Bayes Procedure Research Articles

Osteosarcoma tissues and cell lines from patients with differing serum alkaline phosphatase concentrations display minimal differences in gene expression patterns.

Serum alkaline phosphatase (ALP) concentration is a prognostic factor for osteosarcoma in multiple studies, although its biological significance remains incompletely understood. To determine whether gene expression patterns differed in osteosarcoma from patients with differing serum ALP concentrations, microarray analysis was performed on 18 primary osteosarcoma samples and six osteosarcoma cell lines from dogs with normal and increased serum ALP concentration. No differences in gene expression patterns were noted between tumours or cell lines with differing serum ALP concentration using a gene-specific two-sample t-test. Using a more sensitive empirical Bayes procedure, defective in cullin neddylation 1 domain containing 1 (DCUN1D1) was increased in both the tissue and cell lines of the normal ALP group. Using quantitative PCR (qPCR), differences in DCUN1D1 expression between the two groups failed to reach significance. The homogeneity of gene expression patterns of osteosarcoma associated differing serum ALP concentrations are consistent with previous studies suggesting serum ALP concentration is not associated with intrinsic differences of osteosarcoma cells.

MOCABA: A general Monte Carlo–Bayes procedure for improved predictions of integral functions of nuclear data

MOCABA is a combination of Monte Carlo sampling and Bayesian updating algorithms for the prediction of integral functions of nuclear data, such as reactor power distributions or neutron multiplication factors. Similarly to the established Generalized Linear Least Squares (GLLS) methodology, MOCABA offers the capability to utilize integral experimental data to reduce the prior uncertainty of integral observables. The MOCABA approach, however, does not involve any series expansions and, therefore, does not suffer from the breakdown of first-order perturbation theory for large nuclear data uncertainties. This is related to the fact that, in contrast to the GLLS method, the updating mechanism within MOCABA is applied directly to the integral observables without having to “adjust” any nuclear data. A central part of MOCABA is the nuclear data Monte Carlo program NUDUNA, which performs random sampling of nuclear data evaluations according to their covariance information and converts them into libraries for transport code systems like MCNP or SCALE. What is special about MOCABA is that it can be applied to any integral function of nuclear data, and any integral measurement can be taken into account to improve the prediction of an integral observable of interest. In this paper we present two example applications of the MOCABA framework: the prediction of the neutron multiplication factor of a water-moderated PWR fuel assembly based on 21 criticality safety benchmark experiments and the prediction of the power distribution within a toy model reactor containing 100 fuel assemblies.

Level of Service of Safety Revisited

The concept of the level of service of safety (LOSS) was developed at the Colorado Department of Transportation in 2000. LOSS reflects how a roadway segment or an intersection is performing in reference to the expected frequency and severity of crashes predicted by its safety performance function. The LOSS concept provides quantitative assessment and qualitative description of the degree of safety of a segment or an intersection. In addition, the loss concept facilitates effective communication about safety problems to other professionals, the traveling public, and elected officials. The LOSS concept was first introduced in a paper titled “Level of Service of Safety: Conceptual Blueprint and Analytical Framework,” published in 2003 in the Transportation Research Record: Journal of the Transportation Research Board, No. 1840. LOSS was incorporated into the first edition of the AASHTO Highway Safety Manual and is used by the Departments of Transportation of Colorado, Louisiana, Montana, Oklahoma, and Wyoming and the Ontario Ministry of Transport, in Canada. LOSS lends itself well to the safety decision-making process in departments of transportation. However, the concept did not initially address correction for the regression to the mean bias. A new method is introduced for using LOSS in concert with correction for regression to the mean bias with an empirical Bayes procedure. In addition, distributional assumptions associated with LOSS are revisited, how the LOSS boundaries are calibrated in the population corrected for the regression to the mean bias is explained, and an intuitive percentile-based reporting method is provided. Finally a diagnostic example and a before-and-after study demonstrating the value of LOSS in identifying the safety problem at a real location are worked through.

Bayes factors based on robust TDT-type tests for family trio design.

