Bayesian Decision Theory Approach Research Articles

Probabilistic identification of bacterial essential genes via insertion density using TraDIS data with Tn5 libraries.

MotivationProbabilistic Identification of bacterial essential genes using transposon-directed insertion-site sequencing (TraDIS) data based on Tn5 libraries has received relatively little attention in the literature; most methods are designed for mariner transposon insertions. Analysis of Tn5 transposon-based genomic data is challenging due to the high insertion density and genomic resolution. We present a novel probabilistic Bayesian approach for classifying bacterial essential genes using transposon insertion density derived from transposon insertion sequencing data. We implement a Markov chain Monte Carlo sampling procedure to estimate the posterior probability that any given gene is essential. We implement a Bayesian decision theory approach to selecting essential genes. We assess the effectiveness of our approach via analysis of both simulated data and three previously published Escherichia coli, Salmonella Typhimurium and Staphylococcus aureus datasets. These three bacteria have relatively well characterized essential genes which allows us to test our classification procedure using receiver operating characteristic curves and area under the curves. We compare the classification performance with that of Bio-Tradis, a standard tool for bacterial gene classification.ResultsOur method is able to classify genes in the three datasets with areas under the curves between 0.967 and 0.983. Our simulated synthetic datasets show that both the number of insertions and the extent to which insertions are tolerated in the distal regions of essential genes are both important in determining classification accuracy. Importantly our method gives the user the option of classifying essential genes based on the user-supplied costs of false discovery and false non-discovery.Availability and implementationAn R package that implements the method presented in this paper is available for download from https://github.com/Kevin-walters/insdens.Supplementary information Supplementary data are available at Bioinformatics online.

Bayesian decision theory for tree-based adaptive screening tests with an application to youth delinquency

Crime prevention strategies based on early intervention depend on accurate risk assessment instruments for identifying high risk youth. It is important in this context that the instruments be convenient to administer, which means, in particular, that they must be reasonably brief; adaptive screening tests are useful for this purpose. Although item response theory (IRT) bears a long and rich history in producing reliable adaptive tests, adaptive tests constructed using classification and regression trees are becoming a popular alternative to the traditional IRT approach for item selection. On the upside, unlike IRT, tree-based questionnaires require no real-time parameter estimation during administration. On the downside, while item response theory provides robust criteria for terminating the exam, the stopping criterion for a tree-based adaptive test (the maximum tree depth) is unclear. We present a Bayesian decision theory approach for characterizing the trade-offs of administering tree-based questionnaires of different lengths. This formalism involves specifying 1) a utility function measuring the goodness of the assessment; 2) a target population over which this utility should be maximized; 3) an action space comprised of different-length assessments, populated via a tree-fitting algorithm. Using this framework, we provide uncertainty estimates for the trade-offs of shortening the exam, allowing practitioners to determine an optimal exam length in a principled way. The method is demonstrated through an application to youth delinquency risk assessment in Honduras.

Application of multi-trait Bayesian decision theory for parental genomic selection.

In all breeding programs, the decision about which individuals to select and intermate to form the next selection cycle is crucial. The improvement of genetic stocks requires considering multiple traits simultaneously, given that economic value and net genetic merits depend on many traits; therefore, with the advance of computational and statistical tools and genomic selection (GS), researchers are focusing on multi-trait selection. Selection of the best individuals is difficult, especially in traits that are antagonistically correlated, where improvement in one trait might imply a reduction in other(s). There are approaches that facilitate multi-trait selection, and recently a Bayesian decision theory (BDT) has been proposed. Parental selection using BDT has the potential to be effective in multi-trait selection given that it summarizes all relevant quantitative genetic concepts such as heritability, response to selection and the structure of dependence between traits (correlation). In this study, we applied BDT to provide a treatment for the complexity of multi-trait parental selection using three multivariate loss functions (LF), Kullback–Leibler (KL), Energy Score, and Multivariate Asymmetric Loss (MALF), to select the best-performing parents for the next breeding cycle in two extensive real wheat data sets. Results show that the high ranking lines in genomic estimated breeding value (GEBV) for certain traits did not always have low values for the posterior expected loss (PEL). For both data sets, the KL LF gave similar importance to all traits including grain yield. In contrast, the Energy Score and MALF gave a better performance in three of four traits that were different than grain yield. The BDT approach should help breeders to decide based not only on the GEBV per se of the parent to be selected, but also on the level of uncertainty according to the Bayesian paradigm.

