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.

A cellular automata model to investigate immune cell–tumor cell interactions in growing tumors in two spatial dimensions

We develop a hybrid cellular automata model to describe the effect of the immune system and chemokines on a growing tumor. The hybrid cellular automata model consists of partial differential equations to model chemokine concentrations, and discrete cellular automata to model cell–cell interactions and changes. The computational implementation overlays these two components on the same spatial region. We present representative simulations of the model and show that increasing the number of immature dendritic cells (DCs) in the domain causes a decrease in the number of tumor cells. This result strongly supports the hypothesis that DCs can be used as a cancer treatment. Furthermore, we also use the hybrid cellular automata model to investigate the growth of a tumor in a number of computational “cancer patients.” Using these virtual patients, the model can explain that increasing the number of DCs in the domain causes longer “survival.” Not surprisingly, the model also reflects the fact that the parameter related to tumor division rate plays an important role in tumor metastasis.

Surgical fusion of early onset severe scoliosis increases survival in the child with rett syndrome: A population based study

Introduction. Rett Syndrome is a rare genetic neurodevelopmental disorder usually affecting females. Scoliosis is a common comorbidity and spinal fusion may be recommended if severe. Little is known about long term outcomes. We examined the impact of spinal fusion on survival and risk of severe lower respiratory tract infection (LRTI) in Rett Syndrome. Methods Data were ascertained from hospital medical records, the Australian Rett Syndrome Database, a longitudinal and population-based registry of Rett Syndrome cases established in 1993, and the Australian Institute of Health and Welfare National Death Index database. An extended Cox regression model was used to estimate the effect of spinal surgery on survival in females who developed severe scoliosis (Cobb angle > 45 degrees). Generalized estimating equation modelling was used to estimate the effect of spinal surgery on the odds of developing severe LRTI. Results Severe scoliosis was identified in 140 cases (60.3%) of whom slightly fewer than half (48.6%) developed scoliosis prior to eight years of age. Scoliosis surgery was performed in 98 (69.0%) of those at a median age of 13 years 3 months (IQR 11 years 5 months – 14 years 10 months). After adjusting for mutation type and age of scoliosis onset, the rate of death was lower in the surgery group (HR 0.30, 95% CI 0.12, 0.74, P = 0.009) compared to those without surgery. Rate of death was particularly reduced for those with early onset scoliosis (HR 0.17, 95% CI 0.06, 0.52, P = 0.002). Spinal fusion was not associated with reduction in the occurrence of a severe LRTI overall (OR 0.60, 95%CI 0.27, 1.33, P=0.206) but was associated with a large reduction in odds of severe LRTI among those with early onset scoliosis (OR 0.32, 95%CI 0.11, 0.93, P=0.036). Conclusion With appropriate cautions, spinal fusion confers an advantage to life expectancy in Rett syndrome.

Estimation of the time of a linear trend in monitoring survival time

Change point estimation is recognized as an essential tool of root cause analyses within quality control programs as it enables clinical experts to search for potential causes of change in hospital outcomes more effectively. In this paper, we consider estimation of the time when a linear trend disturbance has occurred in survival time following an in-control clinical intervention in the presence of variable patient mix. To model the process and change point, a linear trend in the survival time of patients who underwent cardiac surgery is formulated using hierarchical models in a Bayesian framework. The data are right censored since the monitoring is conducted over a limited follow-up period. We capture the effect of risk factors prior to the surgery using a Weibull accelerated failure time regression model. We use Markov Chain Monte Carlo to obtain posterior distributions of the change point parameters including the location and the slope size of the trend and also corresponding probabilistic intervals and inferences. The performance of the Bayesian estimator is investigated through simulations and the result shows that precise estimates can be obtained when they are used in conjunction with the risk-adjusted survival time cumulative sum control chart (CUSUM) control charts for different trend scenarios. In comparison with the alternatives, step change point model and built-in CUSUM estimator, more accurate and precise estimates are obtained by the proposed Bayesian estimator over linear trends. These superiorities are enhanced when probability quantification, flexibility and generalizability of the Bayesian change point detection model are also considered.

Rank regression for accelerated failure time model with clustered and censored data

For clustered survival data, the traditional Gehan-type estimator is asymptotically equivalent to using only the between-cluster ranks, and the within-cluster ranks are ignored. The contribution of this paper is two fold: - (i) incorporating within-cluster ranks in censored data analysis, and; - (ii) applying the induced smoothing of Brown and Wang (2005, Biometrika) for computational convenience. Asymptotic properties of the resulting estimating functions are given. We also carry out numerical studies to assess the performance of the proposed approach and conclude that the proposed approach can lead to much improved estimators when strong clustering effects exist. A dataset from a litter-matched tumorigenesis experiment is used for illustration.

