Is the magnitude of the Peccei-Quinn scale set by the landscape?

Rather general considerations of the string theory landscape imply a mild statistical draw towards large soft SUSY breaking terms tempered by the requirement of proper electroweak symmetry breaking where SUSY contributions to the weak scale are not too far from m(weak)~ 100 GeV. Such a picture leads to the prediction that m_h~ 125 GeV while most sparticles are beyond current LHC reach. Here we explore the possibility that the magnitude of the Peccei-Quinn (PQ) scale f_a is also set by string landscape considerations within the framework of a compelling SUSY axion model. First, we examine the case where the PQ symmetry arises as an accidental approximate global symmetry from a more fundamental gravity-safe Z(24)^R symmetry and where the SUSY mu parameter arises from a Kim-Nilles operator. The pull towards large soft terms then also pulls the PQ scale as large as possible. Unless this is tempered by rather severe (unknown) cosmological or anthropic bounds on the density of dark matter, then we would expect a far greater abundance of dark matter than is observed. This conclusion cannot be negated by adopting a tiny axion misalignment angle theta_i because WIMPs are also overproduced at large f_a. Hence, we conclude that setting the PQ scale via anthropics is highly unlikely. Instead, requiring soft SUSY breaking terms of order the gravity-mediation scale m_{3/2}~ 10-100 TeV places the mixed axion-neutralino dark matter abundance into the intermediate scale sweet zone where f_a~ 10^{11}-10^{12} GeV. We compare our analysis to the more general case of a generic SUSY DFSZ axion model with uniform selection on theta_i but leading to the measured dark matter abundance: this approach leads to a preference for f_a~ 10^{12} GeV.Comment: 24 pages plus 10 figure

Variable Selection in Latent Regression IRT Models via Knockoffs: An Application to International Large-scale Assessment in Education

International large-scale assessments (ILSAs) play an important role in educational research and policy making. They collect valuable data on education quality and performance development across many education systems, giving countries the opportunity to share techniques, organizational structures, and policies that have proven efficient and successful. To gain insights from ILSA data, we identify non-cognitive variables associated with students' academic performance. This problem has three analytical challenges: 1) academic performance is measured by cognitive items under a matrix sampling design; 2) there are many missing values in the non-cognitive variables; and 3) multiple comparisons due to a large number of non-cognitive variables. We consider an application to the Programme for International Student Assessment (PISA), aiming to identify non-cognitive variables associated with students' performance in science. We formulate it as a variable selection problem under a general latent variable model framework and further propose a knockoff method that conducts variable selection with a controlled error rate for false selections

Using the bayesmeta R package for Bayesian random-effects meta-regression

BACKGROUND: Random-effects meta-analysis within a hierarchical normal modeling framework is commonly implemented in a wide range of evidence synthesis applications. More general problems may even be tackled when considering meta-regression approaches that in addition allow for the inclusion of study-level covariables. METHODS: We describe the Bayesian meta-regression implementation provided in the bayesmeta R package including the choice of priors, and we illustrate its practical use. RESULTS: A wide range of example applications are given, such as binary and continuous covariables, subgroup analysis, indirect comparisons, and model selection. Example R code is provided. CONCLUSIONS: The bayesmeta package provides a flexible implementation. Due to the avoidance of MCMC methods, computations are fast and reproducible, facilitating quick sensitivity checks or large-scale simulation studies.Comment: 17 pages, 8 figure

Dealing with uncertainty in test assembly

The recent development of computer technologies enabled test institutes to improve their process of item selection for test administration by means of automated test assembly (ATA). A general framework for ATA consists in adopting mixed-integer programming models which are commonly intended to be solved by commercial solvers. Those softwares, notwithstanding their success in handling most of the basic ATA problems, are not always able to find solutions for highly constrained and large-sized instances. Moreover, all the model coefficients are assumed to be fixed and known, an hypothesis that is not true for the item information functions which are derived from the estimates of item response theory parameters. These restrictions motivated us to find an alternative way to specify and solve ATA models. First, we suggest an application of the chance-constrained (CC) approach (see Charnes and Cooper, 1959) which allows to maximize the α-quantile (usually smaller than 0.05) of the sampling distribution function of the test information function obtained by bootstrapping the calibration process. Secondly, for solving the ATA models, CC or not, we adapted a stochastic meta-heuristic called simulated annealing (SA) proposed by Goffe (1996). This technique can handle large-scale models and non-linear functions. A reformulation of the model by the Lagrangian relaxation helps to find the most feasible/optimal solution and, thanks to the SA, more than one neighbourhood of the space is explored avoiding to be trapped in a local optimum. Several simulations on ATA problems are performed and the solutions are compared to CPLEX 12.8.0 Optimizer, a benchmark solver in the linear programming field. Finally, a real data application shows the potential of our approach in practical situations. The algorithms are coded in the open-source framework Julia. Two packages written in Julia are released for solving the estimation and assembly problems described in this dissertation

On sample selection models and skew distributions

This thesis is concerned with methods for dealing with missing data in nonrandom samples and recurrent events data. The first part of this thesis is motivated by scores arising from questionnaires which often follow asymmetric distributions, on a fixed range. This can be due to scores clustering at one end of the scale or selective reporting. Sometimes, the scores are further subjected to sample selection resulting in partial observability. Thus, methods based on complete cases for skew data are inadequate for the analysis of such data and a general sample selection model is required. Heckman proposed a full maximum likelihood estimation method under the normality assumption for sample selection problems, and parametric and non-parametric extensions have been proposed. A general selection distribution for a vector Y 2 Rp has a PDF fY given by fY(y) = fY?(y) P(S? 2 CjY? = y) P(S? 2 C) ; where S? 2 Rq and Y? 2 Rp are two random vectors, and C is a measurable subset of Rq. We use this generalization to develop a sample selection model with underlying skew-normal distribution. A link is established between the continuous component of our model log-likelihood function and an extended version of a generalized skewnormal distribution. This link is used to derive the expected value of the model, which extends Heckman's two-step method. The general selection distribution is also used to establish the closed skew-normal distribution as the continuous component of the usual multilevel sample selection models. Finite sample performances of the maximum likelihood estimator of the models are studied via Monte Carlo simulation. The model parameters are more precisely estimated under the new models, even in the presence of moderate to extreme skewness, than the Heckman selection models. Application to data from a study of neck injuries where the responses are substantially skew successfully discriminates between selection and inherent skewness, and the multilevel model is used to analyze jointly unit and item non-response. We also discuss computational and identification issues, and provide an extension of the model using copula-based sample selection models with truncated marginals. The second part of this thesis is motivated by studies that seek to analyze processes that generate events repeatedly over time. We consider the number of events per subject within a specified study period as the primary outcome of interest. One considerable challenge in the analysis of this type of data is the large proportion of patients that might discontinue before the end of the study, leading to partially observed data. Sophisticated sensitivity analyses tools are therefore necessary for the analysis of such data. We propose the use of two frequentist based imputation methods for dealing with missing data in recurrent event data framework. The recurrent events are modeled as over-dispersed Poisson data, with constant rate function. Different assumptions about future behavior of dropouts depending on reasons for dropout and treatment received are made and evaluated in a simulation study. We illustrate our approach with a clinical trial in patients who suffer from bladder cancer