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PubMed1998

Issues in Bayesian Analysis of Neural Network Models

Stemming from work by Buntine and Weigend (1991) and MacKay (1992), there is a growing interest in Bayesian analysis of neural network models. Although conceptually simple, this problem is computationally involved. We suggest a very efficient Markov chain Monte Carlo scheme for inference and prediction with fixed&hyphenarchitecture feedforward neural networks. The scheme is then extended to the variable architecture case, providing a data&hyphendriven procedure to identify sensible architectures.

Journal Article↗
PubMed2005

Shooting darts: co-evolution and counter-adaptation in hermaphroditic snails.

BACKGROUND: Evolutionary conflicts of interest between the sexes often lead to co-evolutionary arms races consisting of repeated arisal of traits advantageous for one sex but harmful to the other sex, and counter-adaptations by the latter. In hermaphrodites, these antagonistic interactions are at least an equally important driving force. Here, we investigate the evolution of one of the most striking examples of sexual conflict in hermaphrodites, the so-called shooting of love-darts in land snails. Stabbing this calcareous dart through the partner's skin ultimately increases paternity. This trait is obviously beneficial for the shooter, but it manipulates sperm storage in the receiver. Hence, an arms race between the love-dart and the spermatophore receiving organs may be expected. RESULTS: We performed a detailed phylogenetic analysis of 28S ribosomal RNA gene sequences from dart-possessing land snail species. Both the Shimodaira-Hasegawa test and Bayesian posterior probabilities rejected a monophyletic origin of most reproductive structures, including the love-dart, indicating that most traits arose repeatedly. Based on the inferred phylogenetic trees, we calculated phylogenetically independent contrasts for the different reproductive traits. Subsequent principal component and correlation analyses demonstrated that these contrasts covary, meaning that correlated evolution of these traits occurred. CONCLUSION: Our study represents the first comprehensive comparative analysis of reproductive organ characteristics in simultaneous hermaphrodites. Moreover, it strongly suggests that co-evolutionary arms races can result from sexual conflict in these organisms and play a key role in the evolution of hermaphroditic mating systems.

Adaptation, Biological↗
PubMedDate not supplied

Phylogenetics and evolution of nematode-trapping fungi (Orbiliales) estimated from nuclear and protein coding genes.

The systematic classification of nematode-trapping fungi is redefined based on phylogenies inferred from sequence analyses of 28S rDNA, 5.8S rDNA and beta-tubulin genes. Molecular data were analyzed with maximum parsimony, maximum likelihood and Bayesian analysis. An emended generic concept of nematode-trapping fungi is provided. Arthrobotrys is characterized by adhesive networks, Dactylellina by adhesive knobs, and Drechslerella by constricting-rings. Phylogenetic placement of taxa characterized by stalked adhesive knobs and non-constricting rings also is confirmed in Dactylellina. Species that produce unstalked adhesive knobs that grow out to form loops are transferred from Gamsylella to Dactylellina, and those that produce unstalked adhesive knobs that grow out to form networks are transferred from Gamsylella to Arthrobotrys. Gamsylella as currently circumscribed cannot be treated as a valid genus. A hypothesis for the evolution of trapping-devices is presented based on multiple gene data and morphological studies. Predatory and nonpredatory fungi appear to have been derived from nonpredatory members of Orbilia. The adhesive knob is considered to be the ancestral type of trapping device from which constricting rings and networks were derived via two pathways. In the first pathway adhesive knobs retained their adhesive material forming simple two-dimension networks, eventually forming complex three-dimension networks. In the second pathway adhesive knobs lost their adhesive materials, with their ends meeting to form nonconstricting rings and they in turn formed constricting rings with three inflated-cells.

Animals↗
PubMed1991

Estimation of relative potency with sequential dilution errors in radioimmunoassay.

Sequential dilution is a very common procedure in radioimmunoassay, in which the dilution error will be accumulated from the highest to the lowest concentration. A simulated example in relative potency determination is used to demonstrate the potentially wrong conclusion that can be drawn, when the dilution error is not properly included in the model. A Bayesian method is used and an alternative approximation via maximum likelihood is proposed. An alternative experimental design is recommended to increase the precision of the inference.

Bayes Theorem↗
PubMed2002

Bayesian analysis: a new statistical paradigm for new technology.

