Approximate Bayesian Computation for astronomical model analysis : a case study in galaxy demographics and morphological transformation at high redshift

Approximate Bayesian Computation’ (ABC) represents a powerful methodology for the analysis of complex stochastic systems for which the likelihood of the observed data under an arbitrary set of input parameters may be entirely intractable – the latter condition rendering useless the standard machinery of tractable likelihood-based, Bayesian statistical inference [e.g. conventional Markov chain Monte Carlo (MCMC) simulation]. In this paper, we demonstrate the potential of ABC for astronomical model analysis by application to a case study in the morphological transformation of high-redshift galaxies. To this end, we develop, first, a stochastic model for the competing processes of merging and secular evolution in the early Universe, and secondly, through an ABC-based comparison against the observed demographics of massive (Mgal > 1011 M⊙) galaxies (at 1.5 < z < 3) in the Cosmic Assembly Near-IR Deep Extragalatic Legacy Survey (CANDELS)/Extended Groth Strip (EGS) data set we derive posterior probability densities for the key parameters of this model. The ‘Sequential Monte Carlo’ implementation of ABC exhibited herein, featuring both a self-generating target sequence and self-refining MCMC kernel, is amongst the most efficient of contemporary approaches to this important statistical algorithm. We highlight as well through our chosen case study the value of careful summary statistic selection, and demonstrate two modern strategies for assessment and optimization in this regard. Ultimately, our ABC analysis of the high-redshift morphological mix returns tight constraints on the evolving merger rate in the early Universe and favours major merging (with disc survival or rapid reformation) over secular evolution as the mechanism most responsible for building up the first generation of bulges in early-type discs.

Temporal Characterization of Ossification of the Crania in Australian Subadults: New standards for Age Estimation using Computed Tomography

After attending this presentation, attendees will gain awareness of the ontogeny of cranial maturation, specifically: (1) the fusion timings of primary ossification centers in the basicranium; and (2) the temporal pattern of closure of the anterior fontanelle, to develop new population-specific age standards for medicolegal death investigation of Australian subadults. This presentation will impact the forensic science community by demonstrating the potential of a contemporary forensic subadult Computed Tomography (CT) database of cranial scans and population data, to recalibrate existing standards for age estimation and quantify growth and development of Australian children. This research welcomes a study design applicable to all countries faced with paucity in skeletal repositories. Accurate assessment of age-at-death of skeletal remains represents a key element in forensic anthropology methodology. In Australian casework, age standards derived from American reference samples are applied in light of scarcity in documented Australian skeletal collections. Currently practitioners rely on antiquated standards, such as the Scheuer and Black1 compilation for age estimation, despite implications of secular trends and population variation. Skeletal maturation standards are population specific and should not be extrapolated from one population to another, while secular changes in skeletal dimensions and accelerated maturation underscore the importance of establishing modern standards to estimate age in modern subadults. Despite CT imaging becoming the gold standard for skeletal analysis in Australia, practitioners caution the application of forensic age standards derived from macroscopic inspection to a CT medium, suggesting a need for revised methodologies. Multi-slice CT scans of subadult crania and cervical vertebrae 1 and 2 were acquired from 350 Australian individuals (males: n=193, females: n=157) aged birth to 12 years. The CT database, projected at 920 individuals upon completion (January 2014), comprises thin-slice DICOM data (resolution: 0.5/0.3mm) of patients scanned since 2010 at major Brisbane Childrens Hospitals. DICOM datasets were subject to manual segmentation, followed by the construction of multi-planar and volume rendering cranial models, for subsequent scoring. The union of primary ossification centers of the occipital bone were scored as open, partially closed or completely closed; while the fontanelles, and vertebrae were scored in accordance with two stages. Transition analysis was applied to elucidate age at transition between union states for each center, and robust age parameters established using Bayesian statistics. In comparison to reported literature, closure of the fontanelles and contiguous sutures in Australian infants occur earlier than reported, with the anterior fontanelle transitioning from open to closed at 16.7±1.1 months. The metopic suture is closed prior to 10 weeks post-partum and completely obliterated by 6 months of age, independent of sex. Utilizing reverse engineering capabilities, an alternate method for infant age estimation based on quantification of fontanelle area and non-linear regression with variance component modeling will be presented. Closure models indicate that the greatest rate of change in anterior fontanelle area occurs prior to 5 months of age. This study complements the work of Scheuer and Black1, providing more specific age intervals for union and temporal maturity of each primary ossification center of the occipital bone. For example, dominant fusion of the sutura intra-occipitalis posterior occurs before 9 months of age, followed by persistence of a hyaline cartilage tongue posterior to the foramen magnum until 2.5 years; with obliteration at 2.9±0.1 years. Recalibrated age parameters for the atlas and axis are presented, with the anterior arch of the atlas appearing at 2.9 months in females and 6.3 months in males; while dentoneural, dentocentral and neurocentral junctions of the axis transitioned from non-union to union at 2.1±0.1 years in females and 3.7±0.1 years in males. These results are an exemplar of significant sexual dimorphism in maturation (p<0.05), with girls exhibiting union earlier than boys, justifying the need for segregated sex standards for age estimation. Studies such as this are imperative for providing updated standards for Australian forensic and pediatric practice and provide an insight into skeletal development of this population. During this presentation, the utility of novel regression models for age estimation of infants will be discussed, with emphasis on three-dimensional modeling capabilities of complex structures such as fontanelles, for the development of new age estimation methods.

