Gavin J. Gibson

Intelligence and the differentiation hypothesis

Abstract General intelligence (Spearmans g ) accounts for over 50% of the reliable variance in a battery of mental tests in a sample of the general population. In a “differentiation hypothesis” originally suggested by Spearman it is hypothesized that the degree to which g pervades performance on mental tests is greater at lower ability levels. In addition to providing a critical review, the study presented here tests the differentiation hypothesis: (a) at different ability levels and ages; (b) when groups are selected on the basis of a wide range of criterion abilities; and (c) by developing new statistical techniques for sampling groups of different ability levels. Data used were the Differential Aptitude Test results of over 10,500 Irish schoolchildren aged 14 through 17 years. Of groups selected on the basis of verbal, numerical, or spatial ability, the below-average ability groups had a more pervasive g factor, confirming the differentiation hypothesis.

Bayesian Analysis of Lidar Signals with Multiple Returns

Time-correlated single photon counting and burst illumination laser data can be used for range profiling and target classification. In general, the problem is to analyze the response from a histogram of either photon counts or integrated intensities to assess the number, positions, and amplitudes of the reflected returns from object surfaces. The goal of our work is a complete characterization of the 3D surfaces viewed by the laser imaging system. The authors present a unified theory of pixel processing that is applicable to both approaches based on a Bayesian framework, which allows for careful and thorough treatment of all types of uncertainties associated with the data. We use reversible jump Markov chain Monte Carlo (RJMCMC) techniques to evaluate the posterior distribution of the parameters and to explore spaces with different dimensionality. Further, we use a delayed rejection step to allow the generated Markov chain to mix better through the use of different proposal distributions. The approach is demonstrated on simulated and real data, showing that the return parameters can be estimated to a high degree of accuracy. We also show some practical examples from both near and far-range depth imaging.

Empirical models of farmer behaviour using psychological, social and economic variables. Part I: linear modelling

Abstract The analysis of social science data is increasingly dependent on the construction of mathematical models to predict and explain behaviour. This and the following paper have two objectives. The first objective is to describe some of the results of a recent survey on farmer decision-making and to present a number of models which have been developed using the data from this survey. The second objective is to use these models as a framework for a general discussion of the wide range of techniques available for the modelling of psychological, social and economic data. The classification of models into categories such as mechanistic and empirical, and the range of mathematical techniques available are described. The use of linear modelling is illustrated with examples from the data.

Individual response spread in self-report scales: personality correlations and consequences

Abstract We consider the phenomenon of individual differences in the use of questionnaire scales and examine some of its consequences. Results from two illustrative studies on farmers and consultant doctors are used to demonstrate that individual standard deviation of response option usage is a consistent trait which is significantly correlated with the personality dimension of conscientiousness. A mathematical model of individual response spread is also devised and it is shown that significant spurious correlations between responses to independent items can arise. This model is extended by estimating individual response thresholds from our two illustrative data sets; numerical simulation using these thresholds confirms the occurrence of spurious correlations. The distribution of correlation coefficients r is also very different from the standard form used for estimating levels of significance. There are widespread consequences of these observations for standard multivariate methods of analysing self-report data.

Relationships between ability and personality: Three hypotheses tested

Abstract This paper describes some studies of the interrelationship of personality and intelligence using data from a survey of Scottish farmers. (N = 210). Subjects completed the NEO Five Factor Inventory, Ravens Standard Progressive Matrices and the National Adult Reading test (NART). We address three hypotheses from the recent literature: that personality is more differentiated at high than at low levels of ability; that mental abilities are more differentiated at low than at high levels of neuroticism, and that intelligence affects the correlation between certain pairs of personality dimensions. Evidence is found for increased differentiation of neuroticism (N) and Openness (O) at higher levels of ability. It is also found that the level of N moderates the association between different types of mental ability. The Raven-NART correlation is depressed in low-N compared to high-N subjects; evidences is also found of a nonlinear relationship between ability and trait variables for N and O. No significant effects of ablity on correlations between pairs of personality dimensions are found; in particular there is no support for the hypothesis that intelligence affects the correlation between extraversion and conscientiousness. We also examine the effects of ability on reliability of the NEO dimensions. It is found that Cronbach α values are lower for lower ability subjects, particularly for the I dimension. The consequences of this in counfounding effects due to personality differentiation and differential reliability and the resulting difficulty in interpreting experimental observations in this area are discussed. Some possible experimental approaches to this problem are proposed.

