A boundary preserving numerical algorithm for the Wright-Fisher model with mutation

The Wright-Fisher model is an Itô stochastic differential equation that was originally introduced to model genetic drift within finite populations and has recently been used as an approximation to ion channel dynamics within cardiac and neuronal cells. While analytic solutions to this equation remain within the interval [0,1], current numerical methods are unable to preserve such boundaries in the approximation. We present a new numerical method that guarantees approximations to a form of Wright-Fisher model, which includes mutation, remain within [0,1] for all time with probability one. Strong convergence of the method is proved and numerical experiments suggest that this new scheme converges with strong order 1/2. Extending this method to a multidimensional case, numerical tests suggest that the algorithm still converges strongly with order 1/2. Finally, numerical solutions obtained using this new method are compared to those obtained using the Euler-Maruyama method where the Wiener increment is resampled to ensure solutions remain within [0,1].

A hybrid model for studying spatial aspects of infectious diseases

We consider a hybrid model, created by coupling a continuum and an agent-based model of infectious disease. The framework of the hybrid model provides a mechanism to study the spread of infection at both the individual and population levels. This approach captures the stochastic spatial heterogeneity at the individual level, which is directly related to deterministic population level properties. This facilitates the study of spatial aspects of the epidemic process. A spatial analysis, involving counting the number of infectious agents in equally sized bins, reveals when the spatial domain is nonhomogeneous.

Numerical simulation of stochastic ordinary differential equations in biomathematical modelling

In this work we discuss the effects of white and coloured noise perturbations on the parameters of a mathematical model of bacteriophage infection introduced by Beretta and Kuang in [Math. Biosc. 149 (1998) 57]. We numerically simulate the strong solutions of the resulting systems of stochastic ordinary differential equations (SDEs), with respect to the global error, by means of numerical methods of both Euler-Taylor expansion and stochastic Runge-Kutta type.

Distinguishing between mean-field, moment dynamics and stochastic descriptions of birth-death-movement processes

Mathematical descriptions of birth–death–movement processes are often calibrated to measurements from cell biology experiments to quantify tissue growth rates. Here we describe and analyze a discrete model of a birth–death-movement process applied to a typical two–dimensional cell biology experiment. We present three different descriptions of the system: (i) a standard mean–field description which neglects correlation effects and clustering; (ii) a moment dynamics description which approximately incorporates correlation and clustering effects, and; (iii) averaged data from repeated discrete simulations which directly incorporates correlation and clustering effects. Comparing these three descriptions indicates that the mean–field and moment dynamics approaches are valid only for certain parameter regimes, and that both these descriptions fail to make accurate predictions of the system for sufficiently fast birth and death rates where the effects of spatial correlations and clustering are sufficiently strong. Without any method to distinguish between the parameter regimes where these three descriptions are valid, it is possible that either the mean–field or moment dynamics model could be calibrated to experimental data under inappropriate conditions, leading to errors in parameter estimation. In this work we demonstrate that a simple measurement of agent clustering and correlation, based on coordination number data, provides an indirect measure of agent correlation and clustering effects, and can therefore be used to make a distinction between the validity of the different descriptions of the birth–death–movement process.

Bayesian indirect inference using a parametric auxiliary model

Indirect inference (II) is a methodology for estimating the parameters of an intractable (generative) model on the basis of an alternative parametric (auxiliary) model that is both analytically and computationally easier to deal with. Such an approach has been well explored in the classical literature but has received substantially less attention in the Bayesian paradigm. The purpose of this paper is to compare and contrast a collection of what we call parametric Bayesian indirect inference (pBII) methods. One class of pBII methods uses approximate Bayesian computation (referred to here as ABC II) where the summary statistic is formed on the basis of the auxiliary model, using ideas from II. Another approach proposed in the literature, referred to here as parametric Bayesian indirect likelihood (pBIL), we show to be a fundamentally different approach to ABC II. We devise new theoretical results for pBIL to give extra insights into its behaviour and also its differences with ABC II. Furthermore, we examine in more detail the assumptions required to use each pBII method. The results, insights and comparisons developed in this paper are illustrated on simple examples and two other substantive applications. The first of the substantive examples involves performing inference for complex quantile distributions based on simulated data while the second is for estimating the parameters of a trivariate stochastic process describing the evolution of macroparasites within a host based on real data. We create a novel framework called Bayesian indirect likelihood (BIL) which encompasses pBII as well as general ABC methods so that the connections between the methods can be established.

