A Bayesian approach to estimate sensible and latent heat over vegetated land surface

Sensible and latent heat fluxes are often calculated from bulk transfer equations combined with the energy balance. For spatial estimates of these fluxes, a combination of remotely sensed and standard meteorological data from weather stations is used. The success of this approach depends on the accuracy of the input data and on the accuracy of two variables in particular: aerodynamic and surface conductance. This paper presents a Bayesian approach to improve estimates of sensible and latent heat fluxes by using a priori estimates of aerodynamic and surface conductance alongside remote measurements of surface temperature. The method is validated for time series of half-hourly measurements in a fully grown maize field, a vineyard and a forest. It is shown that the Bayesian approach yields more accurate estimates of sensible and latent heat flux than traditional methods.

A Bayesian approach for multi-model downscaling: Seasonal forecasting of regional rainfall and river flows in South America

This study addresses three issues: spatial downscaling, calibration, and combination of seasonal predictions produced by different coupled ocean-atmosphere climate models. It examines the feasibility Of using a Bayesian procedure for producing combined, well-calibrated downscaled seasonal rainfall forecasts for two regions in South America and river flow forecasts for the Parana river in the south of Brazil and the Tocantins river in the north of Brazil. These forecasts are important for national electricity generation management and planning. A Bayesian procedure, referred to here as forecast assimilation, is used to combine and calibrate the rainfall predictions produced by three climate models. Forecast assimilation is able to improve the skill of 3-month lead November-December-January multi-model rainfall predictions over the two South American regions. Improvements are noted in forecast seasonal mean values and uncertainty estimates. River flow forecasts are less skilful than rainfall forecasts. This is partially because natural river flow is a derived quantity that is sensitive to hydrological as well as meteorological processes, and to human intervention in the form of reservoir management.

Forecast calibration and combination: a simple Bayesian approach for ENSO

This study presents a new simple approach for combining empirical with raw (i.e., not bias corrected) coupled model ensemble forecasts in order to make more skillful interval forecasts of ENSO. A Bayesian normal model has been used to combine empirical and raw coupled model December SST Niño-3.4 index forecasts started at the end of the preceding July (5-month lead time). The empirical forecasts were obtained by linear regression between December and the preceding July Niño-3.4 index values over the period 1950–2001. Coupled model ensemble forecasts for the period 1987–99 were provided by ECMWF, as part of the Development of a European Multimodel Ensemble System for Seasonal to Interannual Prediction (DEMETER) project. Empirical and raw coupled model ensemble forecasts alone have similar mean absolute error forecast skill score, compared to climatological forecasts, of around 50% over the period 1987–99. The combined forecast gives an increased skill score of 74% and provides a well-calibrated and reliable estimate of forecast uncertainty.

A Bayesian approach for dose-escalation in a phase I clinical trial incorporating pharmacodynamic endpoints

Bayesian decision procedures have already been proposed for and implemented in Phase I dose-escalation studies in healthy volunteers. The procedures have been based on pharmacokinetic responses reflecting the concentration of the drug in blood plasma and are conducted to learn about the dose-response relationship while avoiding excessive concentrations. However, in many dose-escalation studies, pharmacodynamic endpoints such as heart rate or blood pressure are observed, and it is these that should be used to control dose-escalation. These endpoints introduce additional complexity into the modeling of the problem relative to pharmacokinetic responses. Firstly, there are responses available following placebo administrations. Secondly, the pharmacodynamic responses are related directly to measurable plasma concentrations, which in turn are related to dose. Motivated by experience of data from a real study conducted in a conventional manner, this paper presents and evaluates a Bayesian procedure devised for the simultaneous monitoring of pharmacodynamic and pharmacokinetic responses. Account is also taken of the incidence of adverse events. Following logarithmic transformations, a linear model is used to relate dose to the pharmacokinetic endpoint and a quadratic model to relate the latter to the pharmacodynamic endpoint. A logistic model is used to relate the pharmacokinetic endpoint to the risk of an adverse event.

