Joining Forces of Bayesian and Frequentist Methodology: A Study for Inference in the Presence of Non-Identifiability

Increasingly complex applications involve large datasets in combination with non-linear and high dimensional mathematical models. In this context, statistical inference is a challenging issue that calls for pragmatic approaches that take advantage of both Bayesian and frequentist methods. The elegance of Bayesian methodology is founded in the propagation of information content provided by experimental data and prior assumptions to the posterior probability distribution of model predictions. However, for complex applications experimental data and prior assumptions potentially constrain the posterior probability distribution insufficiently. In these situations Bayesian Markov chain Monte Carlo sampling can be infeasible. From a frequentist point of view insufficient experimental data and prior assumptions can be interpreted as non-identifiability. The profile likelihood approach offers to detect and to resolve non-identifiability by experimental design iteratively. Therefore, it allows one to better constrain the posterior probability distribution until Markov chain Monte Carlo sampling can be used securely. Using an application from cell biology we compare both methods and show that a successive application of both methods facilitates a realistic assessment of uncertainty in model predictions.Comment: Article to appear in Phil. Trans. Roy. Soc.

On linear combinations of generalized involutive matrices

Let X(dagger) denotes the Moore-Penrose pseudoinverse of a matrix X. We study a number of situations when (aA + bB)(dagger) = aA + bB provided a, b is an element of C\{0} and A, B are n x n complex matrices such that A(dagger) = A and B(dagger) = B. (C) 2011 Taylor & FrancisLiu, X.; Wu, L.; Benítez López, J. (2011). On linear combinations of generalized involutive matrices. Linear and Multilinear Algebra. 59(11):1221-1236. doi:10.1080/03081087.2010.496111S12211236591

Estimating Animal Abundance in Ground Beef Batches Assayed with Molecular Markers

Estimating animal abundance in industrial scale batches of ground meat is important for mapping meat products through the manufacturing process and for effectively tracing the finished product during a food safety recall. The processing of ground beef involves a potentially large number of animals from diverse sources in a single product batch, which produces a high heterogeneity in capture probability. In order to estimate animal abundance through DNA profiling of ground beef constituents, two parameter-based statistical models were developed for incidence data. Simulations were applied to evaluate the maximum likelihood estimate (MLE) of a joint likelihood function from multiple surveys, showing superiority in the presence of high capture heterogeneity with small sample sizes, or comparable estimation in the presence of low capture heterogeneity with a large sample size when compared to other existing models. Our model employs the full information on the pattern of the capture-recapture frequencies from multiple samples. We applied the proposed models to estimate animal abundance in six manufacturing beef batches, genotyped using 30 single nucleotide polymorphism (SNP) markers, from a large scale beef grinding facility. Results show that between 411∼1367 animals were present in six manufacturing beef batches. These estimates are informative as a reference for improving recall processes and tracing finished meat products back to source

Life Cycle of the Water Scorpion, Laccotrephes japonensis, in Japanese Rice Fields and a Pond

A Laccotrephes japonensis (Nepidae: Heteroptera) population was studied based upon mark and recapture censuses in order to elucidate the seasonal pattern of habitat utilization in a rice paddy system including an irrigation pond between April and October, in 2006 and 2007. The seasonal pattern of nymphs and adults did not differ markedly between the rice fields and the pond. Survival rates of L. japonensis of all stages did not differ between the rice fields and the pond in 2006, but were lower in 2007 in both habitats. In 2007, however, the survival rate of L. japonensis nymphs in the pond was higher than in the rice fields. In rice fields, 36.3% of the overwintering adults were recaptured the following year. On the other hand, the recapture rate after overwintering in the pond was only 6.4%. Migration from the pond to the paddies and vice versa was observed. In summary, the rice fields and the pond may reinforce each other as reproductive and overwintering sites of L. japonensis, especially during unfavorable years

Sparsest factor analysis for clustering variables: a matrix decomposition approach

We propose a new procedure for sparse factor analysis (FA) such that each variable loads only one common factor. Thus, the loading matrix has a single nonzero element in each row and zeros elsewhere. Such a loading matrix is the sparsest possible for certain number of variables and common factors. For this reason, the proposed method is named sparsest FA (SSFA). It may also be called FA-based variable clustering, since the variables loading the same common factor can be classified into a cluster. In SSFA, all model parts of FA (common factors, their correlations, loadings, unique factors, and unique variances) are treated as fixed unknown parameter matrices and their least squares function is minimized through specific data matrix decomposition. A useful feature of the algorithm is that the matrix of common factor scores is re-parameterized using QR decomposition in order to efficiently estimate factor correlations. A simulation study shows that the proposed procedure can exactly identify the true sparsest models. Real data examples demonstrate the usefulness of the variable clustering performed by SSFA