Adaptive transmission disequilibrium test (aTDT) and MAX3 test are two robust-efficient association tests for case-parent family trio data. Both tests incorporate information of common genetic models including recessive, additive and dominant models and are efficient in power and robust to genetic model specifications. The aTDT uses information of departure from Hardy-Weinberg disequilibrium to identify the potential genetic model underlying the data and then applies the corresponding TDT-type test, and the MAX3 test is defined as the maximum of the absolute value of three TDT-type tests under the three common genetic models. In this article, we propose three robust Bayes procedures, the aTDT based Bayes factor, MAX3 based Bayes factor and Bayes model averaging (BMA), for association analysis with case-parent trio design. The asymptotic distributions of aTDT under the null and alternative hypothesis are derived in order to calculate its Bayes factor. Extensive simulations show that the Bayes factors and the p-values of the corresponding tests are generally consistent and these Bayes factors are robust to genetic model specifications, especially so when the priors on the genetic models are equal. When equal priors are used for the underlying genetic models, the Bayes factor method based on aTDT is more powerful than those based on MAX3 and Bayes model averaging. When the prior placed a small (large) probability on the true model, the Bayes factor based on aTDT (BMA) is more powerful. Analysis of a simulation data about RA from GAW15 is presented to illustrate applications of the proposed methods.

Selecting the best exponential population under Type-II progressive censoring scheme via empirical Bayes approach

ABSTRACTThe problem of selecting a population according to “selection and ranking” is an important statistical problem. The ideas in selecting the best populations with some demands having optimal criterion have been suggested originally by Bechhofer (1954) and Gupta (1956, 1965). In the area of ranking and selection, the large part of literature is connected with a single criterion. However, this may not satisfy the experimenter’s demand. We follow methodology of Huang and Lai (1999) and the main focus of this article is to select a best population under Type-II progressively censored data for the case of right tail exponential distributions with a bounded and unbounded supports for μi. We formulate the problem and develop a Bayesian setup with two kinds of bounded and unbounded prior for μi. We introduce an empirical Bayes procedure and study the large sample behavior of the proposed rule. It is shown that the proposed empirical Bayes selection rule is asymptotically optimal.

Bayesian Inference for Volatility of Stock Prices

Lognormal distribution is widely used in the analysis of failure time data and stock prices. Maximum likelihood and Bayes estimator of the coefficient of variation of lognormal distribution along with confidence/credible intervals are developed. The utility of Bayes procedure is illustrated by analyzing prices of selected stocks.

About the non-asymptotic behaviour of Bayes estimators

This paper investigates the nonasymptotic properties of Bayes procedures for estimating an unknown distribution from n i.i.d. observations. We assume that the prior is supported by a model (S,h) (where h denotes the Hellinger distance) with suitable metric properties involving the number of small balls that are needed to cover larger ones. We also require that the prior put enough probability on small balls.We consider two different situations. The simplest case is the one of a parametric model containing the target density for which we show that the posterior concentrates around the true distribution at rate 1/n. In the general situation, we relax the parametric assumption and take into account a possible misspecification of the model. Provided that the Kullback–Leibler Information between the true distribution and the model S is finite, we establish risk bounds for the Bayes estimators.

Optimal Maintenance Policies for Automated Demand Response Devices

Demand-side participation is now widely recognized as being extremely critical for satisfying the growing electricity demand in the U.S. The primary mechanism for demand management in the U.S. is demand response (DR) programs that attempt to reduce or shift demand by giving incentives to participating customers via price discounts or rebate payments. Utilities that offer DR programs rely on automated DR devices (ADRs) to automate the response to DR signals. The ADRs are faulty, but the working state of the ADR is not directly observable; one can, however, attempt to infer it from the power consumption during DR events. The utility loses revenue when a malfunctioning ADR does not respond to a DR signal; however, sending a maintenance crew to check and reset the ADR also incurs costs. In this paper, we show that the problem of maintaining a pool of ADRs using a limited number of maintenance crews can be formulated as a restless bandit problem, and that one can compute a near-optimal policy for this problem using Whittle indices. We show that the Whittle indices can be efficiently computed using a variational Bayes procedure even when the load-shed magnitude is noisy, and when there is a random mismatch between the clocks at the utility and at the meter. The results of our numerical experiments suggest that the Whittle-index-based approximate policy is within 4% of the optimal solution for all reasonably low values of the signal-to-noise ratio in the meter readings.