A novel Bayesian approach to drug design with simple and complex enzymes: Use with lens aldehyde dehydrogenase and the glyoxalase pathway

Purpose: Acquiring details of kinetic parameters of enzymes is crucial to biochemical understanding, drug development, and clinical diagnosis in ocular diseases. The correct design of an experiment is critical to collecting data suitable for analysis, modelling and deriving the correct information. As classical design methods are not targeted to the more complex kinetics being frequently studied, attention is needed to estimate parameters of such models with low variance. Methods: We have developed Bayesian utility functions to minimise kinetic parameter variance involving differentiation of model expressions and matrix inversion. These have been applied to the simple kinetics of the enzymes in the glyoxalase pathway (of importance in posttranslational modification of proteins in cataract), and the complex kinetics of lens aldehyde dehydrogenase (also of relevance to cataract). Results: Our successful application of Bayesian statistics has allowed us to identify a set of rules for designing optimum kinetic experiments iteratively. Most importantly, the distribution of points in the range is critical; it is not simply a matter of even or multiple increases. At least 60 % must be below the KM (or plural if more than one dissociation constant) and 40% above. This choice halves the variance found using a simple even spread across the range.With both the glyoxalase system and lens aldehyde dehydrogenase we have significantly improved the variance of kinetic parameter estimation while reducing the number and costs of experiments. Conclusions: We have developed an optimal and iterative method for selecting features of design such as substrate range, number of measurements and choice of intermediate points. Our novel approach minimises parameter error and costs, and maximises experimental efficiency. It is applicable to many areas of ocular drug design, including receptor-ligand binding and immunoglobulin binding, and should be an important tool in ocular drug discovery.

A Bayesian approach to disease gene location using allelic association

A Bayesian approach to analysing data from family-based association studies is developed. This permits direct assessment of the range of possible values of model parameters, such as the recombination frequency and allelic associations, in the light of the data. In addition, sophisticated comparisons of different models may be handled easily, even when such models are not nested. The methodology is developed in such a way as to allow separate inferences to be made about linkage and association by including theta, the recombination fraction between the marker and disease susceptibility locus under study, explicitly in the model. The method is illustrated by application to a previously published data set. The data analysis raises some interesting issues, notably with regard to the weight of evidence necessary to convince us of linkage between a candidate locus and disease.

Quantitative precipitation estimation over ocean using Bayesian approach from microwave observations during the typhoon season

We have developed a new Bayesian approach to retrieve oceanic rain rate from the Tropical Rainfall Measuring Mission (TRMM) Microwave Imager (TMI), with an emphasis on typhoon cases in the West Pacific. Retrieved rain rates are validated with measurements of rain gauges located on Japanese islands. To demonstrate improvement, retrievals are also compared with those from the TRMM/Precipitation Radar (PR), the Goddard Profiling Algorithm (GPROF), and a multi-channel linear regression statistical method (MLRS). We have found that qualitatively, all methods retrieved similar horizontal distributions in terms of locations of eyes and rain bands of typhoons. Quantitatively, our new Bayesian retrievals have the best linearity and the smallest root mean square (RMS) error against rain gauge data for 16 typhoon overpasses in 2004. The correlation coefficient and RMS of our retrievals are 0.95 and ~2 mm hr-1, respectively. In particular, at heavy rain rates, our Bayesian retrievals outperform those retrieved from GPROF and MLRS. Overall, the new Bayesian approach accurately retrieves surface rain rate for typhoon cases. Accurate rain rate estimates from this method can be assimilated in models to improve forecast and prevent potential damages in Taiwan during typhoon seasons.

Decision-making in a phase II clinical trial: a new approach combining Bayesian and frequentist concepts

The aim of a phase H clinical trial is to decide whether or not to develop an experimental therapy further through phase III clinical evaluation. In this paper, we present a Bayesian approach to the phase H trial, although we assume that subsequent phase III clinical trials will hat,e standard frequentist analyses. The decision whether to conduct the phase III trial is based on the posterior predictive probability of a significant result being obtained. This fusion of Bayesian and frequentist techniques accepts the current paradigm for expressing objective evidence of therapeutic value, while optimizing the form of the phase II investigation that leads to it. By using prior information, we can assess whether a phase II study is needed at all, and how much or what sort of evidence is required. The proposed approach is illustrated by the design of a phase II clinical trial of a multi-drug resistance modulator used in combination with standard chemotherapy in the treatment of metastatic breast cancer. Copyright (c) 2005 John Wiley & Sons, Ltd.

