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PubMedDate not supplied

Innovations in bayes and empirical bayes methods: estimating parameters, populations and ranks.

By formalizing the relation among components and 'borrowing information' among them, Bayes and empirical Bayes methods can produce more valid, efficient and informative statistical evaluations than those based on traditional methods. In addition, Bayesian structuring of complicated models and goals guides development of appropriate statistical approaches and generates summaries which properly account for sampling and modelling uncertainty. Computing innovations enable implementation of complex and relevant models, thereby substantially increasing the role of Bayes/empirical Bayes methods in important statistical assessments. Policy-relevant statistical assessments involve synthesis of information from a set of related components such as medical clinics, geographic regions or research studies. Typical assessments include inference for individual parameters, synthesis over the collection of components (for example, the parameter histogram) and comparisons among parameters (for example, ranks). The relative importance of these goals depends on the context. Bayesian structuring provides a guide to valid inference. For example, while posterior means are the 'obvious' and optimal estimates for individual components under squared error loss, their empirical distribution function (EDF) is underdispersed and never valid for estimating the EDF of the true, underlying parameters. Effective histogram estimates result from optimizing a loss function based in a distance between the histogram and its estimate. Similarly, ranking observed data usually produces poor estimates and ranking posterior means can be inappropriate. Effective estimates should be based on a loss function that caters directly to ranks. Using examples of 'borrowing information', shrinkage and the variance/bias trade-off we motivate Bayes and empirical Bayes analysis. Then, we outline the formal approach and discuss 'triple-goal' estimates with values that when ranked produce optimal ranks, for which the EDF is an optimal estimate of the parameter EDF and such that the values themselves are effective estimates of co-ordinate-specific parameters. We use basic models and data analysis examples to highlight the conceptual and structural issues.

Animals↗

PubMed2001

Bayesian value-of-information analysis. An application to a policy model of Alzheimer's disease.

A framework is presented that distinguishes the conceptually separate decisions of which treatment strategy is optimal from the question of whether more information is required to inform this choice in the future. The authors argue that the choice of treatment strategy should be based on expected utility, and the only valid reason to characterize the uncertainty surrounding outcomes of interest is to establish the value of acquiring additional information. A Bayesian decision theoretic approach is demonstrated through a probabilistic analysis of a published policy model of Alzheimer's disease. The expected value of perfect information is estimated for the decision to adopt a new pharmaceutical for the population of patients with Alzheimer's disease in the United States. This provides an upper bound on the value of additional research. The value of information is also estimated for each of the model inputs. This analysis can focus future research by identifying those parameters where more precise estimates would be most valuable and indicating whether an experimental design would be required. We also discuss how this type of analysis can also be used to design experimental research efficiently (identifying optimal sample size and optimal sample allocation) based on the marginal cost and marginal benefit of sample information. Value-of-information analysis can provide a measure of the expected payoff from proposed research, which can be used to set priorities in research and development. It can also inform an efficient regulatory framework for new healthcare technologies: an analysis of the value of information would define when a claim for a new technology should be deemed substantiated and when evidence should be considered competent and reliable when it is not cost-effective to gather any more information.

Alzheimer Disease↗

PubMed1999

Prediction of oculocardiac reflex in strabismus surgery using neural networks.

