Representation via Probabilities: Models of Probabilistic Modeling

How do probabilistic models represent their targets and how do they allow us to learn about them? The answer to this question depends on a number of details, in particular on the meaning of the probabilities involved. To classify the options, a minimalist conception of representation (Su\'arez 2004) is adopted: Modelers devise substitutes (``sources'') of their targets and investigate them to infer something about the target. Probabilistic models allow us to infer probabilities about the target from probabilities about the source. This leads to a framework in which we can systematically distinguish between different models of probabilistic modeling. I develop a fully Bayesian view of probabilistic modeling, but I argue that, as an alternative, Bayesian degrees of belief about the target may be derived from ontic probabilities about the source. Remarkably, some accounts of ontic probabilities can avoid problems if they are supposed to apply to sources only.

Cultural models of healing and health: An ethnography of professional nurses and healers

Cultural models of the domains healing and health are important in how people understand health and their behavior regarding it. The biomedicine model has been predominant in Western society. Recent popularity of holistic health and alternative healing modalities contrasts with the biomedical model and the assumptions upon which that model has been practiced. The holistic health movement characterizes an effort by health care providers and others such as nurses to expand the biomedical model and has often incorporated alternative modalities. This research described and compared the cultural models of healing of professional nurses and alternative healers. A group of nursing faculty who promote a holistic model were compared to a group of healers using healing touch. Ethnographic methods of participant observation, free listing and pile sort were used. Theoretical sampling in the free listings reached saturation at 18 in the group of nurses and 21 in the group of healers. Categories consistent for both groups emerged from the data. These were: physical, mental, attitude, relationships, spiritual, self management, and health seeking including biomedical and alternative resources. The healers had little differentiation between the concepts health and healing. The nurses, however, had more elements in self management for health and in health seeking for healing. This reflects the nurse's role in facilitating the shift in locus of responsibility between health and healing. The healers provided more specific information regarding alternative resources. The healer's conceptualization of health was embedded in a spiritual belief system and contrasted dramatically with that of biomedicine. The healer's models also contrasted with holistic health in the areas of holism, locus of responsibility, and dealing with uncertainty. The similarity between the groups and their dissimilarity to biomedicine suggest a larger cultural shift in beliefs regarding health care. ^

Models of DNA sequence evolution

Models of DNA sequence evolution and methods for estimating evolutionary distances are needed for studying the rate and pattern of molecular evolution and for inferring the evolutionary relationships of organisms or genes. In this dissertation, several new models and methods are developed.^ The rate variation among nucleotide sites: To obtain unbiased estimates of evolutionary distances, the rate heterogeneity among nucleotide sites of a gene should be considered. Commonly, it is assumed that the substitution rate varies among sites according to a gamma distribution (gamma model) or, more generally, an invariant+gamma model which includes some invariable sites. A maximum likelihood (ML) approach was developed for estimating the shape parameter of the gamma distribution $(\alpha)$ and/or the proportion of invariable sites $(\theta).$ Computer simulation showed that (1) under the gamma model, $\alpha$ can be well estimated from 3 or 4 sequences if the sequence length is long; and (2) the distance estimate is unbiased and robust against violations of the assumptions of the invariant+gamma model.^ However, this ML method requires a huge amount of computational time and is useful only for less than 6 sequences. Therefore, I developed a fast method for estimating $\alpha,$ which is easy to implement and requires no knowledge of tree. A computer program was developed for estimating $\alpha$ and evolutionary distances, which can handle the number of sequences as large as 30.^ Evolutionary distances under the stationary, time-reversible (SR) model: The SR model is a general model of nucleotide substitution, which assumes (i) stationary nucleotide frequencies and (ii) time-reversibility. It can be extended to SRV model which allows rate variation among sites. I developed a method for estimating the distance under the SR or SRV model, as well as the variance-covariance matrix of distances. Computer simulation showed that the SR method is better than a simpler method when the sequence length $L>1,000$ bp and is robust against deviations from time-reversibility. As expected, when the rate varies among sites, the SRV method is much better than the SR method.^ The evolutionary distances under nonstationary nucleotide frequencies: The statistical properties of the paralinear and LogDet distances under nonstationary nucleotide frequencies were studied. First, I developed formulas for correcting the estimation biases of the paralinear and LogDet distances. The performances of these formulas and the formulas for sampling variances were examined by computer simulation. Second, I developed a method for estimating the variance-covariance matrix of the paralinear distance, so that statistical tests of phylogenies can be conducted when the nucleotide frequencies are nonstationary. Third, a new method for testing the molecular clock hypothesis was developed in the nonstationary case. ^