Efficient and accurate experimental design for enzyme kinetics: Bayesian studies reveal a systematic approach

In areas such as drug development, clinical diagnosis and biotechnology research, acquiring details about the kinetic parameters of enzymes is crucial. The correct design of an experiment is critical to collecting data suitable for analysis, modelling and deriving the correct information. As classical design methods are not targeted to the more complex kinetics being frequently studied, attention is needed to estimate parameters of such models with low variance. We demonstrate that a Bayesian approach (the use of prior knowledge) can produce major gains quantifiable in terms of information, productivity and accuracy of each experiment. Developing the use of Bayesian Utility functions, we have used a systematic method to identify the optimum experimental designs for a number of kinetic model data sets. This has enabled the identification of trends between kinetic model types, sets of design rules and the key conclusion that such designs should be based on some prior knowledge of K-M and/or the kinetic model. We suggest an optimal and iterative method for selecting features of the design such as the substrate range, number of measurements and choice of intermediate points. The final design collects data suitable for accurate modelling and analysis and minimises the error in the parameters estimated. (C) 2003 Elsevier Science B.V. All rights reserved.

The seasonal forecast of electricity demand: A hierarchical Bayesian model with climatological weather generator

In this paper we focus on the one year ahead prediction of the electricity peak-demand daily trajectory during the winter season in Central England and Wales. We define a Bayesian hierarchical model for predicting the winter trajectories and present results based on the past observed weather. Thanks to the flexibility of the Bayesian approach, we are able to produce the marginal posterior distributions of all the predictands of interest. This is a fundamental progress with respect to the classical methods. The results are encouraging in both skill and representation of uncertainty. Further extensions are straightforward at least in principle. The main two of those consist in conditioning the weather generator model with respect to additional information like the knowledge of the first part of the winter and/or the seasonal weather forecast. Copyright (C) 2006 John Wiley & Sons, Ltd.

Bayesian estimation of co-integrating thresholds in the term structure of interest rates.

Threshold Error Correction Models are used to analyse the term structure of interest Rates. The paper develops and uses a generalisation of existing models that encompasses both the Band and Equilibrium threshold models of [Balke and Fomby ((1997) Threshold cointegration. Int Econ Rev 38(3):627–645)] and estimates this model using a Bayesian approach. Evidence is found for threshold effects in pairs of longer rates but not in pairs of short rates. The Band threshold model is supported in preference to the Equilibrium model.

An evaluation of a Bayesian method of dose escalation based on bivariate binary responses

Recently, various approaches have been suggested for dose escalation studies based on observations of both undesirable events and evidence of therapeutic benefit. This article concerns a Bayesian approach to dose escalation that requires the user to make numerous design decisions relating to the number of doses to make available, the choice of the prior distribution, the imposition of safety constraints and stopping rules, and the criteria by which the design is to be optimized. Results are presented of a substantial simulation study conducted to investigate the influence of some of these factors on the safety and the accuracy of the procedure with a view toward providing general guidance for investigators conducting such studies. The Bayesian procedures evaluated use logistic regression to model the two responses, which are both assumed to be binary. The simulation study is based on features of a recently completed study of a compound with potential benefit to patients suffering from inflammatory diseases of the lung.

Bayesian sample size for exploratory clinical trials incorporating historical data

This paper presents a simple Bayesian approach to sample size determination in clinical trials. It is required that the trial should be large enough to ensure that the data collected will provide convincing evidence either that an experimental treatment is better than a control or that it fails to improve upon control by some clinically relevant difference. The method resembles standard frequentist formulations of the problem, and indeed in certain circumstances involving 'non-informative' prior information it leads to identical answers. In particular, unlike many Bayesian approaches to sample size determination, use is made of an alternative hypothesis that an experimental treatment is better than a control treatment by some specified magnitude. The approach is introduced in the context of testing whether a single stream of binary observations are consistent with a given success rate p(0). Next the case of comparing two independent streams of normally distributed responses is considered, first under the assumption that their common variance is known and then for unknown variance. Finally, the more general situation in which a large sample is to be collected and analysed according to the asymptotic properties of the score statistic is explored. Copyright (C) 2007 John Wiley & Sons, Ltd.

Bayesian design and conduct of phase II single-arm clinical trials with binary outcomes: a tutorial

The aim of phase II single-arm clinical trials of a new drug is to determine whether it has sufficient promising activity to warrant its further development. For the last several years Bayesian statistical methods have been proposed and used. Bayesian approaches are ideal for earlier phase trials as they take into account information that accrues during a trial. Predictive probabilities are then updated and so become more accurate as the trial progresses. Suitable priors can act as pseudo samples, which make small sample clinical trials more informative. Thus patients have better chances to receive better treatments. The goal of this paper is to provide a tutorial for statisticians who use Bayesian methods for the first time or investigators who have some statistical background. In addition, real data from three clinical trials are presented as examples to illustrate how to conduct a Bayesian approach for phase II single-arm clinical trials with binary outcomes.