Induced smoothing for rank regression with censored survival times

Adaptions of weighted rank regression to the accelerated failure time model for censored survival data have been successful in yielding asymptotically normal estimates and flexible weighting schemes to increase statistical efficiencies. However, for only one simple weighting scheme, Gehan or Wilcoxon weights, are estimating equations guaranteed to be monotone in parameter components, and even in this case are step functions, requiring the equivalent of linear programming for computation. The lack of smoothness makes standard error or covariance matrix estimation even more difficult. An induced smoothing technique overcame these difficulties in various problems involving monotone but pure jump estimating equations, including conventional rank regression. The present paper applies induced smoothing to the Gehan-Wilcoxon weighted rank regression for the accelerated failure time model, for the more difficult case of survival time data subject to censoring, where the inapplicability of permutation arguments necessitates a new method of estimating null variance of estimating functions. Smooth monotone parameter estimation and rapid, reliable standard error or covariance matrix estimation is obtained.

A spatially explicit multi-competitor coexistence model of penaeid (shrimp) distribution on the Australian Great Barrier Reef

A spatially explicit multi-competitor coexistence model was developed for meta-populations of prawns (shrimp) occupying habitat patches across the Great Barrier Reef, where dispersal was localised and dispersal rates varied between species. Prawns were modelled as individuals moving to and from patches or cells according to pre-set decision rules. The landscape was simulated as a matrix of cells with each cell having a spatially explicit survival index for each species. Mixed species prawn assemblages moved over this simplified spatially explicit landscape. A low level of chronic random environmental disturbance was assumed (cyclone and tropical storm damage) with additional acute spatially confined disturbance due to commercial trawling, modelled as an increase in mortality affecting inter-specific competition. The general form of the results was for increased disturbance to favour good-colonising "generalist" species at the expense of good-competitor "specialists". Increasing fishing mortality (local patch extinctions) combined with poor colonising ability resulted in low equilibrium abundance for even the best competitor, while in the same circumstances the poorest competitor but best coloniser could have the highest equilibrium abundance. This mimics the switch from high-value prawn species to lower-value prawn species as trawl effort increases, reflected in historic catch and effort logbook data and reported anecdotaly from the north Queensland trawl fleet. To match the observed distribution and behaviour of prawn assemblages, a combination inter-species competition, a spatially explicit landscape, and a defined pattern of disturbance (trawling) was required. Modelling this combination could simulate not only general trends in spatial distribution of each of prawn species but also localised concentrations observed in the survey data

Lantana (Lantana camara) Seed Bank Dynamics: Seedling Emergence and Seed Survival.

Seed persistence is poorly quantified for invasive plants of subtropical and tropical environments and Lantana camara, one of the world's worst weeds, is no exception. We investigated germination, seedling emergence, and seed survival of two lantana biotypes (Pink and pink-edged red [PER]) in southeastern Queensland, Australia. Controlled experiments were undertaken in 2002 and repeated in 2004, with treatments comprising two differing environmental regimes (irrigated and natural rainfall) and sowing depths (0 and 2 cm). Seed survival and seedling emergence were significantly affected by all factors (time, biotype, environment, sowing depth, and cohort) (P < 0.001). Seed dormancy varied with treatment (environment, sowing depth, biotype, and cohort) (P < 0.001), but declined rapidly after 6 mo. Significant differential responses by the two biotypes to sowing depth and environment were detected for both seed survival and seedling emergence (P < 0.001). Seed mass was consistently lower in the PER biotype at the population level (P < 0.001), but this variation did not adequately explain the differential responses. Moreover, under natural rainfall the magnitude of the biotype effect was unlikely to result in ecologically significant differences. Seed survival after 36 mo under natural rainfall ranged from 6.8 to 21.3%. Best fit regression analysis of the decline in seed survival over time yielded a five-parameter exponential decay model with a lower asymptote approaching −0.38 (% seed survival = [( 55 − (−0.38)) • e (k • t)] + −0.38; R2 = 88.5%; 9 df). Environmental conditions and burial affected the slope parameter or k value significantly (P < 0.01). Seed survival projections from the model were greatest for buried seeds under natural rainfall (11 yr) and least under irrigation (3 yr). Experimental data and model projections suggest that lantana has a persistent seed bank and this should be considered in management programs, particularly those aimed at eradication.

