Bayesian calibration, validation and uncertainty quantification for predictive modelling of tumour growth: a tutorial

In this work we present a pedagogical tumour growth example, in which we apply calibration and validation techniques to an uncertain, Gompertzian model of tumour spheroid growth. The key contribution of this article is the discussion and application of these methods (that are not commonly employed in the field of cancer modelling) in the context of a simple model, whose deterministic analogue is widely known within the community. In the course of the example we calibrate the model against experimental data that is subject to measurement errors, and then validate the resulting uncertain model predictions. We then analyse the sensitivity of the model predictions to the underlying measurement model. Finally, we propose an elementary learning approach for tuning a threshold parameter in the validation procedure in order to maximize predictive accuracy of our validated model

Using Interpolation to Estimate System Uncertainty in Gene Expression Experiments

The widespread use of high-throughput experimental assays designed to measure the entire complement of a cell's genes or gene products has led to vast stores of data that are extremely plentiful in terms of the number of items they can measure in a single sample, yet often sparse in the number of samples per experiment due to their high cost. This often leads to datasets where the number of treatment levels or time points sampled is limited, or where there are very small numbers of technical and/or biological replicates. Here we introduce a novel algorithm to quantify the uncertainty in the unmeasured intervals between biological measurements taken across a set of quantitative treatments. The algorithm provides a probabilistic distribution of possible gene expression values within unmeasured intervals, based on a plausible biological constraint. We show how quantification of this uncertainty can be used to guide researchers in further data collection by identifying which samples would likely add the most information to the system under study. Although the context for developing the algorithm was gene expression measurements taken over a time series, the approach can be readily applied to any set of quantitative systems biology measurements taken following quantitative (i.e. non-categorical) treatments. In principle, the method could also be applied to combinations of treatments, in which case it could greatly simplify the task of exploring the large combinatorial space of future possible measurements

Validation of a simplified micromodel for analysis of infilled RC frames exposed to cyclic lateral loads

An RC frame structure with masonry infill walls (‘‘framed-masonry’’) exposed to lateral loads acts as a composite structure. Numerical simulation of framed-masonry is difficult and generally unreliable due to many difficulties and uncertainties in its modelling. In this paper, we reviewed the usability of an advanced non-linear FEM computer program to accurately predict the behaviour of framed-masonry elements when exposed to cyclic lateral loading. Numerical results are validated against the test results of framedmasonry specimens, with and without openings. Initial simplified micromodels were calibrated by adjustment of the input parameters within the physically justifiable borders, in order to obtain the best correlation between the experimental and numerical results. It has been shown that the use of simplified micromodels for the investigation of composite masonry-infilled RC frames requires in-depth knowledge and engineering judgement in order to be used with confidence. Modelling problems were identified and explained in detail, which in turn offer an insight to practising engineers on how to deal with them

A heteroskedastic error covariance matrix estimator using a first-order conditional autoregressive Markov simulation for deriving asympotical efficient estimates from ecological sampled Anopheles arabiensis aquatic habitat covariates

<p>Abstract</p> <p>Background</p> <p>Autoregressive regression coefficients for <it>Anopheles arabiensis </it>aquatic habitat models are usually assessed using global error techniques and are reported as error covariance matrices. A global statistic, however, will summarize error estimates from multiple habitat locations. This makes it difficult to identify where there are clusters of <it>An. arabiensis </it>aquatic habitats of acceptable prediction. It is therefore useful to conduct some form of spatial error analysis to detect clusters of <it>An. arabiensis </it>aquatic habitats based on uncertainty residuals from individual sampled habitats. In this research, a method of error estimation for spatial simulation models was demonstrated using autocorrelation indices and eigenfunction spatial filters to distinguish among the effects of parameter uncertainty on a stochastic simulation of ecological sampled <it>Anopheles </it>aquatic habitat covariates. A test for diagnostic checking error residuals in an <it>An. arabiensis </it>aquatic habitat model may enable intervention efforts targeting productive habitats clusters, based on larval/pupal productivity, by using the asymptotic distribution of parameter estimates from a residual autocovariance matrix. The models considered in this research extends a normal regression analysis previously considered in the literature.</p> <p>Methods</p> <p>Field and remote-sampled data were collected during July 2006 to December 2007 in Karima rice-village complex in Mwea, Kenya. SAS 9.1.4^®was used to explore univariate statistics, correlations, distributions, and to generate global autocorrelation statistics from the ecological sampled datasets. A local autocorrelation index was also generated using spatial covariance parameters (i.e., Moran's Indices) in a SAS/GIS^®database. The Moran's statistic was decomposed into orthogonal and uncorrelated synthetic map pattern components using a Poisson model with a gamma-distributed mean (i.e. negative binomial regression). The eigenfunction values from the spatial configuration matrices were then used to define expectations for prior distributions using a Markov chain Monte Carlo (MCMC) algorithm. A set of posterior means were defined in WinBUGS 1.4.3^®. After the model had converged, samples from the conditional distributions were used to summarize the posterior distribution of the parameters. Thereafter, a spatial residual trend analyses was used to evaluate variance uncertainty propagation in the model using an autocovariance error matrix.</p> <p>Results</p> <p>By specifying coefficient estimates in a Bayesian framework, the covariate number of tillers was found to be a significant predictor, positively associated with <it>An. arabiensis </it>aquatic habitats. The spatial filter models accounted for approximately 19% redundant locational information in the ecological sampled <it>An. arabiensis </it>aquatic habitat data. In the residual error estimation model there was significant positive autocorrelation (i.e., clustering of habitats in geographic space) based on log-transformed larval/pupal data and the sampled covariate depth of habitat.</p> <p>Conclusion</p> <p>An autocorrelation error covariance matrix and a spatial filter analyses can prioritize mosquito control strategies by providing a computationally attractive and feasible description of variance uncertainty estimates for correctly identifying clusters of prolific <it>An. arabiensis </it>aquatic habitats based on larval/pupal productivity.</p

Propagation of uncertainty in a rotating pipe mechanism to generate an impinging swirling jet flow for heat transfer from a flat plate

In Computational Fluid Dynamics (CFD) studies composed of the coupling of different simulations, the uncertainty in one stage may be propagated to the following stage and affect the accuracy of the prediction. In this paper, a framework for uncertainty quantification in the computational heat transfer by forced convection is applied to the two-step simulation of the mechanical design of a swirling jet flow generated by a rotating pipe (Simulation 1) impinging on a flat plate (Simulation 2). This is the first probabilistic uncertainty analysis on computational heat transfer by impinging jets in the literature. The conclusion drawn from the analysis of this frequent engineering application is that the simulated system does not exhibit a significant sensitivity to stochastic variations of model input parameters, over the tested uncertainty ranges. Additionally, a set of non-linear regression models for the stochastic velocity and turbulent profiles for the pipe nozzle are created and tested, since impinging jets for heat transfer at Reynolds number of Re = 23000 are very frequent in the literature, but stochastic inlet conditions have never been provided. Numerical results demonstrate a negligible difference in the predicted convective heat transfer with respect to the use of the profiles simulated via CFD. These suggested surrogate models can be directly embedded onto other engineering applications (e.g. arrays of jets, jet flows impinging on plates with different shapes, inlet piping in combustion, chemical mixing, etc.) in which a realistic swirling flow under uncertainty can be of interest