Boolean Models: Maximum Likelihood Estimation from Circular Clumps

This paper deals with the problem of making inferences on the maximum radius and the intensity of the Poisson point process associated to a Boolean Model of circular primary grains with uniformly distributed random radii. The only sample information used is observed radii of circular clumps (DUPAC, 1980). The behaviour of maximum likelihood estimation has been evaluated by means of Monte Carlo methods.     

Estimating the Weighting Components of a Health Quality Index

This paper introduces a maximum likelihood estimation model that uses patients' pretherapy characteristics to determine the weighting components of multipe outcomes of quality health. The resulting health quality index' can then be included in cost-effectiveness analyses to compare alternative treatment plans. A Monte Carlo simulation is performed to test the model's robustness and power.     

Estimating Mean Landmark Triangles

The paper deals with the statistical estimation of mean triangles of landmark data. For the model introduced by Bookstein (1986) three methods of estimating the “ideal” triangle are compared: the maximum likelihood method based on the exact distribution given in Mardia and Dryden (1989a), a moment method and an iterative algorithm yielding a mean triangle in the sense of Fréchet. These methods are compared by Monte Carlo simulation applied also to models with variances greater than those required for Bookstein's normal approximation.     

Estimating the rate of increase for the finless porpoise with special attention to predictions for the Inland Sea population in Japan

The finless porpoise Neophocaena asiaeorientalis inhabits coastal waters and rivers in East Asia and is exposed to various human activities. This species is listed on the IUCN Red List of Threatened Species due to a reduction in abundance. Although human-induced mortality can be a threat to porpoise populations, future anthropogenic impacts have not been quantitatively evaluated due to lack of demographic information. Adequate future population projections are needed to form the basis for conservation measures before the population declines to critical levels. We conducted a population viability analysis for the population of finless porpoise in the Inland Sea, Japan using a Leslie matrix model composed of age-specific survival and fertility rates. We described the uncertainty in the annual rate of increase (λ) for the finless porpoise using randomly sampled estimates of survival rate for other cetaceans with similar life histories. Plausible median estimates of λ ranged from 1.041 (age at first reproduction [AFR] = 7) to 1.056 (AFR = 5). Future population changes and extinction probabilities were predicted after combining these estimates with a predicted human-induced mortality rate (M) and available abundance estimates. The extinction probability after 100 years was 0 %. However, the probability of the quasi-extinction (<100 individuals) was as high as 79.0 % after 100 years. The results also suggest that the persistence of the finless porpoise population could be achieved with a small effort to reduce anthropogenic mortality.     

Estimating and Projecting Trends in HIV/AIDS Generalized Epidemics Using Incremental Mixture Importance Sampling

Summary The Joint United Nations Programme on HIV/AIDS (UNAIDS) has decided to use Bayesian melding as the basis for its probabilistic projections of HIV prevalence in countries with generalized epidemics. This combines a mechanistic epidemiological model, prevalence data, and expert opinion. Initially, the posterior distribution was approximated by sampling‐importance‐resampling, which is simple to implement, easy to interpret, transparent to users, and gave acceptable results for most countries. For some countries, however, this is not computationally efficient because the posterior distribution tends to be concentrated around nonlinear ridges and can also be multimodal. We propose instead incremental mixture importance sampling (IMIS), which iteratively builds up a better importance sampling function. This retains the simplicity and transparency of sampling importance resampling, but is much more efficient computationally. It also leads to a simple estimator of the integrated likelihood that is the basis for Bayesian model comparison and model averaging. In simulation experiments and on real data, it outperformed both sampling importance resampling and three publicly available generic Markov chain Monte Carlo algorithms for this kind of problem.     

Hierarchical proportional hazards regression models for highly stratified data

In clinical trials conducted over several data collection centers, the most common statistically defensible analytic method, a stratified Cox model analysis, suffers from two important defects. First, identification of units that are outlying with respect to the baseline hazard is awkward since this hazard is implicit (rather than explicit) in the Cox partial likelihood. Second (and more seriously), identification of modest treatment effects is often difficult since the model fails to acknowledge any similarity across the strata. We consider a number of hierarchical modeling approaches that preserve the integrity of the stratified design while offering a middle ground between traditional stratified and unstratified analyses. We investigate both fully parametric (Weibull) and semiparametric models, the latter based not on the Cox model but on an extension of an idea by Gelfand and Mallick (1995, Biometrics 51, 843-852), which models the integrated baseline hazard as a mixture of monotone functions. We illustrate the methods using data from a recent multicenter AIDS clinical trial, comparing their ease of use, interpretation, and degree of robustness with respect to estimates of both the unit-specific baseline hazards and the treatment effect.     