A comparison of Markov and generalized linear models of hospital mortality

This paper reports a comparison of three modeling strategies for the analysis of hospital mortality in a sample of general medicine inpatients in a Department of Veterans Affairs medical center. Logistic regression, a Markov chain model, and longitudinal logistic regression were evaluated on predictive performance as measured by the c-index and on accuracy of expected numbers of deaths compared to observed. The logistic regression used patient information collected at admission; the Markov model was comprised of two absorbing states for discharge and death and three transient states reflecting increasing severity of illness as measured by laboratory data collected during the hospital stay; longitudinal regression employed Generalized Estimating Equations (GEE) to model covariance structure for the repeated binary outcome. Results showed that the logistic regression predicted hospital mortality as well as the alternative methods but was limited in scope of application. The Markov chain provides insights into how day to day changes of illness severity lead to discharge or death. The longitudinal logistic regression showed that increasing illness trajectory is associated with hospital mortality. The conclusion is reached that for standard applications in modeling hospital mortality, logistic regression is adequate, but for new challenges facing health services research today, alternative methods are equally predictive, practical, and can provide new insights. ^

Optimizing Models of the North Atlantic Spring Bloom Using Physical, Chemical and Bio-Optical Observations from a Lagrangian Float

The North Atlantic spring bloom is one of the main events that lead to carbon export to the deep ocean and drive oceanic uptake of CO(2) from the atmosphere. Here we use a suite of physical, bio-optical and chemical measurements made during the 2008 spring bloom to optimize and compare three different models of biological carbon export. The observations are from a Lagrangian float that operated south of Iceland from early April to late June, and were calibrated with ship-based measurements. The simplest model is representative of typical NPZD models used for the North Atlantic, while the most complex model explicitly includes diatoms and the formation of fast sinking diatom aggregates and cysts under silicate limitation. We carried out a variational optimization and error analysis for the biological parameters of all three models, and compared their ability to replicate the observations. The observations were sufficient to constrain most phytoplankton-related model parameters to accuracies of better than 15 %. However, the lack of zooplankton observations leads to large uncertainties in model parameters for grazing. The simulated vertical carbon flux at 100 m depth is similar between models and agrees well with available observations, but at 600 m the simulated flux is larger by a factor of 2.5 to 4.5 for the model with diatom aggregation. While none of the models can be formally rejected based on their misfit with the available observations, the model that includes export by diatom aggregation has a statistically significant better fit to the observations and more accurately represents the mechanisms and timing of carbon export based on observations not included in the optimization. Thus models that accurately simulate the upper 100 m do not necessarily accurately simulate export to deeper depths.

ANALYTICAL MODELS OF EXOPLANETARY ATMOSPHERES. I. ATMOSPHERIC DYNAMICS VIA THE SHALLOW WATER SYSTEM

Within the context of exoplanetary atmospheres, we present a comprehensive linear analysis of forced, damped, magnetized shallow water systems, exploring the effects of dimensionality, geometry (Cartesian, pseudo-spherical, and spherical), rotation, magnetic tension, and hydrodynamic and magnetic sources of friction. Across a broad range of conditions, we find that the key governing equation for atmospheres and quantum harmonic oscillators are identical, even when forcing (stellar irradiation), sources of friction (molecular viscosity, Rayleigh drag, and magnetic drag), and magnetic tension are included. The global atmospheric structure is largely controlled by a single key parameter that involves the Rossby and Prandtl numbers. This near-universality breaks down when either molecular viscosity or magnetic drag acts non-uniformly across latitude or a poloidal magnetic field is present, suggesting that these effects will introduce qualitative changes to the familiar chevron-shaped feature witnessed in simulations of atmospheric circulation. We also find that hydrodynamic and magnetic sources of friction have dissimilar phase signatures and affect the flow in fundamentally different ways, implying that using Rayleigh drag to mimic magnetic drag is inaccurate. We exhaustively lay down the theoretical formalism (dispersion relations, governing equations, and time-dependent wave solutions) for a broad suite of models. In all situations, we derive the steady state of an atmosphere, which is relevant to interpreting infrared phase and eclipse maps of exoplanetary atmospheres. We elucidate a pinching effect that confines the atmospheric structure to be near the equator. Our suite of analytical models may be used to develop decisively physical intuition and as a reference point for three-dimensional magnetohydrodynamic simulations of atmospheric circulation.