Successfully predicting an oculocardiac reflex (OCR) is difficult to achieve despite various proposed maneuvers. The aim of this study was to test the models built up by neural networks to predict the occurrence of OCR during strabismus surgery in children. Premedication was not given. Atropine 0.01 mg/kg was medicated just before induction. Induction was performed with fentanyl or ketorolac, followed by propofol. Atracurium or vecuronium was given for intubation. Anesthesia was maintained with O2-N2O with continuous propofol infusion. Chi-square test was performed for induction agents, gender, weight, muscle blockade, repaired muscle, number of repaired muscles, duration of operation to detect any association between the occurrence of OCR and to develop the model of neural networks. The multi-layer perceptron, radial basis function and Bayesian backpropagation network were tested. The occurrence of OCR was significantly associated with gender and repaired muscle (p < 0.05). Gender, repaired muscle and age were considered as input for the multi-layer perceptron, radial basis function and Bayesian backpropagation network. Three neural networks had predicted the same correction rate in the occurrence of OCR as being 87.5% overall among 16 patients' records tested. These models are conceptually different in predicting compared to conventional maneuvers, and have the advantage of testing individually and foretelling the propensity. By comparison neural networks use grouped experiential data and predict OCR by the learning rule. Neural networks require a relatively abundant number of experienced and homogenous patients' records to establish an accurate model. The multi-layer perceptron, radial basis function and Bayesian backpropagation modeling network may be an alternative way, and preferable to vagal tone maneuvers if the associated relationships to the occurrence of OCR are more clearly defined.

Adolescent↗

PubMed2004

A Bayesian approach to reconstructing genetic regulatory networks with hidden factors.

MOTIVATION: We have used state-space models (SSMs) to reverse engineer transcriptional networks from highly replicated gene expression profiling time series data obtained from a well-established model of T cell activation. SSMs are a class of dynamic Bayesian networks in which the observed measurements depend on some hidden state variables that evolve according to Markovian dynamics. These hidden variables can capture effects that cannot be directly measured in a gene expression profiling experiment, for example: genes that have not been included in the microarray, levels of regulatory proteins, the effects of mRNA and protein degradation, etc. RESULTS: We have approached the problem of inferring the model structure of these state-space models using both classical and Bayesian methods. In our previous work, a bootstrap procedure was used to derive classical confidence intervals for parameters representing 'gene-gene' interactions over time. In this article, variational approximations are used to perform the analogous model selection task in the Bayesian context. Certain interactions are present in both the classical and the Bayesian analyses of these regulatory networks. The resulting models place JunB and JunD at the centre of the mechanisms that control apoptosis and proliferation. These mechanisms are key for clonal expansion and for controlling the long term behavior (e.g. programmed cell death) of these cells. AVAILABILITY: Supplementary data is available at http://public.kgi.edu/wild/index.htm and Matlab source code for variational Bayesian learning of SSMs is available at http://www.cse.ebuffalo.edu/faculty/mbeal/software.html.

Bayes Theorem↗

PubMed2026

Efficacy and safety of cannabinoid-based interventions for behavioral and cognitive symptoms in dementia: systematic review and meta-analysis.

BACKGROUND: Behavioral and cognitive symptoms are frequent in Alzheimer's disease and dementia, and available pharmacological options offer limited benefit. Cannabinoid-based therapies have been proposed as alternatives, but evidence remains inconclusive. METHODS: We systematically searched PubMed, Embase, Web of Science, and the Cochrane Library through November 2025 for randomized controlled trials evaluating cannabinoids in Alzheimer's disease or dementia. Primary outcomes were agitation measured by the Cohen-Mansfield Agitation Inventory (CMAI) and neuropsychiatric symptoms assessed by the Neuropsychiatric Inventory-Nursing Home version (NPI-NH). Secondary outcomes included cognition using the Mini-Mental State Examination (MMSE) and adverse events. Standardized Mean Differences (SMDs) and Risk Ratios (RRs) were synthesized using random-effects (REML) and Bayesian random-effects models. Risk of bias was evaluated with RoB 2, and certainty of evidence with GRADE. RESULTS: Nine trials (334 participants) met inclusion criteria. Cannabinoids did not improve CMAI (SMD -0.58, 95% CI -1.71 to 0.55; I2 = 84%), NPI-NH total (SMD -0.02, 95% CI -1.00 to 0.96; I2 = 67%), NPI-NH agitation (SMD -0.44, 95% CI -1.45 to 0.57; I2 = 48%), or MMSE (SMD 0.86, 95% CI -16.33 to 18.06; I2 = 96%). Bayesian posterior estimates were close to zero, supporting the absence of effect. Leave-one-out analyses reduced heterogeneity only after excluding influential trials but did not alter results. Certainty of evidence was moderate for behavioral outcomes and low for cognition. Overall adverse events were similar to placebo, while somnolence was more frequent with cannabinoids (RR 2.03, 95% CI 1.29-3.20). CONCLUSIONS: Cannabinoid-based therapies do not improve agitation, neuropsychiatric symptoms, or cognition in Alzheimer's disease and increase somnolence.