Small Sample Properties of the Likelihood Estimator in Proportional Hazard Regression Models with Omitted Variables

The paper deals with the effects of incorrectly omitted regressor variables in a parametric proportional hazard regression model. By studying conditions for equality between the estimators of correct and incorrect models it is demonstrated analytically that such cases are not to be expected in practise. A small sample Monte Carlo experiment indicates severe negative effects on the retained parameters both in terms of bias and mean square error.     

Jeffreys' Likelihood Ratio for the 2×2-Table — A Monte Carlo Study —

Jeffreys' approach for analyzing a 2×2-table is discussed via a Monte Carlo study. The main findings are reported.     

Estimation of Parameters for Macroparasite Population Evolution Using Approximate Bayesian Computation

Summary We estimate the parameters of a stochastic process model for a macroparasite population within a host using approximate Bayesian computation (ABC). The immunity of the host is an unobserved model variable and only mature macroparasites at sacrifice of the host are counted. With very limited data, process rates are inferred reasonably precisely. Modeling involves a three variable Markov process for which the observed data likelihood is computationally intractable. ABC methods are particularly useful when the likelihood is analytically or computationally intractable. The ABC algorithm we present is based on sequential Monte Carlo, is adaptive in nature, and overcomes some drawbacks of previous approaches to ABC. The algorithm is validated on a test example involving simulated data from an autologistic model before being used to infer parameters of the Markov process model for experimental data. The fitted model explains the observed extra‐binomial variation in terms of a zero‐one immunity variable, which has a short‐lived presence in the host.     

On the Bayesian analysis of ring-recovery data

Vounatsou and Smith (1995, Biometrics 51, 687-708) describe the modern Bayesian analysis of ring-recovery data. Here we discuss and extend their work. We draw different conclusions from two major data analyses. We emphasize the extreme sensitivity of certain parameter estimates to the choice of prior distribution and conclude that naive use of Bayesian methods in this area can be misleading. Additionally, we explain the discrepancy between the Bayesian and classical analyses when the likelihood surface has a flat ridge. In this case, when there is no unique maximum likelihood estimate, the Bayesian estimators are remarkably precise.     

SIDEpro: a novel machine learning approach for the fast and accurate prediction of side-chain conformations

Accurate protein side-chain conformation prediction is crucial for protein modeling and existing methods for the task are widely used; however, faster and more accurate methods are still required. Here we present a new machine learning approach to the problem where an energy function for each rotamer in a structure is computed additively over pairs of contacting atoms. A family of 156 neural networks indexed by amino acid and contacting atom types is used to compute these rotamer energies as a function of atomic contact distances. Although direct energy targets are not available for training, the neural networks can still be optimized by converting the energies to probabilities and optimizing these probabilities using Markov Chain Monte Carlo methods. The resulting predictor SIDEpro makes predictions by initially setting the rotamer probabilities for each residue from a backbone-dependent rotamer library, then iteratively updating these probabilities using the trained neural networks. After convergences of the probabilities, the side-chains are set to the highest probability rotamer. Finally, a post processing clash reduction step is applied to the models. SIDEpro represents a significant improvement in speed and a modest, but statistically significant, improvement in accuracy when compared with the state-of-the-art for rapid side-chain prediction method SCWRL4 on the following datasets: (1) 379 protein test set of SCWRL4; (2) 94 proteins from CASP9; (3) a set of seven large protein-only complexes; and (4) a ribosome with and without the RNA. Using the SCWRL4 test set, SIDEpro's accuracy (χ(1) 86.14%, χ(1+2) 74.15%) is slightly better than SCWRL4-FRM (χ(1) 85.43%, χ(1+2) 73.47%) and it is 7.0 times faster. On the same test set SIDEpro is clearly more accurate than SCWRL4-rigid rotamer model (RRM) (χ(1) 84.15%, χ(1+2) 71.24%) and 2.4 times faster. Evaluation on the additional test sets yield similar accuracy results with SIDEpro being slightly more accurate than SCWRL4-flexible rotamer model (FRM) and clearly more accurate than SCWRL4-RRM; however, the gap in CPU time is much more significant when the methods are applied to large protein complexes. SIDEpro is part of the SCRATCH suite of predictors and available from: http://scratch.proteomics.ics.uci.edu/.     