Analytical Models of Exoplanetary Atmospheres. II. Radiative Transfer via the Two-Stream Approximation

We present a comprehensive analytical study of radiative transfer using the method of moments and include the effects of non-isotropic scattering in the coherent limit. Within this unified formalism, we derive the governing equations and solutions describing two-stream radiative transfer (which approximates the passage of radiation as a pair of outgoing and incoming fluxes), flux-limited diffusion (which describes radiative transfer in the deep interior) and solutions for the temperature-pressure profiles. Generally, the problem is mathematically under-determined unless a set of closures (Eddington coefficients) is specified. We demonstrate that the hemispheric (or hemi-isotropic) closure naturally derives from the radiative transfer equation if energy conservation is obeyed, while the Eddington closure produces spurious enhancements of both reflected light and thermal emission. We concoct recipes for implementing two-stream radiative transfer in stand-alone numerical calculations and general circulation models. We use our two-stream solutions to construct toy models of the runaway greenhouse effect. We present a new solution for temperature-pressure profiles with a non-constant optical opacity and elucidate the effects of non-isotropic scattering in the optical and infrared. We derive generalized expressions for the spherical and Bond albedos and the photon deposition depth. We demonstrate that the value of the optical depth corresponding to the photosphere is not always 2/3 (Milne's solution) and depends on a combination of stellar irradiation, internal heat and the properties of scattering both in optical and infrared. Finally, we derive generalized expressions for the total, net, outgoing and incoming fluxes in the convective regime.

Image-based vs. mesh-based statistical appearance models of the human femur: Implications for finite element simulations.

Statistical appearance models have recently been introduced in bone mechanics to investigate bone geometry and mechanical properties in population studies. The establishment of accurate anatomical correspondences is a critical aspect for the construction of reliable models. Depending on the representation of a bone as an image or a mesh, correspondences are detected using image registration or mesh morphing. The objective of this study was to compare image-based and mesh-based statistical appearance models of the femur for finite element (FE) simulations. To this aim, (i) we compared correspondence detection methods on bone surface and in bone volume; (ii) we created an image-based and a mesh-based statistical appearance models from 130 images, which we validated using compactness, representation and generalization, and we analyzed the FE results on 50 recreated bones vs. original bones; (iii) we created 1000 new instances, and we compared the quality of the FE meshes. Results showed that the image-based approach was more accurate in volume correspondence detection and quality of FE meshes, whereas the mesh-based approach was more accurate for surface correspondence detection and model compactness. Based on our results, we recommend the use of image-based statistical appearance models for FE simulations of the femur.

Functional correction in mouse models of muscular dystrophy using exon-skipping tricyclo-DNA oligomers

Antisense oligonucleotides (AONs) hold promise for therapeutic correction of many genetic diseases via exon skipping, and the first AON-based drugs have entered clinical trials for neuromuscular disorders1, 2. However, despite advances in AON chemistry and design, systemic use of AONs is limited because of poor tissue uptake, and recent clinical reports confirm that sufficient therapeutic efficacy has not yet been achieved. Here we present a new class of AONs made of tricyclo-DNA (tcDNA), which displays unique pharmacological properties and unprecedented uptake by many tissues after systemic administration. We demonstrate these properties in two mouse models of Duchenne muscular dystrophy (DMD), a neurogenetic disease typically caused by frame-shifting deletions or nonsense mutations in the gene encoding dystrophin3, 4 and characterized by progressive muscle weakness, cardiomyopathy, respiratory failure5 and neurocognitive impairment6. Although current naked AONs do not enter the heart or cross the blood-brain barrier to any substantial extent, we show that systemic delivery of tcDNA-AONs promotes a high degree of rescue of dystrophin expression in skeletal muscles, the heart and, to a lesser extent, the brain. Our results demonstrate for the first time a physiological improvement of cardio-respiratory functions and a correction of behavioral features in DMD model mice. This makes tcDNA-AON chemistry particularly attractive as a potential future therapy for patients with DMD and other neuromuscular disorders or with other diseases that are eligible for exon-skipping approaches requiring whole-body treatment.