Comparing probabilistic methods for outlier detection

This paper compares the use of two posterior probability methods to deal with outliers in linear models. We show that putting together diagnostics that come from the mean-shift and variance-shift models yields a procedure that seems to be more effective than the use of probabilities computed from the posterior distributions of actual realized residuals. The relation of the suggested procedure to the use of a certain predictive distribution for diagnostics is derived

A Bayesian look at diagnostics in the univariate linear model

This paper develops diagnostics for data thought to be generated in accordance with the general univariate linear model. A first set of diagnostics is developed by considering posterior probabilities of models that dictate which of k observations form a sample of n observations (k < n/2) are spuriously generated, giving rise to the possible outlyingness of the k observations considered. This in turn gives rise to diagnostics to help assess (estimate) the value of k. A second set of diagnostics is found by using the Kullback-Leibler symmetric divergence, which is found to generate measures of outlyingness and influence. Both sets of diagnostics are compared and related to each other and to other diagnostic statistics suggested in the literature. An example to illustrate to the use of these diagnostic procedures is included

A Bayesian look at diagnostics in the univariate linear model.

This paper develops diagnostics for data thought to be generated in accordance with the general univariate linear model. A first set of diagnostics is developed by considering posterior probabilities of models that dictate which of k observations form a sample of n observations (kspurious and outlying observations; posteriors of models; leverage; Kullback-Leibler measures; outlying and influential observations;

Comparing probabilistic methods for outlier detection.

This paper compares the use of two posterior probability methods to deal with outliers in linear models. We show that putting together diagnostics that come from the mean-shift and variance-shift models yields a procedure that seems to be more effective than the use of probabilities computed from the posterior distributions of actual realized residuals. The relation of the suggested procedure to the use of a certain predictive distribution for diagnostics is derived.Diagnostic; Posterior and Predictive distributions; Leverage; Linear models;

ENRICHING JUDICIAL INDEPENDENCE: SEEKING TO IMPROVE THE RETENTION VOTE PHASE OF AN APPOINTIVE SELECTION SYSTEM

This article discusses the problems and potential solutions with the system of judicial appointment in the state of Nebraska. The article focuses on how improving public awareness about the existing system, its goals, and its current weaknesses, and implementing steps to address those weaknesses, will help to keep everyone moving toward the best possible system. While changing attitudes and interest in judicial retention elections is certainly not an easy task, it is only through seeking such change that reformers of an elective retention system can hope to near its potential effectiveness

A bayesian approach for predicting with polynomial regresión of unknown degree.

This article presents a comparison of four methods to compute the posterior probabilities of the possible orders in polynomial regression models. These posterior probabilities are used for forecasting by using Bayesian model averaging. It is shown that Bayesian model averaging provides a closer relationship between the theoretical coverage of the high density predictive interval (HDPI) and the observed coverage than those corresponding to selecting the best model. The performance of the different procedures are illustrated with simulations and some known engineering data

INFLUENCE OF TISSUE ABSORPTION AND SCATTERING ON DIFFUSE CORRELATION SPECTROSCOPY BLOOD FLOW MEASUREMENTS

This investigation evaluates the influences of optical property assumptions on nearinfrared diffuse correlation spectroscopy (DCS) flow index measurements. Independent variation is induced in optical properties, absorption coefficient (μa) and reduced scattering coefficient (μs’), of liquid phantoms with concurrent measurements of flow indices. A hybrid instrument is incorporated consisting of a dual-wavelength (785 and 830 nm) DCS flow device to obtain flow indices and a frequency-domain tissue-oximeter for optical properties. Flow indices are calculated with measured μa and μs’ or assumed constant μa and μs’. Inaccurate μs’ assumptions produced much larger flow index errors than inaccurate μa. Underestimated/overestimated μs’ from -35%/+175% lead to flow index errors of +110%/-80% and underestimated/overestimated μa from -40%/+150% lead to -20%/+40%, regardless of wavelength. Analysis of a clinical study involving human head and neck tumors indicates flow index errors due to inter-patient optical property variations up to +280%. Collectively, these findings suggest that studies involving significant μa and μs’ changes should measure flow index and optical properties simultaneously to accurately extract blood flow information. This study provides unique insight through the use of liquid phantoms, hybrid instrumentation, incorporation of measurement errors and a generalization into DCS flow index errors due to the influences of optical properties