Estimation of multiple transmission rates for epidemics in heterogeneous populations

One of the principal challenges in epidemiological modeling is to parameterize models with realistic estimates for transmission rates in order to analyze strategies for control and to predict disease outcomes. Using a combination of replicated experiments, Bayesian statistical inference, and stochastic modeling, we introduce and illustrate a strategy to estimate transmission parameters for the spread of infection through a two-phase mosaic, comprising favorable and unfavorable hosts. We focus on epidemics with local dispersal and formulate a spatially explicit, stochastic set of transition probabilities using a percolation paradigm for a susceptible–infected (S–I) epidemiological model. The S–I percolation model is further generalized to allow for multiple sources of infection including external inoculum and host-to-host infection. We fit the model using Bayesian inference and Markov chain Monte Carlo simulation to successive snapshots of damping-off disease spreading through replicated plant populations that differ in relative proportions of favorable and unfavorable hosts and with time-varying rates of transmission. Epidemiologically plausible parametric forms for these transmission rates are compared by using the deviance information criterion. Our results show that there are four transmission rates for a two-phase system, corresponding to each combination of infected donor and susceptible recipient. Knowing the number and magnitudes of the transmission rates allows the dominant pathways for transmission in a heterogeneous population to be identified. Finally, we show how failure to allow for multiple transmission rates can overestimate or underestimate the rate of spread of epidemics in heterogeneous environments, which could lead to marked failure or inefficiency of control strategies.

Bayesian analysis of experimental epidemics of foot-and-mouth disease.

We investigate the transmission dynamics of a certain type of foot–and–mouth disease (FMD) virus under experimental conditions. Previous analyses of experimental data from FMD outbreaks in non–homogeneously mixing populations of sheep have suggested a decline in viraemic level through serial passage of the virus, but these do not take into account possible variation in the length of the chain of viral transmission for each animal, which is implicit in the non–observed transmission process. We consider a susceptible–exposed–infectious–removed non–Markovian compartmental model for partially observed epidemic processes, and we employ powerful methodology (Markov chain Monte Carlo) for statistical inference, to address epidemiological issues under a Bayesian framework that accounts for all available information and associated uncertainty in a coherent approach. The analysis allows us to investigate the posterior distribution of the hidden transmission history of the epidemic, and thus to determine the effect of the length of the infection chain on the recorded viraemic levels, based on the posterior distribution of a p–value. Parameter estimates of the epidemiological characteristics of the disease are also obtained. The results reveal a possible decline in viraemia in one of the two experimental outbreaks. Our model also suggests that individual infectivity is related to the level of viraemia.

Bayesian inference for stochastic epidemics in closed populations

We consider continuous-time stochastic compartmental models that can be applied in veterinary epidemiology to model the within-herd dynamics of infectious diseases. We focus on an extension of Markovian epidemic models, allowing the infectious period of an individual to follow a Weibull distribution, resulting in a more flexible model for many diseases. Following a Bayesian approach we show how approximation methods can be applied to design efficient MCMC algorithms with favourable mixing properties for fitting non-Markovian models to partial observations of epidemic processes. The methodology is used to analyse real data concerning a smallpox outbreak in a human population, and a simulation study is conducted to assess the effects of the frequency and accuracy of diagnostic tests on the information yielded on the epidemic process.

Bayesian estimation for percolation models of disease spread in plant populations

Statistical methods are formulated for fitting and testing percolation-based, spatio-temporal models that are generally applicable to biological or physical processes that evolve in spatially distributed populations. The approach is developed and illustrated in the context of the spread of Rhizoctonia solani, a fungal pathogen, in radish but is readily generalized to other scenarios. The particular model considered represents processes of primary and secondary infection between nearest-neighbour hosts in a lattice, and time-varying susceptibility of the hosts. Bayesian methods for fitting the model to observations of disease spread through space and time in replicate populations are developed. These use Markov chain Monte Carlo methods to overcome the problems associated with partial observation of the process. We also consider how model testing can be achieved by embedding classical methods within the Bayesian analysis. In particular we show how a residual process, with known sampling distribution, can be defined. Model fit is then examined by generating samples from the posterior distribution of the residual process, to which a classical test for consistency with the known distribution is applied, enabling the posterior distribution of the P-value of the test used to be estimated. For the Rhizoctonia-radish system the methods confirm the findings of earlier non-spatial analyses regarding the dynamics of disease transmission and yield new evidence of environmental heterogeneity in the replicate experiments.

Spatio-temporal stochastic modelling of Clostridium difficile

Clostridium difficile-associated diarrhoea (CDAD) occurs sporadically or in small discrete outbreaks. Stochastic models may help to inform hospital infection control strategies. Bayesian framework using data augmentation and Markov chain Monte Carlo methods were applied to a spatio-temporal model of CDAD. Model simulations were validated against 17 months of observed data from two 30-bedded medical wards for the elderly. Simulating the halving of transmission rates of C. difficile from other patients and the environment reduced CDAD cases by 15%. Doubling the rate at which patients become susceptible increased predicted CDAD incidence by 63%. By contrast, doubling environmental load made hardly any difference, increasing CDAD incidence by only 3%. Simulation of different interventions indicates that for the same effect size, reducing patient susceptibility to infection is more effective in reducing the number of CDAD cases than lowering transmission rates.