Exact calculations of survival probability for diffusion on growing lines, disks, and spheres: The role of dimension

Unlike standard applications of transport theory, the transport of molecules and cells during embryonic development often takes place within growing multidimensional tissues. In this work, we consider a model of diffusion on uniformly growing lines, disks, and spheres. An exact solution of the partial differential equation governing the diffusion of a population of individuals on the growing domain is derived. Using this solution, we study the survival probability, S(t). For the standard nongrowing case with an absorbing boundary, we observe that S(t) decays to zero in the long time limit. In contrast, when the domain grows linearly or exponentially with time, we show that S(t) decays to a constant, positive value, indicating that a proportion of the diffusing substance remains on the growing domain indefinitely. Comparing S(t) for diffusion on lines, disks, and spheres indicates that there are minimal differences in S(t) in the limit of zero growth and minimal differences in S(t) in the limit of fast growth. In contrast, for intermediate growth rates, we observe modest differences in S(t) between different geometries. These differences can be quantified by evaluating the exact expressions derived and presented here.

Survival probability for a diffusive process on a growing domain

We consider the motion of a diffusive population on a growing domain, 0 < x < L(t ), which is motivated by various applications in developmental biology. Individuals in the diffusing population, which could represent molecules or cells in a developmental scenario, undergo two different kinds of motion: (i) undirected movement, characterized by a diffusion coefficient, D, and (ii) directed movement, associated with the underlying domain growth. For a general class of problems with a reflecting boundary at x = 0, and an absorbing boundary at x = L(t ), we provide an exact solution to the partial differential equation describing the evolution of the population density function, C(x,t ). Using this solution, we derive an exact expression for the survival probability, S(t ), and an accurate approximation for the long-time limit, S = limt→∞ S(t ). Unlike traditional analyses on a nongrowing domain, where S ≡ 0, we show that domain growth leads to a very different situation where S can be positive. The theoretical tools developed and validated in this study allow us to distinguish between situations where the diffusive population reaches the moving boundary at x = L(t ) from other situations where the diffusive population never reaches the moving boundary at x = L(t ). Making this distinction is relevant to certain applications in developmental biology, such as the development of the enteric nervous system (ENS). All theoretical predictions are verified by implementing a discrete stochastic model.

Survival analysis of time-to-event data in respiratory health research studies

This article provides a review of techniques for the analysis of survival data arising from respiratory health studies. Popular techniques such as the Kaplan–Meier survival plot and the Cox proportional hazards model are presented and illustrated using data from a lung cancer study. Advanced issues are also discussed, including parametric proportional hazards models, accelerated failure time models, time-varying explanatory variables, simultaneous analysis of multiple types of outcome events and the restricted mean survival time, a novel measure of the effect of treatment.

Survival of Hendra Virus in the Environment: Modelling the Effect of Temperature

Hendra virus (HeV), a highly pathogenic zoonotic paramyxovirus recently emerged from bats, is a major concern to the horse industry in Australia. Previous research has shown that higher temperatures led to lower virus survival rates in the laboratory. We develop a model of survival of HeV in the environment as influenced by temperature. We used 20 years of daily temperature at six locations spanning the geographic range of reported HeV incidents to simulate the temporal and spatial impacts of temperature on HeV survival. At any location, simulated virus survival was greater in winter than in summer, and in any month of the year, survival was higher in higher latitudes. At any location, year-to-year variation in virus survival 24 h post-excretion was substantial and was as large as the difference between locations. Survival was higher in microhabitats with lower than ambient temperature, and when environmental exposure was shorter. The within-year pattern of virus survival mirrored the cumulative within-year occurrence of reported HeV cases, although there were no overall differences in survival in HeV case years and non-case years. The model examines the effect of temperature in isolation; actual virus survivability will reflect the effect of additional environmental factors

Biological data and model development for management of longfinned eels

Objectives: 1. Estimate population parameters required for a management model. These include survival, density, age structure, growth, age and size at maturity and at recruitment to the adult eel fishery. Estimate their variability among individuals in a range of habitats. 2. Develop a management population dynamics model and use it to investigate management options. 3. Establish baseline data and sustainability indicators for long-term monitoring. 4. Assess the applicability of the above techniques to other eel fisheries in Australia, in collaboration with NSW. Distribute developed tools via the Australia and New Zealand Eel Reference Group.

