Nonparametric estimation of waiting time distributions in a Markov model based on current status data

We construct nonparametric estimators of state waiting time distribution functions in a Markov multistate model using current status data. This is a particularly difficult problem since neither the entry nor the exit times of a given state are directly observed. These estimators are obtained, using the Markov property, from estimators of counting processes of state entry and exit times, as well as, the size of “at risk” sets of state entry and transitions out of that state. Consistency of our estimators is established. Finite-sample behavior of our estimators is studied by simulation, in which we show that our estimators based on current status data compare well with those based on complete data. We also illustrate our method using a pubertal development data set obtained from the NHANES III [1997. NHANES III Reference Manuals and Reports (CD-ROM). Analytic and Reporting Guidelines: The Third National Health and Nutrition Examination Survey (1988–94). National Center for Health Statistics, Centers for Disease Control and Prevention, Hyattsville, MD] study.     

Two-dimensional generalisations of dynamic programming for image analysis

Dynamic programming (DP) is a fast, elegant method for solving many one-dimensional optimisation problems but, unfortunately, most problems in image analysis, such as restoration and warping, are two-dimensional. We consider three generalisations of DP. The first is iterated dynamic programming (IDP), where DP is used to recursively solve each of a sequence of one-dimensional problems in turn, to find a local optimum. A second algorithm is an empirical, stochastic optimiser, which is implemented by adding progressively less noise to IDP. The final approach replaces DP by a more computationally intensive Forward-Backward Gibbs Sampler, and uses a simulated annealing cooling schedule. Results are compared with existing pixel-by-pixel methods of iterated conditional modes (ICM) and simulated annealing in two applications: to restore a synthetic aperture radar (SAR) image, and to warp a pulsed-field electrophoresis gel into alignment with a reference image. We find that IDP and its stochastic variant outperform the remaining algorithms.     

Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations

Summary.  Structured additive regression models are perhaps the most commonly used class of models in statistical applications. It includes, among others, (generalized) linear models, (generalized) additive models, smoothing spline models, state space models, semiparametric regression, spatial and spatiotemporal models, log-Gaussian Cox processes and geostatistical and geoadditive models. We consider approximate Bayesian inference in a popular subset of structured additive regression models, latent Gaussian models , where the latent field is Gaussian, controlled by a few hyperparameters and with non-Gaussian response variables. The posterior marginals are not available in closed form owing to the non-Gaussian response variables. For such models, Markov chain Monte Carlo methods can be implemented, but they are not without problems, in terms of both convergence and computational time. In some practical applications, the extent of these problems is such that Markov chain Monte Carlo sampling is simply not an appropriate tool for routine analysis. We show that, by using an integrated nested Laplace approximation and its simplified version, we can directly compute very accurate approximations to the posterior marginals. The main benefit of these approximations is computational: where Markov chain Monte Carlo algorithms need hours or days to run, our approximations provide more precise estimates in seconds or minutes. Another advantage with our approach is its generality, which makes it possible to perform Bayesian analysis in an automatic, streamlined way, and to compute model comparison criteria and various predictive measures so that models can be compared and the model under study can be challenged.     

SEMIPARAMETRIC REGRESSION AND GRAPHICAL MODELS

Semiparametric regression models that use spline basis functions with penalization have graphical model representations. This link is more powerful than previously established mixed model representations of semiparametric regression, as a larger class of models can be accommodated. Complications such as missingness and measurement error are more naturally handled within the graphical model architecture. Directed acyclic graphs, also known as Bayesian networks, play a prominent role. Graphical model-based Bayesian 'inference engines', such as bugs and vibes , facilitate fitting and inference. Underlying these are Markov chain Monte Carlo schemes and recent developments in variational approximation theory and methodology.     

VARIATIONAL BAYESIAN ANALYSIS FOR HIDDEN MARKOV MODELS

The variational approach to Bayesian inference enables simultaneous estimation of model parameters and model complexity. An interesting feature of this approach is that it also leads to an automatic choice of model complexity. Empirical results from the analysis of hidden Markov models with Gaussian observation densities illustrate this. If the variational algorithm is initialized with a large number of hidden states, redundant states are eliminated as the method converges to a solution, thereby leading to a selection of the number of hidden states. In addition, through the use of a variational approximation, the deviance information criterion for Bayesian model selection can be extended to the hidden Markov model framework. Calculation of the deviance information criterion provides a further tool for model selection, which can be used in conjunction with the variational approach.     

Adaptive multiple importance sampling for Gaussian processes

In applications of Gaussian processes (GPs) where quantification of uncertainty is a strict requirement, it is necessary to accurately characterize the posterior distribution over Gaussian process covariance parameters. This is normally done by means of standard Markov chain Monte Carlo (MCMC) algorithms, which require repeated expensive calculations involving the marginal likelihood. Motivated by the desire to avoid the inefficiencies of MCMC algorithms rejecting a considerable amount of expensive proposals, this paper develops an alternative inference framework based on adaptive multiple importance sampling (AMIS). In particular, this paper studies the application of AMIS for GPs in the case of a Gaussian likelihood, and proposes a novel pseudo-marginal-based AMIS algorithm for non-Gaussian likelihoods, where the marginal likelihood is unbiasedly estimated. The results suggest that the proposed framework outperforms MCMC-based inference of covariance parameters in a wide range of scenarios.     

Optimal design of the adaptive exponentially weighted moving average control chart over a range of mean shifts

The adaptive exponentially weighted moving average (AEWMA) control chart is a smooth combination of the Shewhart and exponentially weighted moving average (EWMA) control charts. This chart was proposed by Cappizzi and Masarotto (2003) to achieve a reasonable performance for both small and large shifts. Cappizzi and Masarotto (2003) used a pair of shifts in designing their control chart. In this study, however, the process mean shift is considered as a random variable with a certain probability distribution and the AEWMA control chart is optimized for a wide range of mean shifts according to that probability distribution and not just for a pair of shifts. Using the Markov chain technique, the results show that the new optimization design can improve the performance of the AEWMA control chart from an overall point of view relative to the various designs presented by Cappizzi and Masarotto (2003). Optimal design parameters that achieve the desired in-control average run length (ARL) are computed in several cases and formulas used to find approximately their values are given. Using these formulas, the practitioner can compute the optimal design parameters corresponding to any desired in-control ARL without the need to apply the optimization procedure. The results obtained by these formulas are very promising and would particularly facilitate the design of the AEWMA control chart for any in-control ARL value.     

Assessing convergence diagnostic tests for Bayesian Cox regression

The Markov chain Monte Carlo (MCMC) method generates samples from the posterior distribution and uses these samples to approximate expectations of quantities of interest. For the process, researchers have to decide whether the Markov chain has reached the desired posterior distribution. Using convergence diagnostic tests are very important to decide whether the Markov chain has reached the target distribution. Our interest in this study was to compare the performances of convergence diagnostic tests for all parameters of Bayesian Cox regression model with different number of iterations by using a simulation and a real lung cancer dataset.     

Monitoring the coefficient of variation using a variable sample size and sampling interval control chart

This article proposes a CV chart by using the variable sample size and sampling interval (VSSI) feature to improve the performance of the basic CV chart, for detecting small and moderate shifts in the CV. The proposed VSSI CV chart is designed by allowing the sample size and the sampling interval to vary. The VSSI CV chart's statistical performance is measured by using the average time to signal (ATS) and expected average time to signal (EATS) criteria and is compared with that of existing CV charts. The Markov chain approach is employed in the design of the chart.