Generalized fiducial inference for normal linear mixed models

While linear mixed modeling methods are foundational concepts introduced in any statistical education, adequate general methods for interval estimation involving models with more than a few variance components are lacking, especially in the unbalanced setting. Generalized fiducial inference provides a possible framework that accommodates this absence of methodology. Under the fabric of generalized fiducial inference along with sequential Monte Carlo methods, we present an approach for interval estimation for both balanced and unbalanced Gaussian linear mixed models. We compare the proposed method to classical and Bayesian results in the literature in a simulation study of two-fold nested models and two-factor crossed designs with an interaction term. The proposed method is found to be competitive or better when evaluated based on frequentist criteria of empirical coverage and average length of confidence intervals for small sample sizes. A MATLAB implementation of the proposed algorithm is available from the authors.Comment: Published in at http://dx.doi.org/10.1214/12-AOS1030 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

A Preferential Attachment Model for the Stellar Initial Mass Function

Accurate specification of a likelihood function is becoming increasingly difficult in many inference problems in astronomy. As sample sizes resulting from astronomical surveys continue to grow, deficiencies in the likelihood function lead to larger biases in key parameter estimates. These deficiencies result from the oversimplification of the physical processes that generated the data, and from the failure to account for observational limitations. Unfortunately, realistic models often do not yield an analytical form for the likelihood. The estimation of a stellar initial mass function (IMF) is an important example. The stellar IMF is the mass distribution of stars initially formed in a given cluster of stars, a population which is not directly observable due to stellar evolution and other disruptions and observational limitations of the cluster. There are several difficulties with specifying a likelihood in this setting since the physical processes and observational challenges result in measurable masses that cannot legitimately be considered independent draws from an IMF. This work improves inference of the IMF by using an approximate Bayesian computation approach that both accounts for observational and astrophysical effects and incorporates a physically-motivated model for star cluster formation. The methodology is illustrated via a simulation study, demonstrating that the proposed approach can recover the true posterior in realistic situations, and applied to observations from astrophysical simulation data

Nutrient Related Mechanisms of Intervertebral Disc Degeneration

The intervertebral disc (IVD) separates the vertebrae allowing flexibility, strength, as well as a wide range of mechanical motion in the spine. Millions of Americans are afflicted with IVD degeneration which can cause low back pain and limited functionality of the spine. Deviation from physiological nutrient levels due to abnormal mechanical loading and age is believed to be one of the main mechanisms for low back pain associated disc degeneration. Since the IVD is the largest avascular structure in the body, transport of nutrients (e.g., O2 and glucose) is primarily done through the passive transport mechanism of diffusion. Transport of nutrients and solutes through the extracellular matrix is important in maintaining the normal function of tissues, so deviation from physiological levels can cause tissue necrosis and matrix degradation. The objective of this research is to investigate the effect of mechanical loading on nutrient transport and cell nutrition of the IVD in order to develop a 3D imaging based finite element model to better understand in vivo fluid and nutrient transport within the human IVD as well as the biomechanical etiology of disc degeneration. Therefore, our central hypothesis is that sustained mechanical loading can alter solute transport and nutrient concentrations in the IVD, resulting in changes to the cellular metabolism, tissue composition, and mechanical function, ultimately leading to disc degeneration in the human IVD disc. To address this hypothesis, this dissertation established a set of aims including; Aim 1: Determine the metabolic phenotype of human IVD cells. Aim 2: Examine the effect of mechanical strains on glucose and lactate diffusivity values of the cartilage endplate region of human IVDs in vitro. Aim 3: Develop and validate a 3D multiphasic mechano-electrochemical finite element model of the human IVD to quantify and predict changes in nutrient levels under various loading conditions that occur in vivo. The ultimate goal of this project is to characterize the nutrient diffusivities and metabolic phenotype of the IVD to develop and validate a 3D multiphasic mechano-electrochemical finite element model in an effort to quantify and predict changes in nutrient levels under various loading conditions that occur in vivo and better understand low back pain associated disc degeneration. The outcome of this study will yield 1) a new realistic anisotropic mechano-electrochemical theory and finite element model for investigating the transport of fluid and solutes in human IVDs under various loading conditions and 2) the first study to characterize the effect of mechanical strains on nutrient diffusivity values of the cartilage endplate region of human IVDs in vitro. Finally, the project will bring a human biomechanical model for improving clinical diagnosis of disc degeneration

