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PubMed1999

Optimal integration of texture and motion cues to depth.

We report the results of a depth-matching experiment in which subjects were asked to adjust the height of an ellipse until it matched the depth of a simulated cylinder defined by texture and motion cues. In one-third of the trials the shape of the cylinder was primarily given by motion information, in another one-third of the trials it was given by texture information, and on the remaining trials it was given by both sources of information. Two optimal cue combination models are described where optimality is defined in terms of Bayesian statistics. The parameter values of the models are set based on subjects' responses on trials when either the motion cue or the texture cue was informative. These models provide predictions of subjects' responses on trials when both cues were informative. The results indicate that one of the optimal models provides a good fit to the subjects' data, and the second model provides an exceptional fit. Because the predictions of the optimal models closely match the experimental data, we conclude that observers' cue-combination strategies are indeed optimal, at least under the conditions studied here.

Contrast Sensitivity↗
PubMedDate not supplied

Piperacillin-tazobactam pharmacokinetics in patients with intraabdominal infections.

STUDY OBJECTIVE: To determine the appropriate compartmental and noncompartmental pharmacokinetic parameters for intravenous piperacillin and tazobactam. DESIGN: Sequential selection of patients entered into a randomized, open-label clinical efficacy trial. SETTING: Los Angeles County-University of Southern California Medical Center. PARTICIPANTS: Sequential sample of 18 patients admitted for intraabdominal infections and consented into a comparative antibiotic trial. INTERVENTIONS: Patients received piperacillin 4 g plus tazobactam 500 mg by intravenous intermittent infusion every 8 hours. MEASUREMENTS AND MAIN RESULTS: The estimated noncompartmental pharmacokinetic parameters (mean +/- SD) for piperacillin and tazobactam, respectively, were as follows: maximum concentration in plasma 218.7 +/- 48.9 micrograms/ml and 27.8 +/- 9.1 micrograms/ml; half-life 1.07 +/- 0.22 hours and 1.00 +/- 0.27 hours; elimination rate constant 0.67 +/- 0.13 hr-1 and 0.73 +/- 0.18 hr-1; area under the concentration-time curve from zero hour to infinity 288.5 +/- 71.25 mg.hr/L and 36.3 +/- 9.55 mg.hr/L; total plasma clearance 14.75 +/- 3.93 L/hour and 14.78 +/- 4.39 L/hour; renal clearance 5.69 +/- 1.94 L/hour and 7.85 +/- 3.37 L/hour; volume of distribution at steady state 21.00 +/- 4.18 L and 22.47 +/- 8.27 L; and mean residence time 1.72 +/- 0.29 hours and 1.79 +/- 0.35 hours. CONCLUSION: Our findings were similar to those in other surgical patient models. The two-compartmental model best described piperacillin and tazobactam disposition in our patients. Bayesian analyses of the two-compartment models of piperacillin and tazobactam were able to predict trough, peak, and 2-hour postadministration levels without bias.

Abdomen↗
PubMed2005

Model inference or model selection: discussion of Klugkist, Laudy, and Hoijtink (2005).

I. Klugkist, O. Laudy, and H. Hoijtink (2005) presented a Bayesian approach to analysis of variance models with inequality constraints. Constraints may play 2 distinct roles in data analysis. They may represent prior information that allows more precise inferences regarding parameter values, or they may describe a theory to be judged against the data. In the latter case, the authors emphasized the use of Bayes factors and posterior model probabilities to select the best theory. One difficulty is that interpretation of the posterior model probabilities depends on which other theories are included in the comparison. The posterior distribution of the parameters under an unconstrained model allows one to quantify the support provided by the data for inequality constraints without requiring the model selection framework.

Analysis of Variance↗
PubMed2006

Spatiotemporal Bayesian analysis of Lyme disease in New York state, 1990-2000.

Mapping ordinarily increases our understanding of nontrivial spatial and temporal heterogeneities in disease rates. However, the large number of parameters required by the corresponding statistical models often complicates detailed analysis. This study investigates the feasibility of a fully Bayesian hierarchical regression approach to the problem and identifies how it outperforms two more popular methods: crude rate estimates (CRE) and empirical Bayes standardization (EBS). In particular, we apply a fully Bayesian approach to the spatiotemporal analysis of Lyme disease incidence in New York state for the period 1990-2000. These results are compared with those obtained by CRE and EBS in Chen et al. (2005). We show that the fully Bayesian regression model not only gives more reliable estimates of disease rates than the other two approaches but also allows for tractable models that can accommodate more numerous sources of variation and unknown parameters.

Bayes Theorem↗
PubMed2006

Model weights and the foundations of multimodel inference.