Humans↗

PubMed2004

Software reliability prediction using recurrent neural network with Bayesian regularization.

A recurrent neural network modeling approach for software reliability prediction with respect to cumulative failure time is proposed. Our proposed network structure has the capability of learning and recognizing the inherent internal temporal property of cumulative failure time sequence. Further, by adding a penalty term of sum of network connection weights, Bayesian regularization is applied to our network training scheme to improve the generalization capability and lower the susceptibility of overfitting. The performance of our proposed approach has been tested using four real-time control and flight dynamic application data sets. Numerical results show that our proposed approach is robust across different software projects, and has a better performance with respect to both goodness-of-fit and next-step-predictability compared to existing neural network models for failure time prediction.

Algorithms↗

PubMed2005

MEG source localization under multiple constraints: an extended Bayesian framework.

To use Electroencephalography (EEG) and Magnetoencephalography (MEG) as functional brain 3D imaging techniques, identifiable distributed source models are required. The reconstruction of EEG/MEG sources rests on inverting these models and is ill-posed because the solution does not depend continuously on the data and there is no unique solution in the absence of prior information or constraints. We have described a general framework that can account for several priors in a common inverse solution. An empirical Bayesian framework based on hierarchical linear models was proposed for the analysis of functional neuroimaging data [Friston, K., Penny, W., Phillips, C., Kiebel, S., Hinton, G., Ashburner, J., 2002. Classical and Bayesian inference in neuroimaging: theory. NeuroImage 16, 465-483] and was evaluated recently in the context of EEG [Phillips, C., Mattout, J., Rugg, M.D., Maquet, P., Friston, K., 2005. An empirical Bayesian solution to the source reconstruction problem in EEG. NeuroImage 24, 997-1011]. The approach consists of estimating the expected source distribution and its conditional variance that is constrained by an empirically determined mixture of prior variance components. Estimation uses Expectation-Maximization (EM) to give the Restricted Maximum Likelihood (ReML) estimate of the variance components (in terms of hyperparameters) and the Maximum A Posteriori (MAP) estimate of the source parameters. In this paper, we extend the framework to compare different combinations of priors, using a second level of inference based on Bayesian model selection. Using Monte-Carlo simulations, ReML is first compared to a classic Weighted Minimum Norm (WMN) solution under a single constraint. Then, the ReML estimates are evaluated using various combinations of priors. Both standard criterion and ROC-based measures were used to assess localization and detection performance. The empirical Bayes approach proved useful as: (1) ReML was significantly better than WMN for single priors; (2) valid location priors improved ReML source localization; (3) invalid location priors did not significantly impair performance. Finally, we show how model selection, using the log-evidence, can be used to select the best combination of priors. This enables a global strategy for multiple prior-based regularization of the MEG/EEG source reconstruction.

Bayes Theorem↗

PubMed2005

Comparing alignment methods for inferring the history of the new world lizard genus Mabuya (Squamata: Scincidae).

