Numerical Computation of Multivariate Normal and Multivariate t Probabilities over Ellipsoidal Regions

An algorithm for the computation of multivariate normal and multivariate t probabilities over general hyperellipsoidal regions is given. A special case is the calculation of probabilities for central and noncentral F and x^2 distributions. A FORTRAN 90 program MVELPS.FOR incorporates the algorithm.

Calculation of Critical Values for Somerville's FDR Procedures

A Fortran 95 program has been written to calculate critical values for the step-up and step-down FDR procedures developed by Somerville (2004). The program allows for arbitrary selection of number of hypotheses, FDR rate, one- or two-sided hypotheses, common correlation coefficient of the test statistics and degrees of freedom. An MCV (minimum critical value) may be specified, or the program will calculate a specified number of critical values or steps in an FDR procedure. The program can also be used to efficiently ascertain an upper bound to the number of hypotheses which the procedure will reject, given either the values of the test statistics, or their p values. Limiting the number of steps in an FDR procedure can be used to control the number or proportion of false discoveries (Somerville and Hemmelmann 2007). Using the program to calculate the largest critical values makes possible efficient use of the FDR procedures for very large numbers of hypotheses.

FORTRAN 90 and SAS-IML Programs for Computation of Critical Values for Multiple Testing and Simultaneous Confidence Intervals

See paper for mathematical introduction.

Numerical Computation of Multivariate Normal and Multivariate t Probabilities over Ellipsoidal Regions

An algorithm for the computation of multivariate normal and multivariate t probabilities over general hyperellipsoidal regions is given. A special case is the calculation of probabilities for central and noncentral F and x2 distributions. A FORTRAN 90 program MVELPS.FOR incorporates the algorithm

A Fortran 90 Program for Evaluation of Multivariate Normal and Multivariate t Integrals Over Convex Regions

Let X' = (X1,X2, ... ,Xk) have the multivariate normal distribution f(X) = MVN(μ, ∑σ2) where ∑ is a known positive definite matrix, and σ2 is a constant. There are many problems in statistics which require the evaluation of f(x) over some convex region A. That is P = ∫A f(X) dX. If σ2 is known, then without loss of generality, set μ = 0, σ =1 and let ∑ be the correlation matrix. For the case where the region A is rectangular, the problem has been addressed by many authors. They include Gupta (1963), Milton (1972), Schervish (1984), Deak (1986), Wang and Kennedy (1990,1992), Olson and Weissfeld (1991), Drezner (1992) and Genz (1992,1993). However, regions of integration for many statistical applications, for example multiple comparisons, are not rectangular

A Package to Study the Performance of Step-Up and Step-Down Test Procedures

The package can be used to analyze the performance of step-up and step-down procedures. It can be used to compare powers, calculate the “false discovery rate”, to study the effects of reduced step procedures, and to calculate P [U ≤ k], where U is the number of rejected true hypotheses. It can be used to determine the maximum number of steps that can be made and still guarantee (with a given probability) that the number of false rejections will not exceed some specified number. The test statistics are assumed to have a multivariate-t distribution. Examples are included

Calculation of critical values for Somerville\u27s FDR procedures

A Fortran 95 program has been written to calculate critical values for the step-up and step-down FDR procedures developed by Somerville (2004). The program allows for arbitrary selection of number of hypotheses, FDR rate, one- or two-sided hypotheses, common correlation coefficient of the test statistics and degrees of freedom. An MCV (minimum critical value) may be specified, or the program will calculate a specified number of critical values or steps in an FDR procedure. The program can also be used to efficiently ascertain an upper bound to the number of hypotheses which the procedure will reject, given either the values of the test statistics, or their p values. Limiting the number of steps in an FDR procedure can be used to control the number or proportion of false discoveries (Somerville and Hemmelmann 2007). Using the program to calculate the largest critical values makes possible efficient use of the FDR procedures for very large numbers of hypotheses

Supporting perinatal anxiety in the digital age; a qualitative exploration of stressors and support strategies

Background The period surrounding childbirth is one of profound change, which can often be experienced as stressful and overwhelming. Indeed, around 20% of women may experience significant levels of anxiety in the perinatal period. However, most women experiencing perinatal anxiety (PNA) go unrecognised and untreated. The Internet offers a potentially scalable solution to improve access to support, however a dearth of research in this area means that work is needed to better understand women’s experience of PNA, so that potential targets for intervention can be identified and possible barriers to support overcome. This study aimed to qualitatively explore women’s experience of anxiety triggers and support in the perinatal period; and gain insight into what online support is acceptable for women with PNA. Methods Women who were either pregnant or within one-year postpartum were invited to participate in focus groups across the UK. Focus groups were used to allow a diversity of perspectives to be heard, while simultaneously promoting the identification and prioritisation of important support needs and solutions. Interviews were transcribed and thematically analysed. Results Five key themes emerged in relation to women’s experience with PNA: holding unrealistic expectations of birth and motherhood; stigma; the importance of peer support; uncertainty and poor maternal confidence; and a lack of mental health support and knowledge. Perinatal women felt under-supported and poorly prepared for motherhood. A mismatch between their expectations and the reality of their experience, alongside a pressure to be the ‘perfect mum’ was the primary source of their anxiety. Furthermore, stigma associated with PNA may have exacerbated these issues and led to help-seeking avoidance. Overall, women felt these issues could be addressed via online support, through the delivery of more realistic information, providing psychoeducation about PNA symptoms and management, and the inclusion of authentic peer experiences. Thus, delivering evidence-based information and interventions online may provide a solution that is acceptable to this cohort. Conclusions This work provides unique insight into potential sources of anxiety for women in the perinatal period, while also offering potential internet-based support solutions that are likely to be acceptable and helpful for women with PNA

The CAMELS project: Cosmology and Astrophysics with MachinE Learning Simulations

We present the Cosmology and Astrophysics with MachinE Learning Simulations --CAMELS-- project. CAMELS is a suite of 4,233 cosmological simulations of $(25~h^{-1}{\rm Mpc})^3$ volume each: 2,184 state-of-the-art (magneto-)hydrodynamic simulations run with the AREPO and GIZMO codes, employing the same baryonic subgrid physics as the IllustrisTNG and SIMBA simulations, and 2,049 N-body simulations. The goal of the CAMELS project is to provide theory predictions for different observables as a function of cosmology and astrophysics, and it is the largest suite of cosmological (magneto-)hydrodynamic simulations designed to train machine learning algorithms. CAMELS contains thousands of different cosmological and astrophysical models by way of varying $\Omega_m$, $\sigma_8$, and four parameters controlling stellar and AGN feedback, following the evolution of more than 100 billion particles and fluid elements over a combined volume of $(400~h^{-1}{\rm Mpc})^3$. We describe the simulations in detail and characterize the large range of conditions represented in terms of the matter power spectrum, cosmic star formation rate density, galaxy stellar mass function, halo baryon fractions, and several galaxy scaling relations. We show that the IllustrisTNG and SIMBA suites produce roughly similar distributions of galaxy properties over the full parameter space but significantly different halo baryon fractions and baryonic effects on the matter power spectrum. This emphasizes the need for marginalizing over baryonic effects to extract the maximum amount of information from cosmological surveys. We illustrate the unique potential of CAMELS using several machine learning applications, including non-linear interpolation, parameter estimation, symbolic regression, data generation with Generative Adversarial Networks (GANs), dimensionality reduction, and anomaly detection.Comment: 33 pages, 18 figures, CAMELS webpage at https://www.camel-simulations.or