Statistical thinking in wildlife biology and ecology has been profoundly influenced by the introduction of AIC (Akaike's information criterion) as a tool for model selection and as a basis for model averaging. In this paper, we advocate the Bayesian paradigm as a broader framework for multimodel inference, one in which model averaging and model selection are naturally linked, and in which the performance of AIC-based tools is naturally evaluated. Prior model weights implicitly associated with the use of AIC are seen to highly favor complex models: in some cases, all but the most highly parameterized models in the model set are virtually ignored a priori. We suggest the usefulness of the weighted BIC (Bayesian information criterion) as a computationally simple alternative to AIC, based on explicit selection of prior model probabilities rather than acceptance of default priors associated with AIC. We note, however, that both procedures are only approximate to the use of exact Bayes factors. We discuss and illustrate technical difficulties associated with Bayes factors, and suggest approaches to avoiding these difficulties in the context of model selection for a logistic regression. Our example highlights the predisposition of AIC weighting to favor complex models and suggests a need for caution in using the BIC for computing approximate posterior model weights.

Animals↗
PubMed1978

Assessment of the EMIT-(TM) technique as a screening test for opiates and methadone for a methadone maintenance clinic and its calibration by Bayesian statistics.

1. The performance of the semi-quantitative enzyme multiplied immunoassay technique (EMIT, Syva Corp.) for opiates and methadone has been examined as a screening procedure of urine samples from a methadone maintenance programme. The predictive value model that is based upon Bayesian statistics was used to determine screening levels for the EMIT assays. 2. With a predictive value of a negative result of 100%, the EMIT opiate assay can be used to show the absence of the indicated drugs, while positive results can be confirmed by a non-immunological technique. A screening level of 1.0 micrograms/ml for the opiate assay, conforms to this model. 3. The EMIT methadone assay was shown to have a predictive value of a negative result of 28% with respect to thin-layer chromatographic (TLC) results. This discrepancy between EMIT and TLC can not be explained by sensitivity alone. The manufacturer's recommended 0.5 micrograms/ml cutoff has been used therefore for the methadone assay.

Chromatography, Thin Layer↗
PubMedDate not supplied

A novel neural network-based survival analysis model.

A feedforward neural network architecture aimed at survival probability estimation is presented which generalizes the standard, usually linear, models described in literature. The network builds an approximation to the survival probability of a system at a given time, conditional on the system features. The resulting model is described in a hierarchical Bayesian framework. Experiments with synthetic and real world data compare the performance of this model with the commonly used standard ones.

Bayes Theorem↗
PubMed2005

Models of brain function in neuroimaging.

Inferences about brain function, using neuroimaging data, rest on models of how the data were caused. These models can be quite diverse, ranging from conceptual models of functional anatomy to nonlinear mathematical models of hemodynamics. However, they all have to be internally consistent because they model the same thing. This consistency encompasses many levels of description and places constraints on the statistical models, adopted for data analysis, and the experimental designs they embody. The aim of this review is to introduce the key models used in imaging neuroscience and how they relate to each other. We start with anatomical models of functional brain architectures, which motivate some of the fundaments of neuroimaging. We then turn to basic statistical models (e.g., the general linear model) used for making classical and Bayesian inferences about where neuronal responses are expressed. By incorporating biophysical constraints, these basic models can be finessed and, in a dynamic setting, rendered causal. This allows us to infer how interactions among brain regions are mediated.

Biophysical Phenomena↗
PubMed1986

The formation of maintenance of delusions: a Bayesian analysis.

This paper argues that recent research on normal-belief formation is relevant to our understanding of the establishment and maintenance of delusions. Bayesian theory provides a normative model of the way in which evidence relevant to normal beliefs may be evaluated: this makes it possible to classify delusional beliefs in terms of deviations from optimal Bayesian inference. Some hypothetical forms of deviation appear to correspond closely to cognitive processes observed in some groups of deluded patients. Theories of the precise nature of the abnormal judgemental processes also have implications for psychological approaches to treatment of deluded patients. The role of hallucinations in the formation and/or maintenance of delusions and the extent to which the distortions of cognitive processes associated with delusions are content-specific or mood-specific are also considered.

Cognition Disorders↗
PubMed2004

MCMC for hidden Markov models incorporating aggregation of states and filtering.

This paper is concerned with the statistical analysis of single ion channel records. Single channels are modelled by using hidden Markov models and a combination of Bayesian statistics and Markov chain Monte Carlo methods. The techniques presented here provide a straightforward generalization to those in Rosales et al. (2001, Biophys. J., 80, 1088-1103), allowing to consider constraints imposed by a gating mechanism such as the aggregation of states into classes. This paper also presents an extension that allows to consider correlated background noise and filtered data, extending the scope of the analysis toward real experimental conditions. The methods described here are based on a solid probabilistic basis and are less computationally intensive than alternative Bayesian treatments or frequentist approaches that consider correlated data.