Bayesian phylogenetic model selection using reversible jump Markov chain Monte Carlo

A common problem in molecular phylogenetics is choosing a model of DNA substitution that does a good job of explaining the DNA sequence alignment without introducing superfluous parameters. A number of methods have been used to choose among a small set of candidate substitution models, such as the likelihood ratio test, the Akaike Information Criterion (AIC), the Bayesian Information Criterion (BIC), and Bayes factors. Current implementations of any of these criteria suffer from the limitation that only a small set of models are examined, or that the test does not allow easy comparison of non-nested models. In this article, we expand the pool of candidate substitution models to include all possible time-reversible models. This set includes seven models that have already been described. We show how Bayes factors can be calculated for these models using reversible jump Markov chain Monte Carlo, and apply the method to 16 DNA sequence alignments. For each data set, we compare the model with the best Bayes factor to the best models chosen using AIC and BIC. We find that the best model under any of these criteria is not necessarily the most complicated one; models with an intermediate number of substitution types typically do best. Moreover, almost all of the models that are chosen as best do not constrain a transition rate to be the same as a transversion rate, suggesting that it is the transition/transversion rate bias that plays the largest role in determining which models are selected. Importantly, the reversible jump Markov chain Monte Carlo algorithm described here allows estimation of phylogeny (and other phylogenetic model parameters) to be performed while accounting for uncertainty in the model of DNA substitution.     

Bayesian Neural Network Models for Censored Data

Neural networks are considered by many to be very promising tools for classification and prediction. The flexibility of the neural network models often result in over-fit. Shrinking the parameters using a penalized likelihood is often used in order to overcome such over-fit. In this paper we extend the approach proposed by FARAGGI and SIMON (1995a) to modeling censored survival data using the input-output relationship associated with a single hidden layer feed-forward neural network. Instead of estimating the neural network parameters using the method of maximum likelihood, we place normal prior distributions on the parameters and make inferences based on derived posterior distributions of the parameters. This Bayesian formulation will result in shrinking the parameters of the neural network model and will reduce the over-fit compared with the maximum likelihood estimators. We illustrate our proposed method on a simulated and a real example.     

Integration of the M6 Cyberknife in the Moderato Monte Carlo platform and prediction of beam parameters using machine learning

PurposeThis work describes the integration of the M6 Cyberknife in the Moderato Monte Carlo platform, and introduces a machine learning method to accelerate the modelling of a linac.MethodsThe MLC-equipped M6 Cyberknife was modelled and integrated in Moderato, our in-house platform offering independent verification of radiotherapy dose distributions. The model was validated by comparing TPS dose distributions with Moderato and by film measurements. Using this model, a machine learning algorithm was trained to find electron beam parameters for other M6 devices, by simulating dose curves with varying spot size and energy. The algorithm was optimized using cross-validation and tested with measurements from other institutions equipped with a M6 Cyberknife.ResultsOptimal agreement in the Monte Carlo model was reached for a monoenergetic electron beam of 6.75 MeV with Gaussian spatial distribution of 2.4 mm FWHM. Clinical plan dose distributions from Moderato agreed within 2% with the TPS, and film measurements confirmed the accuracy of the model. Cross-validation of the prediction algorithm produced mean absolute errors of 0.1 MeV and 0.3 mm for beam energy and spot size respectively. Prediction-based simulated dose curves for other centres agreed within 3% with measurements, except for one device where differences up to 6% were detected.ConclusionsThe M6 Cyberknife was integrated in Moderato and validated through dose re-calculations and film measurements. The prediction algorithm was successfully applied to obtain electron beam parameters for other M6 devices. This method would prove useful to speed up modelling of new machines in Monte Carlo systems.     

Estimating the life-span of oligodendrocytes from clonal data on their development in cell culture

This paper presents a new method to analyze clonal data on oligodendrocyte development in cell culture. The process of oligodendrocyte generation from precursor cells is modelled as a multi-type Bellman-Harris branching process as suggested in an earlier paper [K. Boucher, A. Zorin, A.Y. Yakovlev, M. Mayer-Proschel, M. Noble, An alternative stochastic model of generation of oligodendrocytes in cell culture, J. Math. Biol. 43 (2001) 22]. This model has been extended to allow for death of oligodendrocytes as well as a dissimilar distribution of the first mitotic cycle duration as compared to the subsequent cycles of precursor cells, which lengths are assumed to be independent and identically distributed random variables. Since the time-span of oligodendrocytes is not directly observable in clonal data, plausible parametric assumptions are invoked to make estimation problems tractable. In particular, the time to cell death follows a two-parameter gamma distribution, while the lapse of time between the event of cell death and the event of cell disintegration is assumed to be exponentially distributed. A simulated pseudo maximum likelihood method for estimation of model parameters has been developed using simulation-based approximations of the expected numbers and variance-covariance matrices for different types of cells. Finite sample properties of the estimation procedure are studied by computer simulations. The proposed method is illustrated with an analysis of the clonal development of O-2A progenitor cells isolated from the rat optic nerve and the corpus callosum.