A Sequential Algorithm for Fast Fitting of Dirichlet Process Mixture Models

In this article, we propose an improvement on the sequential updating and greedy search (SUGS) algorithm for fast fitting of Dirichlet process mixture models. The SUGS algorithm provides a means for very fast approximate Bayesian inference for mixture data which is particularly of use when datasets are so large that many standard Markov chain Monte Carlo (MCMC) algorithms cannot be applied efficiently, or take a prohibitively long time to converge. In particular, these ideas are used to initially interrogate the data, and to refine models such that one can potentially apply exact data analysis later on. SUGS relies upon sequentially allocating data to clusters and proceeding with an update of the posterior on the subsequent allocations and parameters which assumes this allocation is correct. Our modification softens this approach, by providing a probability distribution over allocations, with a similar computational cost; this approach has an interpretation as a variational Bayes procedure and hence we term it variational SUGS (VSUGS). It is shown in simulated examples that VSUGS can outperform, in terms of density estimation and classification, a version of the SUGS algorithm in many scenarios. In addition, we present a data analysis for flow cytometry data, and SNP data via a three-class Dirichlet process mixture model, illustrating the apparent improvement over the original SUGS algorithm.

TigaR: integrative significance analysis of temporal differential gene expression induced by genomic abnormalities.

BackgroundTo determine which changes in the host cell genome are crucial for cervical carcinogenesis, a longitudinal in vitro model system of HPV-transformed keratinocytes was profiled in a genome-wide manner. Four cell lines affected with either HPV16 or HPV18 were assayed at 8 sequential time points for gene expression (mRNA) and gene copy number (DNA) using high-resolution microarrays. Available methods for temporal differential expression analysis are not designed for integrative genomic studies.ResultsHere, we present a method that allows for the identification of differential gene expression associated with DNA copy number changes over time. The temporal variation in gene expression is described by a generalized linear mixed model employing low-rank thin-plate splines. Model parameters are estimated with an empirical Bayes procedure, which exploits integrated nested Laplace approximation for fast computation. Iteratively, posteriors of hyperparameters and model parameters are estimated. The empirical Bayes procedure shrinks multiple dispersion-related parameters. Shrinkage leads to more stable estimates of the model parameters, better control of false positives and improvement of reproducibility. In addition, to make estimates of the DNA copy number more stable, model parameters are also estimated in a multivariate way using triplets of features, imposing a spatial prior for the copy number effect.ConclusionWith the proposed method for analysis of time-course multilevel molecular data, more profound insight may be gained through the identification of temporal differential expression induced by DNA copy number abnormalities. In particular, in the analysis of an integrative oncogenomics study with a time-course set-up our method finds genes previously reported to be involved in cervical carcinogenesis. Furthermore, the proposed method yields improvements in sensitivity, specificity and reproducibility compared to existing methods. Finally, the proposed method is able to handle count (RNAseq) data from time course experiments as is shown on a real data set.Electronic supplementary materialThe online version of this article (doi:10.1186/1471-2105-15-327) contains supplementary material, which is available to authorized users.

Empirical Bayes estimation of parameters in Markov transition probability matrix with computational methods

Empirical Bayes estimator for the transition probability matrix is worked out in the cases where we have belief regarding the parameters, For example, where the states seem to be equal or not. In both cases, priors are in accordance with our beliefs. Using EM algorithm, computational methods for different hyperparameters of the empirical Bayes are described. Also, robustness of empirical Bayes procedure is investigated.

On the Bernstein–von Mises phenomenon for nonparametric Bayes procedures

We continue the investigation of Bernstein-von Mises theorems for nonparametric Bayes procedures from [Ann. Statist. 41 (2013) 1999-2028]. We introduce multiscale spaces on which nonparametric priors and posteriors are naturally defined, and prove Bernstein-von Mises theorems for a variety of priors in the setting of Gaussian nonparametric regression and in the i.i.d. sampling model. From these results we deduce several applications where posterior-based inference coincides with efficient frequentist procedures, including Donsker- and Kolmogorov-Smirnov theorems for the random posterior cumulative distribution functions. We also show that multiscale posterior credible bands for the regression or density function are optimal frequentist confidence bands.

A best linear threshold classification with scale mixture of skew normal populations

This paper describes a threshold classification with $$K$$ K populations whose membership category is associated with the threshold process of a latent variable. It is seen that the optimal procedure (Bayes procedure) for the classification involves a nonlinear classification rule and hence, its analytic properties and an efficient estimation can not be explored due to its complex distribution. As an alternative, this paper proposes the best linear procedure and verifies its effectiveness. For this, the present paper provides the necessary theories for deriving the linear rule and its properties, an efficient inference, and a simulation study that sheds light on the performance of the best linear procedure. It also provides three real data examples to demonstrate the applicability of the best linear procedure.

