Statistical inference for the optimal approximating model

In the setting of high-dimensional linear models with Gaussian noise, we investigate the possibility of confidence statements connected to model selection. Although there exist numerous procedures for adaptive (point) estimation, the construction of adaptive confidence regions is severely limited (cf. Li in Ann Stat 17:1001–1008, 1989). The present paper sheds new light on this gap. We develop exact and adaptive confidence regions for the best approximating model in terms of risk. One of our constructions is based on a multiscale procedure and a particular coupling argument. Utilizing exponential inequalities for noncentral χ2-distributions, we show that the risk and quadratic loss of all models within our confidence region are uniformly bounded by the minimal risk times a factor close to one.

Automatic Segmentation of the Eye in 3D Magnetic Resonance Imaging: A novel Statistical Shape Model for treatment planning of Retinoblastoma

Purpose: Proper delineation of ocular anatomy in 3D imaging is a big challenge, particularly when developing treatment plans for ocular diseases. Magnetic Resonance Imaging (MRI) is nowadays utilized in clinical practice for the diagnosis confirmation and treatment planning of retinoblastoma in infants, where it serves as a source of information, complementary to the Fundus or Ultrasound imaging. Here we present a framework to fully automatically segment the eye anatomy in the MRI based on 3D Active Shape Models (ASM), we validate the results and present a proof of concept to automatically segment pathological eyes. Material and Methods: Manual and automatic segmentation were performed on 24 images of healthy children eyes (3.29±2.15 years). Imaging was performed using a 3T MRI scanner. The ASM comprises the lens, the vitreous humor, the sclera and the cornea. The model was fitted by first automatically detecting the position of the eye center, the lens and the optic nerve, then aligning the model and fitting it to the patient. We validated our segmentation method using a leave-one-out cross validation. The segmentation results were evaluated by measuring the overlap using the Dice Similarity Coefficient (DSC) and the mean distance error. Results: We obtained a DSC of 94.90±2.12% for the sclera and the cornea, 94.72±1.89% for the vitreous humor and 85.16±4.91% for the lens. The mean distance error was 0.26±0.09mm. The entire process took 14s on average per eye. Conclusion: We provide a reliable and accurate tool that enables clinicians to automatically segment the sclera, the cornea, the vitreous humor and the lens using MRI. We additionally present a proof of concept for fully automatically segmenting pathological eyes. This tool reduces the time needed for eye shape delineation and thus can help clinicians when planning eye treatment and confirming the extent of the tumor.

Articulated Statistical Shape Model-Based 2D-3D Reconstruction of a Hip Joint

In this paper, reconstruction of three-dimensional (3D) patient-specific models of a hip joint from two-dimensional (2D) calibrated X-ray images is addressed. Existing 2D-3D reconstruction techniques usually reconstruct a patient-specific model of a single anatomical structure without considering the relationship to its neighboring structures. Thus, when those techniques would be applied to reconstruction of patient-specific models of a hip joint, the reconstructed models may penetrate each other due to narrowness of the hip joint space and hence do not represent a true hip joint of the patient. To address this problem we propose a novel 2D-3D reconstruction framework using an articulated statistical shape model (aSSM). Different from previous work on constructing an aSSM, where the joint posture is modeled as articulation in a training set via statistical analysis, here it is modeled as a parametrized rotation of the femur around the joint center. The exact rotation of the hip joint as well as the patient-specific models of the joint structures, i.e., the proximal femur and the pelvis, are then estimated by optimally fitting the aSSM to a limited number of calibrated X-ray images. Taking models segmented from CT data as the ground truth, we conducted validation experiments on both plastic and cadaveric bones. Qualitatively, the experimental results demonstrated that the proposed 2D-3D reconstruction framework preserved the hip joint structure and no model penetration was found. Quantitatively, average reconstruction errors of 1.9 mm and 1.1 mm were found for the pelvis and the proximal femur, respectively.

