Bayesian discrete latent spatial modeling of crack initiation in orthopaedic hip replacement bone cement

In this paper, we propose a spatial model for the initiation of cracks in the bone cement of hip replacement specimens. The failure of hip replacements can be attributed mainly to damage accumulation, consisting of crack initiation and growth, occurring in the cement mantle that interlocks the hip prosthesis and the femur bone. Since crack initiation is an important factor in determining the lifetime of a replacement, the understanding of the reasons for crack initiation is vital in attempting to prolong the life of the hip replacement. The data consist of crack location coordinates from five laboratory experimental models, together with stress measurements. It is known that stress plays a major role in the initiation of cracks, and it is also known that other unmeasurable factors such as air bubbles (pores) in the cement mantle are also influential. We propose an identity-link spatial Poisson regression model for the counts of cracks in discrete regions of the cement, incorporating both the measured (stress), and through a latent process, any unmeasured factors (possibly pores) that may be influential. All analysis is carried out in a Bayesian framework, allowing for the inclusion of prior information obtained from engineers, and parameter estimation for the model is done via Markov chain Monte Carlo techniques.     

Correlational biases in mean response latency differences

Multifarious psychological constructs are indexed by the mean latency difference (MLD), the within-subject difference between mean response latency on two tasks. Two associations consistently emerge in mean latency data. Firstly, across subjects, mean latencies on distinct tasks are positively correlated. This correlation arises from individual differences in general rates of information processing that are a shared influence on response latency in diverse tasks. Secondly, across tasks, the mean and variance of mean latency are positively correlated. Compared to a simple task, a complex task has both a larger average mean latency and a larger variance of mean latency, across subjects. Taken together, these associations make the interpretation of the MLD problematic by biasing correlations between the MLD and (a) task mean latencies, (b) the average of the mean latencies, (c) external criteria, and (d) other MLDs. A variety of mean latency transformations were evaluated and, while they differed in their effectiveness, they did not satisfactorily rectify MLD biases. An alternative approach, focusing on scale invariant contrasts of within-subject response latency distributions, is introduced in the conclusion.     

BAYESIAN HIDDEN MARKOV MODELS FOR LONGITUDINAL COUNTS

This paper describes a Bayesian approach to modelling carcinogenity in animal studies where the data consist of counts of the number of tumours present over time. It compares two autoregressive hidden Markov models. One of them models the transitions between three latent states: an inactive transient state, a multiplying state for increasing counts and a reducing state for decreasing counts. The second model introduces a fourth tied state to describe non‐zero observations that are neither increasing nor decreasing. Both these models can model the length of stay upon entry of a state. A discrete constant hazards waiting time distribution is used to model the time to onset of tumour growth. Our models describe between‐animal‐variability by a single hierarchy of random effects and the within‐animal variation by first‐order serial dependence. They can be extended to higher‐order serial dependence and multi‐level hierarchies. Analysis of data from animal experiments comparing the influence of two genes leads to conclusions that differ from those of Dunson (2000). The observed data likelihood defines an information criterion to assess the predictive properties of the three‐ and four‐state models. The deviance information criterion is appropriately defined for discrete parameters.     

Residual analysis for spatial point processes (with discussion)

Summary.  We define residuals for point process models fitted to spatial point pattern data, and we propose diagnostic plots based on them. The residuals apply to any point process model that has a conditional intensity; the model may exhibit spatial heterogeneity, interpoint interaction and dependence on spatial covariates. Some existing ad hoc methods for model checking (quadrat counts, scan statistic, kernel smoothed intensity and Berman's diagnostic) are recovered as special cases. Diagnostic tools are developed systematically, by using an analogy between our spatial residuals and the usual residuals for (non-spatial) generalized linear models. The conditional intensity λ plays the role of the mean response. This makes it possible to adapt existing knowledge about model validation for generalized linear models to the spatial point process context, giving recommendations for diagnostic plots. A plot of smoothed residuals against spatial location, or against a spatial covariate, is effective in diagnosing spatial trend or co-variate effects. Q – Q -plots of the residuals are effective in diagnosing interpoint interaction.     

Approximation of power in multivariate analysis

We consider the calculation of power functions in classical multivariate analysis. In this context, power can be expressed in terms of tail probabilities of certain noncentral distributions. The necessary noncentral distribution theory was developed between the 1940s and 1970s by a number of authors. However, tractable methods for calculating the relevant probabilities have been lacking. In this paper we present simple yet extremely accurate saddlepoint approximations to power functions associated with the following classical test statistics: the likelihood ratio statistic for testing the general linear hypothesis in MANOVA; the likelihood ratio statistic for testing block independence; and Bartlett's modified likelihood ratio statistic for testing equality of covariance matrices.     

Estimation of the intercept parameter for linear regression model with uncertain non-sample prior information

This paper considers alternative estimators of the intercept parameter of the linear regression model with normal error when uncertain non-sample prior information about the value of the slope parameter is available. The maximum likelihood, restricted, preliminary test and shrinkage estimators are considered. Based on their quadratic biases and mean square errors the relative performances of the estimators are investigated. Both analytical and graphical comparisons are explored. None of the estimators is found to be uniformly dominating the others. However, if the non-sample prior information regarding the value of the slope is not too far from its true value, the shrinkage estimator of the intercept parameter dominates the rest of the estimators.