The rapid increase in the ability to generate molecular data, and the focus on model-based methods for tree reconstruction have greatly advanced the use of phylogenetics in many fields. The recent flurry of new analytical techniques has focused almost solely on tree reconstruction, whereas alignment issues have received far less attention. In this paper, we use a diverse sampling of gene regions from lizards of the genus Mabuya to compare the impact, on phylogeny estimation, of new maximum likelihood alignment algorithms with more widely used methods. Sequences aligned under different optimality criteria are analyzed using partitioned Bayesian analysis with independent models and parameter settings for each gene region, and the most strongly supported phylogenetic hypothesis is then used to test the hypothesis of two colonizations of the New World by African scincid lizards. Our results show that the consistent use of model-based methods in both alignment and tree reconstruction leads to trees with more optimal likelihood scores than the use of independent criteria in alignment and tree reconstruction. We corroborate and extend earlier evidence for two independent colonizations of South America by scincid lizards. Relationships within South American Mabuya are found to be in need of taxonomic revision, specifically complexes under the names M. heathi, M. agilis, and M. bistriata (sensu, M.T. Rodrigues, Papeis Avulsos de Zoologia 41 (2000) 313).

Animals↗

PubMed2002

Being sceptical about meta-analyses: a Bayesian perspective on magnesium trials in myocardial infarction.

BACKGROUND: There has been extensive discussion of the apparent conflict between meta-analyses and a mega-trial investigating the benefits of intravenous magnesium following myocardial infarction, in which the early trial results have been said to be 'too good to be true'. METHODS: We apply Bayesian methods of meta-analysis to the trials available before and after the publication of the ISIS-4 results. We show how scepticism can be formally incorporated into an analysis as a Bayesian prior distribution, and how Bayesian meta-analysis models allow appropriate exploration of hypotheses that the treatment effect depends on the size of the trial or the risk in the control group. RESULTS: Adoption of a sceptical prior would have led early enthusiasm for magnesium to be suitably tempered, but only if combined with a random effects meta-analysis, rather than the fixed effect analysis that was actually conducted. CONCLUSIONS: We argue that neither a fixed effect nor a random effects analysis is appropriate when the mega-trial is included. The Bayesian framework provides many possibilities for flexible exploration of clinical hypotheses, but there can be considerable sensitivity to apparently innocuous assumptions.

Bayes Theorem↗

PubMed2002

Bayesian analysis of overdispersed chromosome aberration data with the negative binomial model.

The usual assumption of a Poisson model for the number of chromosome aberrations in controlled calibration experiments implies variance equal to the mean. However, it is known that chromosome aberration data from experiments involving high linear energy transfer radiations can be overdispersed, i.e. the variance is greater than the mean. Present methods for dealing with overdispersed chromosome data rely on frequentist statistical techniques. In this paper. the problem of overdispersion is considered from a Bayesian standpoint. The Bayes Factor is used to compare Poisson and negative binomial models for two previously published calibration data sets describing the induction of dicentric chromosome aberrations by high doses of neutrons. Posterior densities for the model parameters, which characterise dose response and overdispersion are calculated and graphed. Calibrative densities are derived for unknown neutron doses from hypothetical radiation accident data to deterimine the impact of different model assumptions on dose estimates. The main conclusion is that an initial assumption of a negative binomial model is the conservative approach to chromosome dosimetry for high LET radiations.

Bayes Theorem↗

PubMed2000

Bayesian accelerated failure time analysis with application to veterinary epidemiology.

Standard methods for analysing survival data with covariates rely on asymptotic inferences. Bayesian methods can be performed using simple computations and are applicable for any sample size. We propose a practical method for making prior specifications and discuss a complete Bayesian analysis for parametric accelerated failure time regression models. We emphasize inferences for the survival curve rather than regression coefficients. A key feature of the Bayesian framework is that model comparisons for various choices of baseline distribution are easily handled by the calculation of Bayes factors. Such comparisons between non-nested models are difficult in the frequentist setting. We illustrate diagnostic tools and examine the sensitivity of the Bayesian methods.

Abortion, Veterinary↗

PubMed2002

Classical and Bayesian inference in neuroimaging: applications.