Model choice problems using approximate Bayesian computation with applications to pathogen transmission data sets

Analytically or computationally intractable likelihood functions can arise in complex statistical inferential problems making them inaccessible to standard Bayesian inferential methods. Approximate Bayesian computation (ABC) methods address such inferential problems by replacing direct likelihood evaluations with repeated sampling from the model. ABC methods have been predominantly applied to parameter estimation problems and less to model choice problems due to the added difficulty of handling multiple model spaces. The ABC algorithm proposed here addresses model choice problems by extending Fearnhead and Prangle (2012, Journal of the Royal Statistical Society, Series B 74, 1–28) where the posterior mean of the model parameters estimated through regression formed the summary statistics used in the discrepancy measure. An additional stepwise multinomial logistic regression is performed on the model indicator variable in the regression step and the estimated model probabilities are incorporated into the set of summary statistics for model choice purposes. A reversible jump Markov chain Monte Carlo step is also included in the algorithm to increase model diversity for thorough exploration of the model space. This algorithm was applied to a validating example to demonstrate the robustness of the algorithm across a wide range of true model probabilities. Its subsequent use in three pathogen transmission examples of varying complexity illustrates the utility of the algorithm in inferring preference of particular transmission models for the pathogens.

Varenicline decreases ethanol intake and increases dopamine release via neuronal nicotinic acetylcholine receptors in the nucleus accumbens

BACKGROUND AND PURPOSE Varenicline, a neuronal nicotinic acetylcholine receptor (nAChR) modulator, decreases ethanol consumption in rodents and humans. The proposed mechanism of action for varenicline to reduce ethanol consumption has been through modulation of dopamine (DA) release in the nucleus accumbens (NAc) via α4*-containing nAChRs in the ventral tegmental area (VTA). However, presynaptic nAChRs on dopaminergic terminals in the NAc have been shown to directly modulate dopaminergic signalling independently of neuronal activity from the VTA. In this study, we determined whether nAChRs in the NAc play a role in varenicline’s effects on ethanol consumption. EXPERIMENTAL APPROACH Rats were trained to consume ethanol using the intermittent-access two-bottle choice protocol for 10 weeks. Ethanol intake was measured after varenicline or vehicle was microinfused into the NAc (core, shell or core-shell border) or the VTA (anterior or posterior). The effect of varenicline treatment on DA release in the NAc was measured using both in vivo microdialysis and in vitro fast-scan cyclic voltammetry (FSCV). KEY RESULTS Microinfusion of varenicline into the NAc core and core-shell border, but not into the NAc shell or VTA, reduced ethanol intake following long-term ethanol consumption. During microdialysis, a significant enhancement in accumbal DA release occurred following systemic administration of varenicline and FSCV showed that varenicline also altered the evoked release of DA in the NAc. CONCLUSION AND IMPLICATIONS Following long-term ethanol consumption, varenicline in the NAc reduces ethanol intake, suggesting that presynaptic nAChRs in the NAc are important for mediating varenicline’s effects on ethanol consumption.