Acoustic insights into the zooplankton dynamics of the eastern Weddell Sea

The success of any efforts to determine the effects of climate change on marine ecosystems depends on understanding in the first instance the natural variations, which contemporarily occur on the interannual and shorter time scales. Here we present results on the environmental controls of zooplankton distribution patterns and behaviour in the eastern Weddell Sea, Southern Ocean. Zooplankton abundance and vertical migration are derived from the mean volume backscattering strength (MVBS) and the vertical velocity measured by moored acoustic Doppler current profilers (ADCPs), which were deployed simultaneously at 64°S, 66.5°S and 69°S along the Greenwich Meridian from February, 2005, until March, 2008. While these time series span a period of full three years they resolve hourly changes. A highly persistent behavioural pattern found at all three mooring locations is the synchronous diel vertical migration (DVM) of two distinct groups of zooplankton that migrate between a deep residence depth during daytime and a shallow depth during nighttime. The DVM was closely coupled to the astronomical daylight cycles. However, while the DVM was symmetric around local noon, the annual modulation of the DVM was clearly asymmetric around winter solstice or summer solstice, respectively, at all three mooring sites. DVM at our observation sites persisted throughout winter, even at the highest latitude exposed to the polar night. Since the magnitude as well as the relative rate of change of illumination is minimal at this time, we propose that the ultimate causes of DVM separated from the light-mediated proximal cue that coordinates it. In all three years, a marked change in the migration behaviour occurred in late spring (late October/early November), when DVM ceased. The complete suspension of DVM after early November is possibly caused by the combination of two factors: (1) increased availability of food in the surface mixed layer provided by the phytoplankton spring bloom, and (2) vanishing diurnal enhancement of the threat from visually oriented predators when the illumination is quasi-continuous during the polar and subpolar summer. Zooplankton abundance in the water column, estimated as the mean MVBS in the depth range 50–300 m, was highest end of summer and lowest mid to end winter on the average annual cycle. However, zooplankton abundance varied several-fold between years and between locations. Based on satellite and in situ data of chlorophyll and sea ice as well as on hydrographic measurements, the interannual and spatial variations of zooplankton mean abundance can be explained by differences in the magnitude of the phytoplankton spring bloom, which develops during the seasonal sea ice retreat. Whereas the vernal ice melt appears necessary to stimulate the blooming of phytoplankton, it is not the determinator of the blooms magnitude, its areal extent and duration. A possible explanation for the limitation of the phytoplankton bloom in some years is top-down control. We hypothesise that the phytoplankton spring development can be curbed by grazing when the zooplankton had attained high abundance by growth during the preceding summer

Meridional and interannual variations of the seasonally modulated Zooplankton diel vertical migration in the Lazarev Sea and their possible physical-biological controls

Acoustic Doppler current profilers (ADCPs) not only take measurements of the water velocity components but also of the backscatter strength, which can be used to infer distribution patterns of zooplankton and small nekton. Here we present results obtained from ADCPs that were moored at 64°S, 66.5°S and 69°S along the Greenwich Meridian during the three-years period February 2005 until March 2008. A diel vertical migration (DVM) pattern – downward at dawn and upward at dusk - of two distinct groups of migrators persisted during most part of the years at all moorings sites, closely related to the astronomical daylight cycles. While the DVM was symmetric around local noon, the annual modulation of the DVM was asymmetric relative to the summer/winter solstices at the three mooring sites. This annual asymmetry resulted from a change in the migration behaviour that occurred in late spring (October - November), when the DVM ceases for around three months. In contrast to many previous studies in other regions, DVM at our observation sites persisted throughout winter, even at the highest latitude during the polar night. Using in-situ physical and biological data collected during deployment and recovery of the moorings, ice-thickness time series measured by Upward Looking Sonars, and satellite maps of remotely sensed sea ice coverage and surface chlorophyll concentration we can explain part of the seasonal to interannual variations in the inferred zooplankton distribution patterns by environmental cues. For a more complete explanation of the observed organisms’ behaviour, however, we hypothesize controls by internal drivers that need also be taken into account

The Eccentricity Distribution of Short-Period Planet Candidates Detected by Kepler in Occultation

We characterize the eccentricity distribution of a sample of ~50 short-period planet candidates using transit and occultation measurements from NASA's Kepler Mission. First, we evaluate the sensitivity of our hierarchical Bayesian modeling and test its robustness to model misspecification using simulated data. When analyzing actual data assuming a Rayleigh distribution for eccentricity, we find that the posterior mode for the dispersion parameter is $\sigma=0.081 \pm^{0.014}_{0.003}$. We find that a two-component Gaussian mixture model for $e \cos \omega$ and $e \sin \omega$ provides a better model than either a Rayleigh or Beta distribution. Based on our favored model, we find that $\sim90\%$ of planet candidates in our sample come from a population with an eccentricity distribution characterized by a small dispersion ($\sim0.01$), and $\sim10\%$ come from a population with a larger dispersion ($\sim0.22$). Finally, we investigate how the eccentricity distribution correlates with selected planet and host star parameters. We find evidence that suggests systems around higher metallicity stars and planet candidates with smaller radii come from a more complex eccentricity distribution.Comment: Accepted for publication in Ap