Non-rigid Free-Form 2D-3D Registration Using Statistical Deformation Model

This paper presents a non-rigid free-from 2D-3D registration approach using statistical deformation model (SDM). In our approach the SDM is first constructed from a set of training data using a non-rigid registration algorithm based on b-spline free-form deformation to encode a priori information about the underlying anatomy. A novel intensity-based non-rigid 2D-3D registration algorithm is then presented to iteratively fit the 3D b-spline-based SDM to the 2D X-ray images of an unseen subject, which requires a computationally expensive inversion of the instantiated deformation in each iteration. In this paper, we propose to solve this challenge with a fast B-spline pseudo-inversion algorithm that is implemented on graphics processing unit (GPU). Experiments conducted on C-arm and X-ray images of cadaveric femurs demonstrate the efficacy of the present approach.

Assessment of the effect on statistical power of regression model misspecification by using techniques of mathematical statistics and simulation study

Objectives. This paper seeks to assess the effect on statistical power of regression model misspecification in a variety of situations. ^ Methods and results. The effect of misspecification in regression can be approximated by evaluating the correlation between the correct specification and the misspecification of the outcome variable (Harris 2010).In this paper, three misspecified models (linear, categorical and fractional polynomial) were considered. In the first section, the mathematical method of calculating the correlation between correct and misspecified models with simple mathematical forms was derived and demonstrated. In the second section, data from the National Health and Nutrition Examination Survey (NHANES 2007-2008) were used to examine such correlations. Our study shows that comparing to linear or categorical models, the fractional polynomial models, with the higher correlations, provided a better approximation of the true relationship, which was illustrated by LOESS regression. In the third section, we present the results of simulation studies that demonstrate overall misspecification in regression can produce marked decreases in power with small sample sizes. However, the categorical model had greatest power, ranging from 0.877 to 0.936 depending on sample size and outcome variable used. The power of fractional polynomial model was close to that of linear model, which ranged from 0.69 to 0.83, and appeared to be affected by the increased degrees of freedom of this model.^ Conclusion. Correlations between alternative model specifications can be used to provide a good approximation of the effect on statistical power of misspecification when the sample size is large. When model specifications have known simple mathematical forms, such correlations can be calculated mathematically. Actual public health data from NHANES 2007-2008 were used as examples to demonstrate the situations with unknown or complex correct model specification. Simulation of power for misspecified models confirmed the results based on correlation methods but also illustrated the effect of model degrees of freedom on power.^

A statistical mechanical model for β-hairpin kinetics

Understanding the mechanism of protein secondary structure formation is an essential part of the protein-folding puzzle. Here, we describe a simple statistical mechanical model for the formation of a β-hairpin, the minimal structural element of the antiparallel β-pleated sheet. The model accurately describes the thermodynamic and kinetic behavior of a 16-residue, β-hairpin-forming peptide, successfully explaining its two-state behavior and apparent negative activation energy for folding. The model classifies structures according to their backbone conformation, defined by 15 pairs of dihedral angles, and is further simplified by considering only the 120 structures with contiguous stretches of native pairs of backbone dihedral angles. This single sequence approximation is tested by comparison with a more complete model that includes the 215 possible conformations and 15 × 215 possible kinetic transitions. Finally, we use the model to predict the equilibrium unfolding curves and kinetics for several variants of the β-hairpin peptide.

Statistical tests of load-unload response ratio signals by lattice solid model: Implication to tidal triggering and earthquake prediction

Statistical tests of Load-Unload Response Ratio (LURR) signals are carried in order to verify statistical robustness of the previous studies using the Lattice Solid Model (MORA et al., 2002b). In each case 24 groups of samples with the same macroscopic parameters (tidal perturbation amplitude A, period T and tectonic loading rate k) but different particle arrangements are employed. Results of uni-axial compression experiments show that before the normalized time of catastrophic failure, the ensemble average LURR value rises significantly, in agreement with the observations of high LURR prior to the large earthquakes. In shearing tests, two parameters are found to control the correlation between earthquake occurrence and tidal stress. One is, A/(kT) controlling the phase shift between the peak seismicity rate and the peak amplitude of the perturbation stress. With an increase of this parameter, the phase shift is found to decrease. Another parameter, AT/k, controls the height of the probability density function (Pdf) of modeled seismicity. As this parameter increases, the Pdf becomes sharper and narrower, indicating a strong triggering. Statistical studies of LURR signals in shearing tests also suggest that except in strong triggering cases, where LURR cannot be calculated due to poor data in unloading cycles, the larger events are more likely to occur in higher LURR periods than the smaller ones, supporting the LURR hypothesis.