Can measures of limb loading and dynamic stability during the squat maneuver provide an index of early functional recovery following unilateral total hip arthroplasty?

Objective: To investigate limb loading and dynamic stability during squatting in the early functional recovery of total hip arthroplasty (THA) patients. Design: Cohort study Setting: Inpatient rehabilitation clinic. Participants: A random sample of 61 THA patients (34♂/27♀; 62±9 yrs, 77±14 kg, 174±9 cm) was assessed twice, 13.2±3.8 days (PRE) and 26.6±3.3 days post-surgery (POST), and compared with a healthy reference group (REF) (22♂/16♀; 47±12yrs; 78±20kg; 175±10cm). Interventions: THA patients received two weeks of standard in-patient rehabilitation. Main Outcome Measure(s): Inter-limb vertical force distribution and dynamic stability during the squat maneuver, as defined by the root mean square (RMS) of the center of pressure in antero-posterior and medio-lateral directions, of operated (OP) and non-operated (NON)limbs. Self-reported function was assessed via FFb-H-OA 2.0 questionnaire. Results: At PRE, unloading of the OP limb was 15.8% greater (P<.001, d=1.070) and antero-posterior and medio-lateral center of pressure RMS were 30-34% higher in THA than REF P<.05). Unloading was reduced by 12.8% towards a more equal distribution from PRE to POST (P<.001, d=0.874). Although medio-lateral stability improved between PRE and POST (OP: 14.8%, P=.024, d=0.397; NON: 13.1%, P=.015, d=0.321), antero-posterior stability was not significantly different. Self-reported physical function improved by 15.8% (P<.001, d=0.965). Conclusion(s): THA patients unload the OP limb and are dynamically more unstable during squatting in the early rehabilitation phase following total hip replacement than healthy adults. Although loading symmetry and medio-lateral stability improved to the level of healthy adults with rehabilitation, antero-posterior stability remained impaired. Measures of dynamic stability and load symmetry during squatting provide quantitative information that can be used to clinically monitor early functional recovery from THA.

On adaptive HMM state estimation

In this paper new online adaptive hidden Markov model (HMM) state estimation schemes are developed, based on extended least squares (ELS) concepts and recursive prediction error (RPE) methods. The best of the new schemes exploit the idempotent nature of Markov chains and work with a least squares prediction error index, using a posterior estimates, more suited to Markov models then traditionally used in identification of linear systems.

Corneal changes following short-term miniscleral contact lens wear

Purpose To examine the influence of short-term miniscleral contact lens wear on corneal shape, thickness and anterior surface aberrations. Methods Scheimpflug imaging was captured before, immediately following and 3 hours after a short period (3 hours) of miniscleral contact lens wear for 10 young (mean 27 ± 5 years), healthy participants. Natural diurnal variations were considered by measuring baseline diurnal changes obtained on a separate control day without contact lens wear. Results Small but significant anterior corneal flattening was observed immediately following lens removal (overall mean 0.02 ± 0.03 mm, p < 0.001) which returned to baseline levels three hours after lens removal. During the three hour recovery period significant corneal thinning (-13.4 ± 10.5 μm) and posterior surface flattening (0.03 ± 0.02 mm) were also observed (both p < 0.01). The magnitude of posterior corneal flattening during recovery correlated with the amount of corneal thinning (r = 0.69, p = 0.03). Central corneal clearance (maximum tear reservoir depth) was not associated with corneal swelling following lens removal (r = -0.24, p > 0.05). An increase in lower-order corneal astigmatism Z(2,2) was also observed following lens wear (mean -0.144 ± 0.075 μm, p = 0.02). Conclusions Flattening of the anterior corneal surface was observed immediately following lens wear, while ‘rebound’ thinning and flattening of the posterior surface was evident following the recovery period. Modern miniscleral contact lenses that vault the cornea may slightly influence corneal shape and power but do not induce clinically significant corneal oedema during short-term wear.