Bayes Theorem↗
PubMed2000

Neural coding: higher-order temporal patterns in the neurostatistics of cell assemblies.

Recent advances in the technology of multiunit recordings make it possible to test Hebb's hypothesis that neurons do not function in isolation but are organized in assemblies. This has created the need for statistical approaches to detecting the presence of spatiotemporal patterns of more than two neurons in neuron spike train data. We mention three possible measures for the presence of higher-order patterns of neural activation--coefficients of log-linear models, connected cumulants, and redundancies--and present arguments in favor of the coefficients of log-linear models. We present test statistics for detecting the presence of higher-order interactions in spike train data by parameterizing these interactions in terms of coefficients of log-linear models. We also present a Bayesian approach for inferring the existence or absence of interactions and estimating their strength. The two methods, the frequentist and the Bayesian one, are shown to be consistent in the sense that interactions that are detected by either method also tend to be detected by the other. A heuristic for the analysis of temporal patterns is also proposed. Finally, a Bayesian test is presented that establishes stochastic differences between recorded segments of data. The methods are applied to experimental data and synthetic data drawn from our statistical models. Our experimental data are drawn from multiunit recordings in the prefrontal cortex of behaving monkeys, the somatosensory cortex of anesthetized rats, and multiunit recordings in the visual cortex of behaving monkeys.

Action Potentials↗
PubMed2002

Modelling developmental instability as the joint action of noise and stability: a Bayesian approach.

BACKGROUND: Fluctuating asymmetry is assumed to measure individual and population level developmental stability. The latter may in turn show an association with stress, which can be observed through asymmetry-stress correlations. However, the recent literature does not support an ubiquitous relationship. Very little is known why some studies show relatively strong associations while others completely fail to find such a correlation. We propose a new Bayesian statistical framework to examine these associations RESULTS: We are considering developmental stability - i.e. the individual buffering capacity - as the biologically relevant trait and show that (i) little variation in developmental stability can explain observed variation in fluctuating asymmetry when the distribution of developmental stability is highly skewed, and (ii) that a previously developed tool (i.e. the hypothetical repeatability of fluctuating asymmetry) contains only limited information about variation in developmental stability, which stands in sharp contrast to the earlier established close association between the repeatability and developmental instability. CONCLUSION: We provide tools to generate valuable information about the distribution of between-individual variation in developmental stability. A simple linear transformation of a previous model lead to completely different conclusions. Thus, theoretical modelling of asymmetry and stability appears to be very sensitive to the scale of inference. More research is urgently needed to get better insights in the developmental mechanisms of noise and stability. In spite of the fact that the model is likely to represent an oversimplification of reality, the accumulation of new insights could be incorporated in the Bayesian statistical approach to obtain more reliable estimation.

Bayes Theorem↗
PubMed1990

Practical Bayesian analysis of a simple logistic regression: predicting corneal transplants.

The Bayesian analysis of a logistic regression model is described using an example of predicting the need for a corneal transplant in keratoconus. Controversy over the use of subjective prior information in Bayesian methods is avoided by a formulation representing negligible prior information. Simple computational procedures are described, and it is argued that the results are more accurate, clearer and make fuller use of the information contained in the data. Analysis of more complex models is considered. In particular, it is argued that classical methods as implemented in the computer package GLIM can be used as approximations to Bayesian methods, particularly at the initial stage of model selection.

Bayes Theorem↗
PubMed2003

Detection of deleterious genotypes in multigenerational studies. III. Estimation of selection components in highly selfing populations.

New paradigms in genetics have increased the chance of finding genes that appear redundant but in fact may have been preserved due to a small level of positive selection potential acting during each generation. Monitoring changes in genotypic frequencies within and between generations allows the dissection of the fertility, viability and meiotic drive selection components acting on such genes in natural and experimental populations. Here, a formal maximum likelihood procedure is developed to identify and estimate these selection components in highly selfing populations by fitting the time-dependent solutions for genotypic frequencies to observed multigenerational counts. With adult census alone, we can not simultaneously estimate all three selection components considered. In such cases, we instead consider a hierarchy of 11 models with either fewer selection components, complete dominance, or multiplicative meiotic drive with a single parameter. We identify the best-fitting of these models by applying likelihood ratio tests to nested models and Akaike's Information Criterion (AIC) and the Bayesian Information Criterion (BIC) to non-nested models. With seed census, fertility and viability selection are not distinguishable and thus can only be estimated jointly. A combination of joint seed and adult census data allows us to estimate all three selection components simultaneously. Simulated data validate the estimation procedure and provide some practical guidelines for experimental design. An application to Arabidopsis data establishes that viability selection is the major selective force acting on the ACT2 actin gene in laboratory-grown Arabidopsis populations.