In Friston et al. ((2002) Neuroimage 16: 465-483) we introduced empirical Bayes as a potentially useful way to estimate and make inferences about effects in hierarchical models. In this paper we present a series of models that exemplify the diversity of problems that can be addressed within this framework. In hierarchical linear observation models, both classical and empirical Bayesian approaches can be framed in terms of covariance component estimation (e.g., variance partitioning). To illustrate the use of the expectation-maximization (EM) algorithm in covariance component estimation we focus first on two important problems in fMRI: nonsphericity induced by (i) serial or temporal correlations among errors and (ii) variance components caused by the hierarchical nature of multisubject studies. In hierarchical observation models, variance components at higher levels can be used as constraints on the parameter estimates of lower levels. This enables the use of parametric empirical Bayesian (PEB) estimators, as distinct from classical maximum likelihood (ML) estimates. We develop this distinction to address: (i) The difference between response estimates based on ML and the conditional means from a Bayesian approach and the implications for estimates of intersubject variability. (ii) The relationship between fixed- and random-effect analyses. (iii) The specificity and sensitivity of Bayesian inference and, finally, (iv) the relative importance of the number of scans and subjects. The forgoing is concerned with within- and between-subject variability in multisubject hierarchical fMRI studies. In the second half of this paper we turn to Bayesian inference at the first (within-voxel) level, using PET data to show how priors can be derived from the (between-voxel) distribution of activations over the brain. This application uses exactly the same ideas and formalism but, in this instance, the second level is provided by observations over voxels as opposed to subjects. The ensuing posterior probability maps (PPMs) have enhanced anatomical precision and greater face validity, in relation to underlying anatomy. Furthermore, in comparison to conventional SPMs they are not confounded by the multiple comparison problem that, in a classical context, dictates high thresholds and low sensitivity. We conclude with some general comments on Bayesian approaches to image analysis and on some unresolved issues.

Algorithms↗

PubMed1997

A Bayesian formulation of the Kalman filter applied to the estimation of individual pharmacokinetic parameters.

A general method of Bayesian forecasting employing the dynamic linear model has been adapted to the problem of estimating individual pharmacokinetic parameters. The Bayesian forecasting method incorporates an efficient Kalman filter algorithm for updating pharmacokinetic parameter estimates when further observations are made. The Kalman filter is more general and flexible than other Bayesian methods currently used and simulation studies have demonstrated its practicality for three different pharmacokinetic models. The method serves as the basis for a computer program for general clinical use.

Algorithms↗

PubMed1991

Individualising gentamicin dosage regimens. A comparative review of selected models, data fitting methods and monitoring strategies.

The various components required for individualising clinical drug dosage regimens are reviewed, including a study of 3 types of fitting procedures, 2 types of gentamicin pharmacokinetic model and the utility of D-optimal times for obtaining serum gentamicin concentrations. The combination of the current Bayesian fitting procedure, the kslope pharmacokinetic model [in which the elimination rate constant (kel) can change from dose to dose with changing creatinine clearance] and the explicit measurement of the assay error pattern yielded predictions of future serum gentamicin concentrations which were (a) slightly better than those found using weighted nonlinear least squares; (b) somewhat better than those found with Bayesian fitting and a fixed-kel model; (c) better than those found using the traditional linear regression fitting procedure and a fixed kel model. D-Optimally timed pairs of concentrations also predicted future concentrations at least as well, and more cost effectively.

Data Interpretation, Statistical↗

PubMed2006

Spatio-temporal modeling and analysis of fMRI data using NARX neural network.

This paper presents spatio-temporal modeling and analysis methods to fMRI data. Based on the nonlinear autoregressive with exogenous inputs (NARX) model realized by the Bayesian radial basis function (RBF) neural networks, two methods (NARX-1 and NARX-2) are proposed to capture the unknown complex dynamics of the brain activities. Simulation results on both synthetic and real fMRI data clearly show that the proposed schemes outperform the conventional t-test method in detecting the activated regions of the brain.

Bayes Theorem↗

PubMed2001

Individualising aminoglycoside dosage regimens after therapeutic drug monitoring: simple or complex pharmacokinetic methods?