MULTIMODAL NONCONTACT DIFFUSE OPTICAL REFLECTANCE IMAGING OF BLOOD FLOW AND FLUORESCENCE CONTRASTS

In this study we design a succession of three increasingly adept diffuse optical devices towards the simultaneous 3D imaging of blood flow and fluorescence contrasts in relatively deep tissues. These metrics together can provide future insights into the relationship between blood flow distributions and fluorescent or fluorescently tagged agents. A noncontact diffuse correlation tomography (ncDCT) device was firstly developed to recover flow by mechanically scanning a lens-based apparatus across the sample. The novel flow reconstruction technique and measuring boundary curvature were advanced in tandem. The establishment of CCD camera detection with a high sampling density and flow recovery by speckle contrast followed with the next instrument, termed speckle contrast diffuse correlation tomography (scDCT). In scDCT, an optical switch sequenced coherent near-infrared light into contact-based source fibers around the sample surface. A fully noncontact reflectance mode device finalized improvements by combining noncontact scDCT (nc_scDCT) and diffuse fluorescence tomography (DFT) techniques. In the combined device, a galvo-mirror directed polarized light to the sample surface. Filters and a cross polarizer in stackable tubes promoted extracting flow indices, absorption coefficients, and fluorescence concentrations (indocyanine green, ICG). The scDCT instrumentation was validated through detection of a cubical solid tissue-like phantom heterogeneity beneath a liquid phantom (background) surface where recovery of its center and dimensions agreed with the known values. The combined nc_scDCT/DFT identified both a cubical solid phantom and a tube of stepwise varying ICG concentration (absorption and fluorescence contrast). The tube imaged by nc_scDCT/DFT exhibited expected trends in absorption and fluorescence. The tube shape, orientation, and localization were recovered in general agreement with actuality. The flow heterogeneity localization was successfully extracted and its average relative flow values in agreement with previous studies. Increasing ICG concentrations induced notable disturbances in the tube region (≥ 0.25 μM/1 μM for 785 nm/830 nm) suggesting the graduating absorption (320% increase at 785 nm) introduced errors. We observe that 830 nm is lower in the ICG absorption spectrum and the correspondingly measured flow encountered less influence than 785 nm. From these results we anticipate the best practice in future studies to be utilization of a laser source with wavelength in a low region of the ICG absorption spectrum (e.g., 830 nm) or to only monitor flow prior to ICG injection or post-clearance. In addition, ncDCT was initially tested in a mouse tumor model to examine tumor size and averaged flow changes over a four-day interval. The next steps in forwarding the combined device development include the straightforward automation of data acquisition and filter rotation and applying it to in vivo tumor studies. These animal/clinical models may seek information such as simultaneous detection of tumor flow, fluorescence, and absorption contrasts or analyzing the relationship between variably sized fluorescently tagged nanoparticles and their tumor deposition relationship to flow distributions

A Bayesian Approach for Predicting with Polynomial Regresión of Unknown Degree.

This article presents a comparison of four methods to compute the posterior probabilities of the possible orders in polynomial regression models. These posterior probabilities are used for forecasting by using Bayesian model averaging. It is shown that Bayesian model averaging provides a closer relationship between the theoretical coverage of the high density predictive interval (HDPI) and the observed coverage than those corresponding to selecting the best model. The performance of the different procedures are illustrated with simulations and some known engineering data.

JESUS AND THE VISIBILITY OF GOD: SIGHT AND BELIEF IN THE FOURTH GOSPEL

This thesis establishes the value of the physical incarnation of God for belief. It asserts that the theological nature of belief derives from a God who can make himself physically visible in the world. While scholars have often debated the relationship between the empirical senses and belief in John, few have queried the presuppositions about God’s invisibility that inform their positions. In response, this thesis argues across six chapters that unless God becomes physically visible in Jesus, belief does not obtain. Chapter 1 shows that God himself is ultimately the cause, content, and consequence of the belief that John 20:30-31 describes as the purpose of the Gospel. It establishes the theological nature of belief and thus the fact that the Gospel endeavours to draw humanity close to God via faith in Jesus. The remaining five chapters argue that seeing God in Jesus is both possible and desirable. Chapter 2 re-evaluates the metaphysics of divine visibility in Early Judaism and in John and concludes that God can be physically visible in Jesus’s body. John does not regard divinity as invisible in itself; rather, he claims that seeing Jesus is seeing God. Two long chapters follow and substantiate the claims of Chapter 2. They point up the entwined nature of divine presence and material reality by arguing that Jesus’s body is a divine place. This fact – coupled with John’s depiction of Jesus as a man in divine places – stresses his divinity on earth even as it reveals his localized humanity. Chapter 5 argues that sight itself is the primary catalyst for belief in John. Although human hearts occlude proper vision, seeing remains key to human apprehension of God and belief in him. Chapter 6 draws the foregoing together by arguing that seeing Jesus is seeing God across the Johannine narratives, both despite and because of their deeply counterintuitive climax in the crucifixion