Arabidopsis↗
PubMed2004

Nonlinear mixed-effects modeling: individualization and prediction.

The development of biomathematical models for the prediction of fatigue and performance relies on statistical techniques to analyze experimental data and model simulations. Statistical models of empirical data have adjustable parameters with a priori unknown values. Interindividual variability in estimates of those values requires a form of smoothing. This traditionally consists of averaging observations across subjects, or fitting a model to the data of individual subjects first and subsequently averaging the parameter estimates. However, the standard errors of the parameter estimates are assessed inaccurately by such averaging methods. The reason is that intra- and inter-individual variabilities are intertwined. They can be separated by mixed-effects modeling in which model predictions are not only determined by fixed effects (usually constant parameters or functions of time) but also by random effects, describing the sampling of subject-specific parameter values from probability distributions. By estimating the parameters of the distributions of the random effects, mixed-effects models can describe experimental observations involving multiple subjects properly (i.e., yielding correct estimates of the standard errors) and parsimoniously (i.e., estimating no more parameters than necessary). Using a Bayesian approach, mixed-effects models can be "individualized" as observations are acquired that capture the unique characteristics of the individual at hand. Mixed-effects models, therefore, have unique advantages in research on human neurobehavioral functions, which frequently show large inter-individual differences. To illustrate this we analyzed laboratory neurobehavioral performance data acquired during sleep deprivation, using a nonlinear mixed-effects model. The results serve to demonstrate the usefulness of mixed-effects modeling for data-driven development of individualized predictive models of fatigue and performance.

Bayes Theorem↗
PubMed2006

FGX: a frequentist gene expression index for Affymetrix arrays.

We consider a new frequentist gene expression index for Affymetrix oligonucleotide DNA arrays, using a similar probe intensity model as suggested by Hein and others (2005), called the Bayesian gene expression index (BGX). According to this model, the perfect match and mismatch values are assumed to be correlated as a result of sharing a common gene expression signal. Rather than a Bayesian approach, we develop a maximum likelihood algorithm for estimating the underlying common signal. In this way, estimation is explicit and much faster than the BGX implementation. The observed Fisher information matrix, rather than a posterior credibility interval, gives an idea of the accuracy of the estimators. We evaluate our method using benchmark spike-in data sets from Affymetrix and GeneLogic by analyzing the relationship between estimated signal and concentration, i.e. true signal, and compare our results with other commonly used methods.

DNA Probes↗
PubMed2005

Genetic parameters estimated with multitrait and linear spline-random regression models using Gelbvieh early growth data.

Estimates of direct and maternal genetic parameters in beef cattle were obtained with a random regression model with a linear spline function (SFM) and were compared with those obtained by a multitrait model (MTM). Weight data of 18,900 Gelbvieh calves were used, of which 100, 75, and 17% had birth (BWT), weaning (WWT), and yearling (YWT) weights, respectively. The MTM analysis was conducted with a three-trait maternal animal model. The MTM included an overall linear partial fixed regression on age at recording for WWT and YWT, and direct-maternal genetic and maternal permanent environmental effects. The SFM included the same effects as MTM, plus a direct permanent environmental effect and heterogeneous residual variance. Three knots, or breakpoints, were set to 1, 205, and 365 d. (Co)variance components in both models were estimated with a Bayesian implementation via Gibbs sampling using flat priors. Because BWT had no variability of age at recording, there was good agreement between corresponding components of variance estimated from both models. For WWT and YWT, with the exception of the sum of direct permanent environmental and residual variances, there was a general tendency for SFM estimates of variances to be lower than MTM estimates. Direct and maternal heritability estimates with SFM tended to be lower than those estimated with MTM. For example, the direct heritability for YWT was 0.59 with MTM, and 0.48 with SFM. Estimated genetic correlations for direct and maternal effects with SFM were less negative than those with MTM. For example, the direct-maternal correlation for WWT was -0.43 with MTM and -0.33 with SFM. Estimates with SFM may be superior to MTM due to better modeling of age in both fixed and random effects.

Animals↗
PubMed2003

Semiparametric regression splines in matched case-control studies.

We develop semiparametric methods for matched case-control studies using regression splines. Three methods are developed: 1) an approximate cross-validation scheme to estimate the smoothing parameter inherent in regression splines, as well as 2) Monte Carlo expectation maximization (MCEM) and 3) Bayesian methods to fit the regression spline model. We compare the approximate cross-validation approach, MCEM, and Bayesian approaches using simulation, showing that they appear approximately equally efficient; the approximate cross-validation method is computationally the most convenient. An example from equine epidemiology that motivated the work is used to demonstrate our approaches.

Animals↗