Using GeneReg to construct time delay gene regulatory networks

<p>Abstract</p> <p>Background</p> <p>Understanding gene expression and regulation is essential for understanding biological mechanisms. Because gene expression profiling has been widely used in basic biological research, especially in transcription regulation studies, we have developed GeneReg, an easy-to-use R package, to construct gene regulatory networks from time course gene expression profiling data; More importantly, this package can provide information about time delays between expression change in a regulator and that of its target genes.</p> <p>Findings</p> <p>The R package GeneReg is based on time delay linear regression, which can generate a model of the expression levels of regulators at a given time point against the expression levels of their target genes at a later time point. There are two parameters in the model, time delay and regulation coefficient. Time delay is the time lag during which expression change of the regulator is transmitted to change in target gene expression. Regulation coefficient expresses the regulation effect: a positive regulation coefficient indicates activation and negative indicates repression. GeneReg was implemented on a real Saccharomyces cerevisiae cell cycle dataset; more than thirty percent of the modeled regulations, based entirely on gene expression files, were found to be consistent with previous discoveries from known databases.</p> <p>Conclusions</p> <p>GeneReg is an easy-to-use, simple, fast R package for gene regulatory network construction from short time course gene expression data. It may be applied to study time-related biological processes such as cell cycle, cell differentiation, or causal inference.</p

Gender differentials in the evolution of cigarette smoking habits in a general European adult population from 1993–2003

BACKGROUND: Describe the recent evolution of cigarette smoking habits by gender in Geneva, where incidence rates of lung cancer have been declining in men but increasing in women. METHODS: Continuous cross-sectional surveillance of the general adult (35–74 yrs) population of Geneva, Switzerland for 11 years (1993–2003) using a locally-validated smoking questionnaire, yielding a representative random sample of 12,271 individuals (6,164 men, 6,107 women). RESULTS: In both genders, prevalence of current cigarette smoking was stable over the 11-year period, at about one third of men and one quarter of women, even though smoking began at an earlier age in more recent years. Older men were more likely to be former smokers than older women. Younger men, but not women, tended to quit smoking at an earlier age. CONCLUSION: This continuous (1993–2003) risk factor surveillance system, unique in Europe, shows stable prevalence of smoking in both genders. However, sharp contrasts in age-specific prevalence of never and former smoking and of ages at smoking initiation indicate that smoking continues a long-term decline in men but has still not reached its peak in women

Feature signature prediction of a boring process using neural network modeling with confidence bounds

Prediction of machine tool failure has been very important in modern metal cutting operations in order to meet the growing demand for product quality and cost reduction. This paper presents the study of building a neural network model for predicting the behavior of a boring process during its full life cycle. This prediction is achieved by the fusion of the predictions of three principal components extracted as features from the joint time–frequency distributions of energy of the spindle loads observed during the boring process. Furthermore, prediction uncertainty is assessed using nonlinear regression in order to quantify the errors associated with the prediction. The results show that the implemented Elman recurrent neural network is a viable method for the prediction of the feature behavior of the boring process, and that the constructed confidence bounds provide information crucial for subsequent maintenance decision making based on the predicted cutting tool degradation.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45845/1/170_2005_Article_114.pd

Evaluation of Two Methods to Estimate and Monitor Bird Populations

Background: Effective management depends upon accurately estimating trends in abundance of bird populations over time, and in some cases estimating abundance. Two population estimation methods, double observer (DO) and double sampling (DS), have been advocated for avian population studies and the relative merits and short-comings of these methods remain an area of debate. Methodology/Principal Findings: We used simulations to evaluate the performances of these two population estimation methods under a range of realistic scenarios. For three hypothetical populations with different levels of clustering, we generated DO and DS population size estimates for a range of detection probabilities and survey proportions. Population estimates for both methods were centered on the true population size for all levels of population clustering and survey proportions when detection probabilities were greater than 20%. The DO method underestimated the population at detection probabilities less than 30 % whereas the DS method remained essentially unbiased. The coverage probability of 95 % confidence intervals for population estimates was slightly less than the nominal level for the DS method but was substantially below the nominal level for the DO method at high detection probabilities. Differences in observer detection probabilities did not affect the accuracy and precision of population estimates of the DO method. Population estimates for the DS method remained unbiased as the proportion of units intensively surveyed changed, but the variance of th