Bayesian hierarchical models for analysing spatial point-based data at a grid level: A comparison of approaches

Spatial data are now prevalent in a wide range of fields including environmental and health science. This has led to the development of a range of approaches for analysing patterns in these data. In this paper, we compare several Bayesian hierarchical models for analysing point-based data based on the discretization of the study region, resulting in grid-based spatial data. The approaches considered include two parametric models and a semiparametric model. We highlight the methodology and computation for each approach. Two simulation studies are undertaken to compare the performance of these models for various structures of simulated point-based data which resemble environmental data. A case study of a real dataset is also conducted to demonstrate a practical application of the modelling approaches. Goodness-of-fit statistics are computed to compare estimates of the intensity functions. The deviance information criterion is also considered as an alternative model evaluation criterion. The results suggest that the adaptive Gaussian Markov random field model performs well for highly sparse point-based data where there are large variations or clustering across the space; whereas the discretized log Gaussian Cox process produces good fit in dense and clustered point-based data. One should generally consider the nature and structure of the point-based data in order to choose the appropriate method in modelling a discretized spatial point-based data.

Interpreting scratch assays using pair density dynamics and approximate Bayesian computation

Quantifying the impact of biochemical compounds on collective cell spreading is an essential element of drug design, with various applications including developing treatments for chronic wounds and cancer. Scratch assays are a technically simple and inexpensive method used to study collective cell spreading; however, most previous interpretations of scratch assays are qualitative and do not provide estimates of the cell diffusivity, D, or the cell proliferation rate,l. Estimating D and l is important for investigating the efficacy of a potential treatment and provides insight into the mechanism through which the potential treatment acts. While a few methods for estimating D and l have been proposed, these previous methods lead to point estimates of D and l, and provide no insight into the uncertainty in these estimates. Here, we compare various types of information that can be extracted from images of a scratch assay, and quantify D and l using discrete computational simulations and approximate Bayesian computation. We show that it is possible to robustly recover estimates of D and l from synthetic data, as well as a new set of experimental data. For the first time, our approach also provides a method to estimate the uncertainty in our estimates of D and l. We anticipate that our approach can be generalized to deal with more realistic experimental scenarios in which we are interested in estimating D and l, as well as additional relevant parameters such as the strength of cell-to-cell adhesion or the strength of cell-to-substrate adhesion.

A rating aggregation method for generating product reputations

Many websites offer the opportunity for customers to rate items and then use customers' ratings to generate items reputation, which can be used later by other users for decision making purposes. The aggregated value of the ratings per item represents the reputation of this item. The accuracy of the reputation scores is important as it is used to rank items. Most of the aggregation methods didn't consider the frequency of distinct ratings and they didn't test how accurate their reputation scores over different datasets with different sparsity. In this work we propose a new aggregation method which can be described as a weighted average, where weights are generated using the normal distribution. The evaluation result shows that the proposed method outperforms state-of-the-art methods over different sparsity datasets.

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.

Muramidases found in the foregut microbiome of the Tammar wallaby can direct cell aggregation and biofilm formation

We describe here the role of muramidases present in clones of metagenomic DNA that result in cell aggregation and biofilm formation by Escherichia coli. The metagenomic clones were obtained from uncultured Lachnospiraceae-affiliated bacteria resident in the foregut microbiome of the Tammar wallaby. One of these fosmid clones (p49C2) was chosen for more detailed studies and a variety of genetic methods were used to delimit the region responsible for the phenotype to an open reading frame of 1425 bp. Comparative sequence analysis with other fosmid clones giving rise to the same phenotype revealed the presence of muramidase homologues with the same modular composition. Phylogenetic analysis of the fosmid sequence data assigned these fosmid inserts to recently identified, but uncultured, phylogroups of Lachnospiraceae believed to be numerically dominant in the foregut microbiome of the Tammar wallaby. The muramidase is a modular protein containing putative N-acetylmuramoyl--alanine amidase and an endo-β-N-acetylglucosaminidase catalytic module, with a similar organization and functional properties to some Staphylococcal autolysins that also confer adhesive properties and biofilm formation. We also show here that the cloned muramidases result in the production of extracellular DNA, which appears to be the key for biofilm formation and autoaggregation. Collectively, these findings suggest that biofilm formation and cell aggregation in gut microbiomes might occur via the concerted action of carbohydrate-active enzymes and the production of extracellular DNA to serve as a biofilm scaffold.

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.

A pseudo-marginal sequential Monte Carlo algorithm for random effects models in Bayesian sequential design

A computationally efficient sequential Monte Carlo algorithm is proposed for the sequential design of experiments for the collection of block data described by mixed effects models. The difficulty in applying a sequential Monte Carlo algorithm in such settings is the need to evaluate the observed data likelihood, which is typically intractable for all but linear Gaussian models. To overcome this difficulty, we propose to unbiasedly estimate the likelihood, and perform inference and make decisions based on an exact-approximate algorithm. Two estimates are proposed: using Quasi Monte Carlo methods and using the Laplace approximation with importance sampling. Both of these approaches can be computationally expensive, so we propose exploiting parallel computational architectures to ensure designs can be derived in a timely manner. We also extend our approach to allow for model uncertainty. This research is motivated by important pharmacological studies related to the treatment of critically ill patients.

Understanding Uncertainties in Non-Linear Population Trajectories: A Bayesian Semi-Parametric Hierarchical Approach to Large-Scale Surveys of Coral Cover

Recently, attempts to improve decision making in species management have focussed on uncertainties associated with modelling temporal fluctuations in populations. Reducing model uncertainty is challenging; while larger samples improve estimation of species trajectories and reduce statistical errors, they typically amplify variability in observed trajectories. In particular, traditional modelling approaches aimed at estimating population trajectories usually do not account well for nonlinearities and uncertainties associated with multi-scale observations characteristic of large spatio-temporal surveys. We present a Bayesian semi-parametric hierarchical model for simultaneously quantifying uncertainties associated with model structure and parameters, and scale-specific variability over time. We estimate uncertainty across a four-tiered spatial hierarchy of coral cover from the Great Barrier Reef. Coral variability is well described; however, our results show that, in the absence of additional model specifications, conclusions regarding coral trajectories become highly uncertain when considering multiple reefs, suggesting that management should focus more at the scale of individual reefs. The approach presented facilitates the description and estimation of population trajectories and associated uncertainties when variability cannot be attributed to specific causes and origins. We argue that our model can unlock value contained in large-scale datasets, provide guidance for understanding sources of uncertainty, and support better informed decision making

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.