A Bayesian Decision Theory Approach for Genomic Selection

Plant and animal breeders are interested in selecting the best individuals from a candidate set for the next breeding cycle. In this paper, we propose a formal method under the Bayesian decision theory framework to tackle the selection problem based on genomic selection (GS) in single- and multi-trait settings. We proposed and tested three univariate loss functions (Kullback-Leibler, KL; Continuous Ranked Probability Score, CRPS; Linear-Linear loss, LinLin) and their corresponding multivariate generalizations (Kullback-Leibler, KL; Energy Score, EnergyS; and the Multivariate Asymmetric Loss Function, MALF). We derived and expressed all the loss functions in terms of heritability and tested them on a real wheat dataset for one cycle of selection and in a simulated selection program. The performance of each univariate loss function was compared with the standard method of selection (Std) that does not use loss functions. We compared the performance in terms of the selection response and the decrease in the population’s genetic variance during recurrent breeding cycles. Results suggest that it is possible to obtain better performance in a long-term breeding program using the single-trait scheme by selecting 30% of the best individuals in each cycle but not by selecting 10% of the best individuals. For the multi-trait approach, results show that the population mean for all traits under consideration had positive gains, even though two of the traits were negatively correlated. The corresponding population variances were not statistically different from the different loss function during the 10th selection cycle. Using the loss function should be a useful criterion when selecting the candidates for selection for the next breeding cycle.

Interacting agricultural pests and their effect on crop yield: application of a Bayesian decision theory approach to the joint management of Bromus tectorum and Cephus cinctus.

Worldwide, the landscape homogeneity of extensive monocultures that characterizes conventional agriculture has resulted in the development of specialized and interacting multitrophic pest complexes. While integrated pest management emphasizes the need to consider the ecological context where multiple species coexist, management recommendations are often based on single-species tactics. This approach may not provide satisfactory solutions when confronted with the complex interactions occurring between organisms at the same or different trophic levels. Replacement of the single-species management model with more sophisticated, multi-species programs requires an understanding of the direct and indirect interactions occurring between the crop and all categories of pests. We evaluated a modeling framework to make multi-pest management decisions taking into account direct and indirect interactions among species belonging to different trophic levels. We adopted a Bayesian decision theory approach in combination with path analysis to evaluate interactions between Bromus tectorum (downy brome, cheatgrass) and Cephus cinctus (wheat stem sawfly) in wheat (Triticum aestivum) systems. We assessed their joint responses to weed management tactics, seeding rates, and cultivar tolerance to insect stem boring or competition. Our results indicated that C. cinctus oviposition behavior varied as a function of B. tectorum pressure. Crop responses were more readily explained by the joint effects of management tactics on both categories of pests and their interactions than just by the direct impact of any particular management scheme on yield. In accordance, a C. cinctus tolerant variety should be planted at a low seeding rate under high insect pressure. However as B. tectorum levels increase, the C. cinctus tolerant variety should be replaced by a competitive and drought tolerant cultivar at high seeding rates despite C. cinctus infestation. This study exemplifies the necessity of accounting for direct and indirect biological interactions occurring within agroecosystems and propagating this information from the statistical analysis stage to the management stage.

A Bayesian decision theory approach for the techno-economic analysis of an all-optical router (extended version)

Typically, core networks are provided with both optical and electronic physical layers. However, the interaction between the two layers is at present limited, since most of the traditional transport functionalities, such as traffic engineering, switching and restoration, are carried in the IP/MPLS layer. In the light of this, the research community has paid little attention to the potential benefits of the interaction between layers, multilayer capabilities, on attempts to improve quality of service control. This paper shows when to move incoming label switched paths (LSPs) between layers based on a multilayer mechanism that trades off a QoS metric, such as end-to-end delay, and techno-economic aspects. Such a mechanism follows the Bayesian decision theory, and is tested with a set of representative case scenarios.

A decision theoretical approach to wavelet regression on curves with a high number of regressors

Here we consider a possibly multivariate regression setting where data arise as curves and where the number of predictors greatly exceeds the number of observations. We present typical applications in spectral calibration. We employ wavelets and transform curves into sets of wavelet coefficients describing local features of the spectra. We then apply a Bayesian decision theory approach to select those coefficients that predict well the response. The method requires cost specifications and we employ cost functions that depend on the wavelet scale. Stochastic optimization methods are needed to find optimal subsets. We investigate both simulated annealing and genetic algorithms.

A Bayesian decision theory approach to variable selection for discrimination

Motivated by examples in spectroscopy, we study variable selection for discrimination in problems with very many predictor variables. Assuming multivariate normal distributions with common variance for the predictor variables within groups, we develop a Bayesian decision theory approach that balances costs for variables against a loss due to classification errors. The approach is computationally intensive, requiring a simulation to approximate the intractable expected loss and a search, using simulated annealing, over a large space of possible subsets of variables. It is illustrated by application to a spectroscopic example with 3 groups, 100 variables, and 71 training cases, where the approach finds subsets of between 5 and 14 variables whose discriminatory power is comparable with that of linear discriminant analysis using principal components derived from the full 100 variables. We study both the evaluation of expected loss and the tuning of the simulated annealing for the example, and conclude that computational effort should be concentrated on the search.

The choice of variables in multivariate regression: a non-conjugate Bayesian decision theory approach

We consider the choice of explanatory variables in multivariate linear regression. Our approach balances prediction accuracy against costs attached to variables:in a multivariate version of a decision theory approach pioneered by Lindley (1968). We also employ a non-conjugate proper prior distribution for the parameters of the regression model, extending the standard normal-inverse Wishart by adding a component of error which is unexplainable by any number of predictor variables, thus avoiding the determinism identified by Dawid (1988). Simulated annealing and fast updating algorithms are used to search for good subsets when there are very many regressors. The technique is illustrated on a near infrared spectroscopy example involving 39 observations and 300 explanatory variables. This demonstrates the effectiveness of multivariate regression as opposed to separate univariate regressions. It also emphasises that within a Bayesian framework more variables than observations can be utilised.