Spatial prediction of N2O emissions in pasture : a Bayesian model averaging analysis

Nitrous oxide (N2O) is one of the greenhouse gases that can contribute to global warming. Spatial variability of N2O can lead to large uncertainties in prediction. However, previous studies have often ignored the spatial dependency to quantify the N2O - environmental factors relationships. Few researches have examined the impacts of various spatial correlation structures (e.g. independence, distance-based and neighbourhood based) on spatial prediction of N2O emissions. This study aimed to assess the impact of three spatial correlation structures on spatial predictions and calibrate the spatial prediction using Bayesian model averaging (BMA) based on replicated, irregular point-referenced data. The data were measured in 17 chambers randomly placed across a 271 m(2) field between October 2007 and September 2008 in the southeast of Australia. We used a Bayesian geostatistical model and a Bayesian spatial conditional autoregressive (CAR) model to investigate and accommodate spatial dependency, and to estimate the effects of environmental variables on N2O emissions across the study site. We compared these with a Bayesian regression model with independent errors. The three approaches resulted in different derived maps of spatial prediction of N2O emissions. We found that incorporating spatial dependency in the model not only substantially improved predictions of N2O emission from soil, but also better quantified uncertainties of soil parameters in the study. The hybrid model structure obtained by BMA improved the accuracy of spatial prediction of N2O emissions across this study region.

Motion planning and stochastic control with experimental validation on a planetary rover

Motion planning for planetary rovers must consider control uncertainty in order to maintain the safety of the platform during navigation. Modelling such control uncertainty is difficult due to the complex interaction between the platform and its environment. In this paper, we propose a motion planning approach whereby the outcome of control actions is learned from experience and represented statistically using a Gaussian process regression model. This model is used to construct a control policy for navigation to a goal region in a terrain map built using an on-board RGB-D camera. The terrain includes flat ground, small rocks, and non-traversable rocks. We report the results of 200 simulated and 35 experimental trials that validate the approach and demonstrate the value of considering control uncertainty in maintaining platform safety.

Enhanced stochastic mobility prediction with multi-output Gaussian processes

Outdoor robots such as planetary rovers must be able to navigate safely and reliably in order to successfully perform missions in remote or hostile environments. Mobility prediction is critical to achieving this goal due to the inherent control uncertainty faced by robots traversing natural terrain. We propose a novel algorithm for stochastic mobility prediction based on multi-output Gaussian process regression. Our algorithm considers the correlation between heading and distance uncertainty and provides a predictive model that can easily be exploited by motion planning algorithms. We evaluate our method experimentally and report results from over 30 trials in a Mars-analogue environment that demonstrate the effectiveness of our method and illustrate the importance of mobility prediction in navigating challenging terrain.

Commitment to internationalisation : an extension of the internationalisation process model

Notwithstanding the interest over many years by scholars in modeling the internationalization of the firm, the initial transition for the firm from domestic to international operations remains under-researched. We identify the behavioral factors that are important at the pre-internationalization state and discuss how they may interrelate to influence a decision to commit to internationalization through export commencement. We study export commitment by proposing and constructing an index that incorporates the factors that influence a firm’s propensity to commit to export activities. Utilizing the items from this index in a logistic regression analysis, we distinguish between the pre-internationalization characteristics of exporting and non-exporting firms to better understand the key influences in export commitment. Implications are discussed.

Examining the cost efficiency of Chinese hydroelectric companies using a finite mixture model

This paper evaluates the operational activities of Chinese hydroelectric power companies over the period 2000-2010 using a finite mixture model that controls for unobserved heterogeneity. In so doing, a stochastic frontier latent class model, which allows for the existence of different technologies, is adopted to estimate cost frontiers. This procedure not only enables us to identify different groups among the hydro-power companies analysed, but also permits the analysis of their cost efficiency. The main result is that three groups are identified in the sample, each equipped with different technologies, suggesting that distinct business strategies need to be adapted to the characteristics of China's hydro-power companies. Some managerial implications are developed. © 2012 Elsevier B.V.

Learned stochastic mobility prediction for planning with control uncertainty on unstructured terrain

Motion planning for planetary rovers must consider control uncertainty in order to maintain the safety of the platform during navigation. Modelling such control uncertainty is difficult due to the complex interaction between the platform and its environment. In this paper, we propose a motion planning approach whereby the outcome of control actions is learned from experience and represented statistically using a Gaussian process regression model. This mobility prediction model is trained using sample executions of motion primitives on representative terrain, and predicts the future outcome of control actions on similar terrain. Using Gaussian process regression allows us to exploit its inherent measure of prediction uncertainty in planning. We integrate mobility prediction into a Markov decision process framework and use dynamic programming to construct a control policy for navigation to a goal region in a terrain map built using an on-board depth sensor. We consider both rigid terrain, consisting of uneven ground, small rocks, and non-traversable rocks, and also deformable terrain. We introduce two methods for training the mobility prediction model from either proprioceptive or exteroceptive observations, and report results from nearly 300 experimental trials using a planetary rover platform in a Mars-analogue environment. Our results validate the approach and demonstrate the value of planning under uncertainty for safe and reliable navigation.

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.

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.

Corporate credit risk prediction under stochastic volatility and jumps

This paper examines the impact of allowing for stochastic volatility and jumps (SVJ) in a structural model on corporate credit risk prediction. The results from a simulation study verify the better performance of the SVJ model compared with the commonly used Merton model, and three sources are provided to explain the superiority. The empirical analysis on two real samples further ascertains the importance of recognizing the stochastic volatility and jumps by showing that the SVJ model decreases bias in spread prediction from the Merton model, and better explains the time variation in actual CDS spreads. The improvements are found particularly apparent in small firms or when the market is turbulent such as the recent financial crisis.