An Empirical Bayes Method for Multivariate Meta-analysis with an Application in Clinical Trials

We propose an empirical Bayes method for evaluating overall and study-specific treatment effects in multivariate meta-analysis with binary outcome. Instead of modeling transformed proportions or risks via commonly used multivariate general or generalized linear models, we directly model the risks without any transformation. The exact posterior distribution of the study-specific relative risk is derived. The hyperparameters in the posterior distribution can be inferred through an empirical Bayes procedure. As our method does not rely on the choice of transformation, it provides a flexible alternative to the existing methods and in addition, the correlation parameter can be intuitively interpreted as the correlation coefficient between risks.

Posterior concentration rates for empirical Bayes procedures with applications to Dirichlet process mixtures

In this paper we provide general conditions to check on the model and the prior to derive posterior concentration rates for data-dependent priors (or empirical Bayes approaches). We aim at providing conditions that are close to the conditions provided in the seminal paper by Ghosal & van der Vaart (2007). We then apply the general theorem to two different settings: the estimation of a density using Dirichlet process mixtures of Gaussian random variables with base measure depending on some empirical quantities and the estimation of the intensity of a counting process under the Aalen model. A simulation study for inhomogeneous Poisson processes also illustrates our results. In the former case we also derive some results on the estimation of the mixing density and on the deconvolution problem. In the latter, we provide a general theorem on posterior concentration rates for counting processes with Aalen multiplicative intensity with priors not depending on the data.

Empirical Bayes methods in classical and Bayesian inference

Empirical Bayes methods are often thought of as a bridge between classical and Bayesian inference. In fact, in the literature the term empirical Bayes is used in quite diverse contexts and with different motivations. In this article, we provide a brief overview of empirical Bayes methods highlighting their scopes and meanings in different problems. We focus on recent results about merging of Bayes and empirical Bayes posterior distributions that regard popular, but otherwise debatable, empirical Bayes procedures as computationally convenient approximations of Bayesian solutions.

On selection of optimal stochastic model for accelerated life testing

This paper deals with the problem of proper lifetime model selection in the context of statistical reliability analysis. Namely, we consider regression models describing the dependence of failure intensities on a covariate, for instance, a stressor. Testing the model fit is standardly based on the so-called martingale residuals. Their analysis has already been studied by many authors. Nevertheless, the Bayes approach to the problem, in spite of its advantages, is just developing. We shall present the Bayes procedure of estimation in several semi-parametric regression models of failure intensity. Then, our main concern is the Bayes construction of residual processes and goodness-of-fit tests based on them. The method is illustrated with both artificial and real-data examples.

Bayesian evaluation of inequality constrained hypotheses.

Bayesian evaluation of inequality constrained hypotheses enables researchers to investigate their expectations with respect to the structure among model parameters. This article proposes an approximate Bayes procedure that can be used for the selection of the best of a set of inequality constrained hypotheses based on the Bayes factor in a very general class of statistical models. The software package BIG is provided such that psychologists can use the approach proposed for the analysis of their own data. To illustrate the approximate Bayes procedure and the use of BIG, we evaluate inequality constrained hypotheses in a path model and a logistic regression model. Two simulation studies on the performance of our approximate Bayes procedure show that it results in accurate Bayes factors.

Modeling of Marriage Preferences: Baysian Approach

Empirical Bayes estimation for marriage preferences are worked under two kinds of beliefs regarding the parameters, e.g., where the marriage preferences seem to be equal or not. In both cases priors are in accordance with beliefs. Computational methods for different hyperparameters of the empirical Bayes are developed. It is seen from the data that a male of age i has preferences of marrying a woman in age category j . A general model of preferences is given using empirical Bayes procedure. Real life data are considered, preference patterns are analysed and a smooth estimate is given.

Normality of Posterior Distribution Under Misspecification and Nonsmoothness, and Bayes Factor for Davies' Problem

We examine the large sample properties of Bayes procedures in a general framework, where data may be dependent and models may be misspecified and nonsmooth. The posterior distribution of parameters is shown to be asymptotically normal, centered at the quasi maximum likelihood estimator, under mild conditions. In this framework, the Bayes factor for the test problem of Davies (1997, 1987), where a parameter is unidentified under the null hypothesis, is analyzed. The probability that the Bayes factor leads to a correct conclusion about the hypotheses in Davies’ problem is shown to approach to one.