Full Bayesian analysis is an alternative statistical paradigm, as opposed to traditionally used methods, usually called frequentist statistics. Bayesian analysis is controversial because it requires assuming a prior distribution, which can be arbitrarily chosen; thus there is a subjective element, which is considered to be a major weakness. However, this could also be considered a strength since it provides a formal way of incorporating prior knowledge. Since it is flexible and permits repeated looks at evolving data, Bayesian analysis is particularly well suited to the evaluation of new medical technology. Bayesian analysis can refer to a range of things: from a simple, noncontroversial formula for inverting probabilities to an alternative approach to the philosophy of science. Its advantages include: (1) providing direct probability statements--which are what most people wrongly assume they are getting from conventional statistics; (2) formally incorporating previous information in statistical inference of a data set, a natural approach which we follow in everyday reasoning; and (3) flexible, adaptive research designs allowing multiple looks at accumulating study data. Its primary disadvantage is the element of subjectivity which some think is not scientific. We discuss and compare frequentist and Bayesian approaches and provide three examples of Bayesian analysis: (1) EKG interpretation, (2) a coin-tossing experiment, and (3) assessing the thromboembolic risk of a new mechanical heart valve.

Bayes Theorem↗
PubMed2005

Bayesian analysis of hierarchical pattern-mixture models for clinical trials data with attrition and comparisons to commonly used ad-hoc and model-based approaches.

This article addresses the problem of making scientifically sound inferences from clinical trials data with attrition, when reasons of attrition seem related to the outcomes of interest. The problem is particularly difficult when the effect of a covariate is to be estimated and if the dropout mechanism appears to operate differently at different levels of the covariate. In this context, multiple imputation under a multilevel pattern-mixture model that allows random variation across dropout groups is presented. Using simulated data generated around an alcoholic hepatitis trial, we compare the performance of this model and commonly used ad-hoc and model-based approaches.

Algorithms↗
PubMedDate not supplied

A Bayesian approach to a general regression model for ROC curves.

A fully Bayesian approach to a general nonlinear ordinal regression model for ROC-curve analysis is presented. Samples from the marginal posterior distributions of the model parameters are obtained by a Markov-chain Monte Carlo (MCMC) technique--Gibbs sampling. These samples facilitate the calculation of point estimates and credible regions as well as inferences for the associated areas under the ROC curves. The analysis of an example using freely available software shows that the use of noninformative vague prior distributions for all model parameters yields posterior summary statistics very similar to the conventional maximum-likelihood estimates. Clinically important advantages of this Bayesian approach are: the possible inclusion of prior knowledge and beliefs into the ROC analysis (via the prior distributions), the possible calculation of the posterior predictive distribution of a future patient outcome, and the potential to address questions such as: "What is the probability that a certain diagnostic test is better in one setting than in another?"

Bayes Theorem↗
PubMed1994

Extending a Bayesian analysis of the two-period crossover to allow for baseline measurements.

In the context of a two-period crossover study with baseline measurements a graphical method is developed for displaying the dependence of posterior inferences concerning the treatment effect on unavoidable prior beliefs about the 'correct' model. The method is a generalization of the approach developed by Grieve for the corresponding case without baselines.

Administration, Cutaneous↗
PubMedDate not supplied

The probability of inevitability: the inherent impossibility of validating criteria for brain death or 'irreversibility' through clinical studies.

A great need persists for diagnostic criteria for both brain death in young children and irreversible loss of consciousness at all ages. This article examines the inferences derived from a hypothetical confirmatory study in which all of the N patients who fulfilled the criterion did in fact experience brain death (irreversibility). A Bayesian methodology proves that, for N in the range of a large clinical study, estimations of prior probabilities are, for all practical purposes, irrelevant to the calculation of the posterior probabilities. The risk of a false positive diagnosis for the next patient who meets the criterion is approximately 1/(N + 2). The chance of at least one false positive diagnosis among the next (N + 1) patients who meet the criterion is around 50 per cent. Thus, achievement of the requisite moral certainty of a declaration of death (irreversibility) necessitates an impossibly large N for the study. This does not mean that one cannot diagnose death, but rather that the validity of the diagnostic criteria must be self-evident on a priori grounds, and that confirmatory studies are necessarily either inadequate or superfluous.

Adult↗
PubMed2006

From mere coincidences to meaningful discoveries.

People's reactions to coincidences are often cited as an illustration of the irrationality of human reasoning about chance. We argue that coincidences may be better understood in terms of rational statistical inference, based on their functional role in processes of causal discovery and theory revision. We present a formal definition of coincidences in the context of a Bayesian framework for causal induction: a coincidence is an event that provides support for an alternative to a currently favored causal theory, but not necessarily enough support to accept that alternative in light of its low prior probability. We test the qualitative and quantitative predictions of this account through a series of experiments that examine the transition from coincidence to evidence, the correspondence between the strength of coincidences and the statistical support for causal structure, and the relationship between causes and coincidences. Our results indicate that people can accurately assess the strength of coincidences, suggesting that irrational conclusions drawn from coincidences are the consequence of overestimation of the plausibility of novel causal forces. We discuss the implications of our account for understanding the role of coincidences in theory change.