Bayesian individualization via sampling-based methods.

We consider the situation where we wish to adjust the dosage regimen of a patient based on (in general) sparse concentration measurements taken on-line. A Bayesian decision theory approach is taken which requires the specification of an appropriate prior distribution and loss function. A simple method for obtaining samples from the posterior distribution of the pharmacokinetic parameters of the patient is described. In general, these samples are used to obtain a Monte Carlo estimate of the expected loss which is then minimized with respect to the dosage regimen. Some special cases which yield analytic solutions are described. When the prior distribution is based on a population analysis then a method of accounting for the uncertainty in the population parameters is described. Two simulation studies showing how the methods work in practice are presented.

A Bayesian Decision Theory Approach to Classification Problems

We address the classification problem where an item is declared to be from populationπjif certain of its characteristicsvare assumed to be sampled from the distribution with pdf fj(v∣θj), wherej=1, 2, …, m. We first solve the two population classification problem and then extend the results to the generalmpopulation classification problem. Usually only the form of the pdf's is known. To use the classical classification rule the parameters,θj, must be replaced by their estimates. In this paper we allow the parameters of the underlying distributions to be generated from prior distributions. With this added structure, we obtain Bayes rules based on predictive distributions and these are completely determined. Using the first-order expansion of the predictive density, where the coefficients of powers ofn−1remain uniformly bounded innwhen integrated, we obtain an asymptotic bound for the Bayes risk.

Constructing Release Targets for Drug Products: a Bayesian Decision Theory Approach

Constructing Release Targets for Drug Products: a Bayesian Decision Theory Approach

Constructing Release Targets for Drug Products: A Bayesian Decision Theory Approach

Constructing release targets for drug products in the pharmaceutical industry is considered. to account for the cost and profit of the drug company, a Bayesian decision theory approach is proposed. The release targets are constructed by minimizing the company's expected loss (or maximizing the expected gain). An example from a pharmaceutical company concerning the decision of releasing a batch of drug product is presented.

Optimal regression design for control in linear regression

SIUMMARY A Bayesian decision theory approach to the choice of regression design is considered when it is intended to use the regression to help control the dependent variable at a chosen value, the control to be effected by choosing certain of the independent variables and fixing them at selected values. Some key word8: Bayesian decision theory; Control; D-optimum; Linear regression; Preposterior analysis; Regression design. 1. INTRODIUCTION This paper is concerned with the design of a regression experiment in which observations of a dependent variable are obtained at selected values of a set of independent variables. Using Bayesian decision theory, Lindley (1968) considered the analysis of data from a regression experiment in two situations, namely when it is desired to choose the best subset of independent variables (a) to predict a future value of the dependent variable, (b) to control the level of the dependent variable at a preassigned value. The first situation he termed a 'prediction problem' and the second a 'control problem'. The optimal choice of a designed regression experiment for Lindley's approach to the prediction problem was considered by Brooks (1972). In the present paper, the optimal choice of designed experiment for the control problem is considered, whe-n the regression is linear in the independent variables. To do this, a decision-theoretic analysis of the following sequence of decisions and events is considered. First, the size n of the experiment is decided, and then n sets of values X1, ..., X,

Public administration planning in developing countries a Bayesian decision theory approach

Decisionmaking under uncertainty is visualized as a game against nature. The policymaker is the player and has a set of alternatives or strategies from which he desires to choose the most effective. He is confronted with a variety of possible states of nature that may evolve after his decision is made. The key states of nature are identified and their interactive relationship to the strategy options are specified. Important roles in the resulting analysis are played by the probabilities of successful project initiation and implementation. It is shown that neglect of the inherent uncertainty aspects leads to evaluations (benefit-cost ratios) of proposed reforms and projects which can be seriously upward biased.

Optimal unsupervised learning multicategory dependent hypotheses pattern recognition

A Bayesian decision theory approach is applied to the solution of the problem of unsupervised parametric pattern recognition. The parametric model for this investigation includes the cases where both constant and time-varying unknown parameters are present, and, most significantly, the unknown hypotheses do not constitute a statistically independent sequence. They are restricted only to be from a source with finite-order Markov dependence. The resulting optimal learning system is found and shown to grow initially in size and memory until the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</tex> th observation (where <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</tex> is the highest Markov order), and subsequently to remain of fixed size and memory. It can, therefore, operate indefinitely and continue to improve its ability to recognize patterns utilizing only a fixed size memory. In summary, the main contributions of this paper are the following: \begin{enumerate} \item the extension of previous investigations of the unsupervised parametric pattern recognition problem to include cases where both constant and time-varying unknown parameter vectors are simultaneously present; \item that the a priori probabilities of the hypotheses, the time-varying parameters, and their transition laws may, if constant, be expressed as functions of the constant unknown parameter and, thus, also be learned; and \item the removal of the assumption of statistical independence between hypotheses for the sequence of observations. \end{enumerate}