Measurements of aminoglycoside concentration in serum are used to individualise dosage regimens (dose per administration and/or administration interval) with the goal of attaining the desired therapeutic range as quickly as possible. Therapeutic range is defined in terms of peak concentration (to monitor effectiveness) and trough concentration (to avoid toxicity). This article focuses on methods to individualise aminoglycoside dosage regimens in the context of extended dosage intervals. Simple pharmacokinetic methods involve linear dosage adjustment based on peak or trough concentrations or area under the concentration-time curve, or nomograms. The once daily aminoglycoside nomogram determines the dosage interval for aminoglycosides given as a fixed dose per administration, based on a single concentration measurement drawn 6 to 14 hours after the start of the first infusion. This is a preferred method because of its simplicity, strong pharmacodynamic rationale and prospective validation in a large population. However, it does not work when the fixed dose assumed is not relevant, for example for patients with burns, cystic fibrosis, ascites or pregnancy. Furthermore, it has not been validated in children. In these cases, a more sophisticated method is required. Complex pharmacokinetic methods require dedicated software. Non-Bayesian least-squares methods allow the optimisation of both the dose and the dosage interval, but require aminoglycoside concentrations from two or more samples taken in the post-distributive phase during a single dosage interval. With Bayesian least-squares methods, only one concentration measurement is required, although any number of samples can be taken into account. In the Bayesian maximum a posteriori (MAP) method, the parameter estimates are taken as the values corresponding to the maximum of the posterior density. In 'full' Bayesian approaches (also called stochastic control), all the information about the parameters revealed by the posterior distribution is taken into account, and the optimal regimen is found by minimising the expected value of the weighted sum of squared deviations between predicted and target concentrations. If the population model is reasonably well known, Bayesian methods (MAP or stochastic control) should be used because of their good predictive performance. Although only one concentration measurement is required, better precision is afforded by a two-sample strategy, preferably drawn 1 and 6 hours after the start of the first infusion. If the population model is not known, then the non-Bayesian least-squares method is the method of choice, because of its robustness and lack of requirement for prior information about the distribution of parameters in the population.

Aminoglycosides↗

PubMed2003

Mixture models and the probabilistic structure of depth cues.

Monocular cues to depth derive their informativeness from a combination of perspective projection and prior constraints on the way scenes in the world are structured. For many cues, the appropriate priors are best described as mixture models, each of which characterizes a different category of objects, surfaces, or scenes. This paper provides a Bayesian analysis of the resulting model selection problem, showing how the mixed structure of priors creates the potential for non-linear, cooperative interactions between cues and how the information provided by a single cue can effectively determine the appropriate constraint to apply to a given image. The analysis also leads to a number of psychophysically testable predictions. We test these predictions by applying the framework to the problem of perceiving planar surface orientation from texture. A number of psychophysical experiments are described that show that the visual system is biased to interpret textures as isotropic, but that when sufficient image data is available, the system effectively turns off the isotropy constraint and interprets texture information using only a homogeneity assumption. Human performance is qualitatively similar to an optimal estimator that assumes a mixed prior on surface textures--some proportion being isotropic and homogeneous and some proportion being anisotropic and homogeneous.

Adult↗

PubMedDate not supplied

Open-loop-feedback control of serum drug concentrations: pharmacokinetic approaches to drug therapy.

Recent developments to optimize open-loop-feedback control of drug dosage regimens, generally applicable to pharmacokinetically oriented therapy with many drugs, involve computation of patient-individualized strategies for obtaining desired serum drug concentrations. Analyses of past therapy are performed by least squares, extended least squares, and maximum a posteriori probability Bayesian methods of fitting pharmacokinetic models to serum level data. Future possibilities for truly optimal open-loop-feedback therapy with full Bayesian methods, and conceivably for optimal closed-loop therapy in such data-poor clinical situations, are also discussed. Implementation of these various therapeutic strategies, using automated, locally controlled infusion devices, has also been achieved in prototype form.

Aged↗