Bayes Theorem↗
PubMed2006

Approximate likelihood-ratio test for branches: A fast, accurate, and powerful alternative.

We revisit statistical tests for branches of evolutionary trees reconstructed upon molecular data. A new, fast, approximate likelihood-ratio test (aLRT) for branches is presented here as a competitive alternative to nonparametric bootstrap and Bayesian estimation of branch support. The aLRT is based on the idea of the conventional LRT, with the null hypothesis corresponding to the assumption that the inferred branch has length 0. We show that the LRT statistic is asymptotically distributed as a maximum of three random variables drawn from the chi(0)2 + chi(1)2 distribution. The new aLRT of interior branch uses this distribution for significance testing, but the test statistic is approximated in a slightly conservative but practical way as 2(l1- l2), i.e., double the difference between the maximum log-likelihood values corresponding to the best tree and the second best topological arrangement around the branch of interest. Such a test is fast because the log-likelihood value l2 is computed by optimizing only over the branch of interest and the four adjacent branches, whereas other parameters are fixed at their optimal values corresponding to the best ML tree. The performance of the new test was studied on simulated 4-, 12-, and 100-taxon data sets with sequences of different lengths. The aLRT is shown to be accurate, powerful, and robust to certain violations of model assumptions. The aLRT is implemented within the algorithm used by the recent fast maximum likelihood tree estimation program PHYML (Guindon and Gascuel, 2003).

Classification↗
PubMed2004

A nucleotide substitution model with nearest-neighbour interactions.

MOTIVATION: It is well known that neighbouring nucleotides in DNA sequences do not mutate independently of each other. In this paper, we introduce a context-dependent substitution model and derive an algorithm to calculate the likelihood of sequences evolving under this model. We use this algorithm to estimate neighbour-dependent substitution rates, as well as rates for dinucleotide substitutions, using a Bayesian sampling procedure. The model is irreversible, giving an arrow to time, and allowing the position of the root between a pair of sequences to be inferred without using out-groups. RESULTS: We applied the model upon aligned human-mouse non-coding data. Clear neighbour dependencies were observed, including 17-18-fold increased CpG to TpG/CpA rates compared with other substitutions. Root inference positioned the root halfway the mouse and human tips, suggesting an approximately clock-like behaviour of the irreversible part of the substitution process.

Algorithms↗
PubMed2005

A transformation approach for incorporating monotone or unimodal constraints.

Samples of curves are collected in many applications, including studies of reproductive hormone levels in the menstrual cycle. Many approaches have been proposed for correlated functional data of this type, including smoothing spline methods and other flexible parametric modeling strategies. In many cases, the underlying biological processes involved restrict the curve to follow a particular shape. For example, progesterone levels in healthy women increase during the menstrual cycle to a peak achieved at random location with decreases thereafter. Reproductive epidemiologists are interested in studying the distribution of the peak and the trajectory for women in different groups. Motivated by this application, we propose a simple approach for restricting each woman's mean trajectory to follow an umbrella shape. An unconstrained hierarchical Bayesian model is used to characterize the data, and draws from the posterior distribution obtained using a Gibbs sampler are then mapped to the constrained space. Inferences are based on the resulting quasi-posterior distribution for the peak and individual woman trajectories. The methods are applied to a study comparing progesterone trajectories for conception and nonconception cycles.

Bayes Theorem↗
PubMed2005

Phylogeny of Arthropoda inferred from mitochondrial sequences: strategies for limiting the misleading effects of multiple changes in pattern and rates of substitution.

