiments with phantom PET images show that the semi-local paradigm provides superior denoising compared to standard application of the GCV technique. An asymptotic analysis demonstrates that, under some regularity conditions, semi-local denoising is asymptotically consistent on the logarithmic scale. The paper concludes with a discussion on the nature of semi-local denoising and some topics for future research.

Robustness of Tube Formula Based Confidence Bands

Abstract Simultaneous confidence bands of a regression curve may be used to quantify the uncertainty of an estimate of the curve. The tube formula for volumes of tubular neighborhoods of a manifold provides a very powerful method for obtaining such bands at a prescribed level, when errors are Gaussian. This article studies robustness of the tube formula for non-Gaussian errors. The formula holds without modification for an error vector with a spherically symmetric distribution. Simulations are used for a variety of independent non-Gaussian error distributions. The results are acceptable for contaminated and heavy tailed error distributions. The formula can break down in some extreme cases for discrete and highly skewed errors. Computational issues involved in applying the tube formula are also discussed.

Sums and maxima of discrete stationary processes

This paper considers the joint limiting behavior of sums and maxima of stationary discrete-valued processes. The asymptotic behavior is a cross between a central limit theorem and asymptotic bounds for the distribution of the maxima. Some applications and simulations are also included. DISCRETE ARMA PROCESSES; EXTREME VALUES; LIMITING DISTRIBUTIONS AMS 1991 SUBJECT CLASSIFICATION: PRIMARY 60F05 SECONDARY 62 E20, 62 M 10