Studies on Plant Demography: Ranunculus Repens L., R. Bulbosus L. and R. Acris L.: III. A Mathematical Model Incorporating Multiple Modes of Reproduction

This paper presents a comparative population dynamics study of three closely related species of buttercups (Ranunculus repens, R. acris, and R. bulbosus). The study is based on an investigation of the behaviour of the seeds in soil under field conditions and a continuous monitoring of survival and reproduction of some 9000 individual plants over a period of 21/2 years in a coastal grassland in North Wales. The data were analysed with the help of an extension of Leslie's matrix method which makes possible an simultaneous treatment of vegetative and sexual reproduction. It was found that R. repens (a) depends more heavily on vegetative as compared with sexual reproduction, (b) shows indications of negatively density-dependent population regulation, and (c) exhibits little variation in population growth rates from site to site and from one year to the next. In contrast, R. bulbosus (a) depends exclusively on sexual reproduction, (b) shows indications of a positively density-dependent population behaviour, and (c) exhibits great variation in population growth rates from site to site and from one year to the next. R. acris exhibits an intermediate behaviour in all these respects. It is suggested that the attributes of R. repens are those expected of a species inhabiting a stable environment, while R. bulbosus exhibits some of the characteristics of a fugitive species.

Endoplasmic reticulum stress and cell death mechanisms in the cell model of Huntington’s disease

This thesis clarifies important molecular pathways that are activated during the cell death observed in Huntington’s disease. Huntington’s disease is one of the most common inherited neurodegenerative diseases, which is primarily inherited in an autosomal dominant manner. HD is caused by an expansion of CAG repeats in the first exon of the IT15 gene. IT15 encodes the production of a Huntington’s disease protein huntingtin. Mutation of the IT15 gene results in a long stretch of polyQ residues close to the amino-terminal region of huntingtin. Huntington’s disease is a fatal autosomal neurodegenerative disorder. Despite the current knowledge of HD, the precise mechanism behind the selective neuronal death, and how the disease propagates, still remains an enigma. The studies mainly focused on the control of endoplasmic reticulum (ER) stress triggered by the mutant huntingtin proteins. The ER is a delicate organelle having essential roles in protein folding and calcium regulation. Even the slightest perturbations on ER homeostasis are effective enough to trigger ER stress and its adaptation pathways, called unfolded protein response (UPR). UPR is essential for cellular homeostasis and it adapts ER to the changing environment and decreases ER stress. If adaptation processes fail and stress is excessive and prolonged; irreversible cell death pathways are engaged. The results showed that inhibition of ER stress with chemical agents are able to decrease cell death and formation of toxic cell aggregates caused by mutant huntingtin proteins. The study concentrated also to the NF-κB (nuclear factor-kappaB) pathway, which is activated during ER stress. NF-κB pathway is capable to regulate the levels of important cellular antioxidants. Cellular antioxidants provide a first line of defence against excess reactive oxygen species. Excess accumulation of reactive oxygen species and subsequent activation of oxidative stress damages motley of vital cellular processes and induce cell degeneration. Data showed that mutant huntingtin proteins downregulate the expression levels of NF-κB and vital antioxidants, which was followed by increased oxidative stress and cell death. Treatment with antioxidants and inhibition of oxidative stress were able to counteract these adverse effects. In addition, thesis connects ER stress caused by mutant huntingtin to the cytoprotective autophagy. Autophagy sustains cellular balance by degrading potentially toxic cell proteins and components observed in Huntington’s disease. The results revealed that cytoprotective autophagy is active at the early points (24h) of ER stress after expression of mutant huntingtin proteins. GADD34 (growth arrest and DNA damage-inducible gene 34), which is previously connected to the regulation of translation during cell stress, was shown to control the stimulation of autophagy. However, GADD34 and autophagy were downregulated at later time points (48h) during mutant huntingtin proteins induced ER stress, and subsequently cell survival decreased. Overexpression GADD34 enhanced autophagy and decreased cell death, indicating that GADD34 plays a critical role in cell protection. The thesis reveales new interesting data about the neuronal cell death pathways seen in Huntington’s disease, and how cell degeneration is partly counteracted by various therapeutic agents. Expression of mutant huntingtin proteins is shown to alter signaling events that control ER stress, oxidative stress and autophagy. Despite that Huntington’s disease is mainly an untreatable disorder; these findings offer potential targets and neuroprotective strategies in designing novel therapies for Huntington’s disease.