In this study, mitochondrial sequences were used to investigate the relationships among the major lineages of Arthropoda. The data matrix used for the analyses includes 84 taxa and 3918 nucleotides representing six mitochondrial protein-coding genes (atp6 and 8, cox1-3, and nad2). The analyses of nucleotide composition show that a reverse strand-bias, i.e., characterized by an excess of T relative to A nucleotides and of G relative to C nucleotides, was independently acquired in six different lineages of Arthropoda: (1) the honeybee mite (Varroa), (2) Opisthothelae spiders (Argiope, Habronattus, and Ornithoctonus), (3) scorpions (Euscorpius and Mesobuthus), (4) Hutchinsoniella (Cephalocarid), (5) Tigriopus (Copepod), and (6) whiteflies (Aleurodicus and Trialeurodes). Phylogenetic analyses confirm that these convergences in nucleotide composition can be particularly misleading for tree reconstruction, as unrelated taxa with reverse strand-bias tend to group together in MP, ML, and Bayesian analyses. However, the use of a specific model for minimizing effects of the bias, the "Neutral Transition Exclusion" (NTE) model, allows Bayesian analyses to rediscover most of the higher taxa of Arthropoda. Furthermore, the analyses of branch lengths suggest that three main factors explain accelerated rates of substitution: (1) genomic rearrangements, including duplication of the control region and gene translocation, (2) parasitic lifestyle, and (3) small body size. The comparisons of Bayesian Bootstrap percentages show that the support for many nodes increases when taxa with long branches are excluded from the analyses. It is therefore recommended to select taxa and genes of the mitochondrial genome for inferring phylogenetic relationships among arthropod lineages. The phylogenetic analyses support the existence of a major dichotomy within Arthropoda, separating Pancrustacea and Paradoxopoda. Basal relationships between Pancrustacean lineages are not robust, and the question of Hexapod monophyly or polyphyly cannot be answered with the available mitochondrial sequences. Within Paradoxopoda, Chelicerata and Myriapoda are each found to be monophyletic, and Endeis (Pycnogonida) is, surprisingly, associated with Acari.

Animals↗
PubMed2005

Semi-parametric modelling for costs of health care technologies.

Cost data that arise in the evaluation of health care technologies usually exhibit highly skew, heavy-tailed and, possibly, multi-modal distributions. Distribution-free methods for analysing these data, such as the bootstrap, or those based on the asymptotic normality of sample means, may often lead to inefficient or misleading inferences. On the other hand, parametric models that fit the data (or a transformation of the data) equally well can produce very different answers. We consider a Bayesian approach, and model cost data with a distribution composed of a piecewise constant density up to an unknown endpoint, and a generalized Pareto distribution for the remaining tail.

Animals↗
PubMed2006

A graphical approach to relatedness inference.

The estimation of relatedness structure in natural populations using molecular marker data has become an important tool in population biology, resulting in a variety of estimation procedures for specific sampling scenarios. In this article a general approach is proposed, in which the detailed relationship structure, typically a pedigree graph or partition, is considered to be the object of inference. This makes available tools used in complex model selection theory which have demonstrated effectiveness. An important advantage of this approach is that it permits a fully Bayesian approach to the problem, providing a principled and accessible way to measure statistical error. The approach is demonstrated by applying the minimum description length principle. This technique is used in model selection to provide a rational way of comparing models of varying complexity. We show how the resulting score may be interpreted and applied as a Bayesian posterior density.

Bayes Theorem↗
PubMed2005

NovoHMM: a hidden Markov model for de novo peptide sequencing.

De novo sequencing of peptides poses one of the most challenging tasks in data analysis for proteome research. In this paper, a generative hidden Markov model (HMM) of mass spectra for de novo peptide sequencing which constitutes a novel view on how to solve this problem in a Bayesian framework is proposed. Further extensions of the model structure to a graphical model and a factorial HMM to substantially improve the peptide identification results are demonstrated. Inference with the graphical model for de novo peptide sequencing estimates posterior probabilities for amino acids rather than scores for single symbols in the sequence. Our model outperforms state-of-the-art methods for de novo peptide sequencing on a large test set of spectra.

Amino Acid Sequence↗
PubMed2001

Interpreting results from trials of pneumococcal conjugate vaccines: a statistical test for detecting vaccine-induced increases in carriage of nonvaccine serotypes.

Conjugate vaccines against Streptococcus pneumoniae (pneumococcus) protect against nasopharyngeal carriage of serotypes included in the vaccine. However, in several clinical trials, vaccinees have shown increased carriage of nonvaccine serotypes of pneumococcus. These increases may be due to serotype replacement, if vaccine-induced protection against carriage of vaccine serotypes increases susceptibility to carriage of nonvaccine serotypes. Alternatively, observed increases may be an artifact of "unmasking," in which nonvaccine serotypes are more readily detected among vaccinees than among controls because vaccine serotypes are not present. In this paper, a statistical test for distinguishing serotype replacement from unmasking is described. The test attempts to reject a null model of unmasking alone; serotype replacement is inferred if the observed increase in detectable nonvaccine serotype carriage among vaccinees is significantly greater than that expected under the null model. Significance is assessed using the Bayesian "posterior predictive p value" as modified by Robins et al. (J Am Stat Assoc 2000;95:1143-56). Analysis of data from a South African trial suggests that replacement may have occurred in the study, but results do not reach the conventional level of significance in rejecting the null hypothesis of unmasking (p = 0.074). The author performs sensitivity analyses for the prior and for unmeasured confounding by differences in susceptibility to pneumococcus carriage. The implications of the findings and the assumptions and limitations of this technique are then discussed.

Bayes Theorem↗