Macular retinal layer thickness in childhood

Purpose To examine macular retinal thickness and retinal layer thickness with spectral domain optical coherence tomography (OCT) in a population of children with normal ocular health and minimal refractive errors. Methods High resolution macular OCT scans from 196 children aged from 4 to 12 years (mean age 8 ± 2 years) were analysed to determine total retinal thickness and the thickness of 6 different retinal layers across the central 5 mm of the posterior pole. Automated segmentation with manual correction was used to derive retinal thickness values. Results The mean total retinal thickness in the central 1 mm foveal zone was 255 ± 16 μm, and this increased significantly with age (mean increase of 1.8 microns per year) in childhood (p<0.001). Age-related increases in thickness of some retinal layers were also observed, with changes of highest statistical significance found in the outer retinal layers in the central foveal region (p<0.01). Significant topographical variations in thickness of each of the retinal layers were also observed (p<0.001). Conclusions Small magnitude, statistically significant increases in total retinal thickness and retinal layer thickness occur from early childhood to adolescence. The most prominent changes appear to occur in the outer retinal layers of the central fovea.

Combining opinions for use in Bayesian networks: A measurement error approach

Bayesian networks (BNs) are graphical probabilistic models used for reasoning under uncertainty. These models are becoming increasing popular in a range of fields including ecology, computational biology, medical diagnosis, and forensics. In most of these cases, the BNs are quantified using information from experts, or from user opinions. An interest therefore lies in the way in which multiple opinions can be represented and used in a BN. This paper proposes the use of a measurement error model to combine opinions for use in the quantification of a BN. The multiple opinions are treated as a realisation of measurement error and the model uses the posterior probabilities ascribed to each node in the BN which are computed from the prior information given by each expert. The proposed model addresses the issues associated with current methods of combining opinions such as the absence of a coherent probability model, the lack of the conditional independence structure of the BN being maintained, and the provision of only a point estimate for the consensus. The proposed model is applied an existing Bayesian Network and performed well when compared to existing methods of combining opinions.

Approximation of Bayesian predictive p-values with regression ABC

In the Bayesian framework a standard approach to model criticism is to compare some function of the observed data to a reference predictive distribution. The result of the comparison can be summarized in the form of a p-value, and it's well known that computation of some kinds of Bayesian predictive p-values can be challenging. The use of regression adjustment approximate Bayesian computation (ABC) methods is explored for this task. Two problems are considered. The first is the calibration of posterior predictive p-values so that they are uniformly distributed under some reference distribution for the data. Computation is difficult because the calibration process requires repeated approximation of the posterior for different data sets under the reference distribution. The second problem considered is approximation of distributions of prior predictive p-values for the purpose of choosing weakly informative priors in the case where the model checking statistic is expensive to compute. Here the computation is difficult because of the need to repeatedly sample from a prior predictive distribution for different values of a prior hyperparameter. In both these problems we argue that high accuracy in the computations is not required, which makes fast approximations such as regression adjustment ABC very useful. We illustrate our methods with several samples.

Contributions to Bayesian experimental design

This thesis progresses Bayesian experimental design by developing novel methodologies and extensions to existing algorithms. Through these advancements, this thesis provides solutions to several important and complex experimental design problems, many of which have applications in biology and medicine. This thesis consists of a series of published and submitted papers. In the first paper, we provide a comprehensive literature review on Bayesian design. In the second paper, we discuss methods which may be used to solve design problems in which one is interested in finding a large number of (near) optimal design points. The third paper presents methods for finding fully Bayesian experimental designs for nonlinear mixed effects models, and the fourth paper investigates methods to rapidly approximate the posterior distribution for use in Bayesian utility functions.

Head-of-bed elevation improves end-expiratory lung volumes in mechanically ventilated subjects : a prospective observational study

BACKGROUND: Head-of-bed elevation (HOBE) has been shown to assist in reducing respiratory complications associated with mechanical ventilation; however, there is minimal research describing changes in end-expiratory lung volume. This study aims to investigate changes in end-expiratory lung volume in a supine position and 2 levels of HOBE. METHODS: Twenty postoperative cardiac surgery subjects were examined using electrical impedance tomography. End-expiratory lung impedance (EELI) was recorded as a surrogate measurement of end-expiratory lung volume in a supine position and at 20° and then 30°. RESULTS: Significant increases in end-expiratory lung volume were seen at both 20° and 30° HOBE in all lung regions, except the anterior, with the largest changes from baseline (supine) seen at 30°. From baseline to 30° HOBE, global EELI increased by 1,327 impedance units (95% CI 1,080–1,573, P < .001). EELI increased by 1,007 units (95% CI 880–1,134, P < .001) in the left lung region and by 320 impedance units (95% CI 188–451, P < .001) in the right lung. Posterior increases of 1,544 impedance units (95% CI 1,405–1,682, P < .001) were also seen. EELI decreased anteriorly, with the largest decreases occurring at 30° (−335 impedance units, 95% CI −486 to −183, P < .001). CONCLUSIONS: HOBE significantly increases global and regional end-expiratory lung volume; therefore, unless contraindicated, all mechanically ventilated patients should be positioned with HOBE.

Melanoma cell colony expansion parameters revealed by approximate Bayesian computation

In vitro studies and mathematical models are now being widely used to study the underlying mechanisms driving the expansion of cell colonies. This can improve our understanding of cancer formation and progression. Although much progress has been made in terms of developing and analysing mathematical models, far less progress has been made in terms of understanding how to estimate model parameters using experimental in vitro image-based data. To address this issue, a new approximate Bayesian computation (ABC) algorithm is proposed to estimate key parameters governing the expansion of melanoma cell (MM127) colonies, including cell diffusivity, D, cell proliferation rate, λ, and cell-to-cell adhesion, q, in two experimental scenarios, namely with and without a chemical treatment to suppress cell proliferation. Even when little prior biological knowledge about the parameters is assumed, all parameters are precisely inferred with a small posterior coefficient of variation, approximately 2–12%. The ABC analyses reveal that the posterior distributions of D and q depend on the experimental elapsed time, whereas the posterior distribution of λ does not. The posterior mean values of D and q are in the ranges 226–268 µm2h−1, 311–351 µm2h−1 and 0.23–0.39, 0.32–0.61 for the experimental periods of 0–24 h and 24–48 h, respectively. Furthermore, we found that the posterior distribution of q also depends on the initial cell density, whereas the posterior distributions of D and λ do not. The ABC approach also enables information from the two experiments to be combined, resulting in greater precision for all estimates of D and λ.

The relationship between stress, HPA axis functioning and brain structure in first episode psychosis over the first 12 weeks of treatment

Stress and abnormal hypothalamic-pituitary-adrenal axis functioning have been implicated in the early phase of psychosis and may partly explain reported changes in brain structure. This study used magnetic resonance imaging to investigate whether biological measures of stress were related to brain structure at baseline and to structural changes over the first 12 weeks of treatment in first episode patients (n=22) compared with matched healthy controls (n=22). At baseline, no significant group differences in biological measures of stress, cortical thickness or hippocampal volume were observed, but a significantly stronger relationship between baseline levels of cortisol and smaller white matter volumes of the cuneus and anterior cingulate was found in patients compared with controls. Over the first 12 weeks of treatment, patients showed a significant reduction in thickness of the posterior cingulate compared with controls. Patients also showed a significant positive relationship between baseline cortisol and increases in hippocampal volume over time, suggestive of brain swelling in association with psychotic exacerbation, while no such relationship was observed in controls. The current findings provide some support for the involvement of stress mechanisms in the pathophysiology of early psychosis, but the changes are subtle and warrant further investigation.