Size and Power of Tests of Hypotheses on Survival Parameters from the Lindley Distribution with Covariates

The Lindley model is considered as an alternative model facilitating analyses of time-to-event data with covariates. Covariate information is incorporated using the Cox’s proportional hazard model with the Lindley model at the timedependent component. Simulation studies are performed to assess the size and power of tests of hypotheses on parameters arising from maximum likelihood estimators of parameters in the Lindley model. Results are contrasted with that arising from Cox’s partial maximum likelihood estimator. The Linley model is used to analyze a publicly available data set and contrasted with other models

Monitoring for Adverse Events Post Marketing Approval of Drugs

This brief communication provides information to those developing monitoring plans for serious adverse events (SAE’s) following regulatory approval of a new drug. In addition, we (1) illustrate how many patients would need to be treated in order to have high confidence of seeing at least 1 pre-specified SAE, (2) show that absence of proof of a SAE is not proof of absence of that SAE, and (3) identify statistical methodology that could be used for formal statistical monitoring of SAE’s

The effects of velocities and lensing on moments of the Hubble diagram

We consider the dispersion on the supernova distance-redshift relation due to peculiar velocities and gravitational lensing, and the sensitivity of these effects to the amplitude of the matter power spectrum. We use the MeMo lensing likelihood developed by Quartin, Marra & Amendola (2014), which accounts for the characteristic non-Gaussian distribution caused by lensing magnification with measurements of the first four central moments of the distribution of magnitudes. We build on the MeMo likelihood by including the effects of peculiar velocities directly into the model for the moments. In order to measure the moments from sparse numbers of supernovae, we take a new approach using Kernel Density Estimation to estimate the underlying probability density function of the magnitude residuals. We also describe a bootstrap re-sampling approach to estimate the data covariance matrix. We then apply the method to the Joint Light-curve Analysis (JLA) supernova catalogue. When we impose only that the intrinsic dispersion in magnitudes is independent of redshift, we find $\sigma_8=0.44^{+0.63}_{-0.44}$ at the one standard deviation level, although we note that in tests on simulations, this model tends to overestimate the magnitude of the intrinsic dispersion, and underestimate $\sigma_8$. We note that the degeneracy between intrinsic dispersion and the effects of $\sigma_8$ is more pronounced when lensing and velocity effects are considered simultaneously, due to a cancellation of redshift dependence when both effects are included. Keeping the model of the intrinsic dispersion fixed as a Gaussian distribution of width 0.14 mag, we find $\sigma_8 = 1.07^{+0.50}_{-0.76}$.Comment: 16 pages, updated to match version accepted in MNRA

Fidelity of Hyperbolic Space for Bayesian Phylogenetic Inference

Bayesian inference for phylogenetics is a gold standard for computing distributions of phylogenies. It faces the challenging problem of. moving throughout the high-dimensional space of trees. However, hyperbolic space offers a low dimensional representation of tree-like data. In this paper, we embed genomic sequences into hyperbolic space and perform hyperbolic Markov Chain Monte Carlo for Bayesian inference. The posterior probability is computed by decoding a neighbour joining tree from proposed embedding locations. We empirically demonstrate the fidelity of this method on eight data sets. The sampled posterior distribution recovers the splits and branch lengths to a high degree. We investigated the effects of curvature and embedding dimension on the Markov Chain's performance. Finally, we discuss the prospects for adapting this method to navigate tree space with gradients

Inequalities and Approximations of Weighted Distributions by Lindley Reliability Measures, and the Lindley-Cox Model with Applications

In this note, stochastic comparisons and results for weighted and Lindley models are presented. Approximation of weighted distributions via Lindley distribution in the class of increasing failure rate (IFR) and decreasing failure rate (DFR) weighted distributions with monotone weight functions are obtained including approximations via the length-biased Lindley distribution. Some useful bounds and moment-type inequality for weighted life distributions and applications are presented. Incorporation of covariates into Lindley model is considered and an application to illustrate the usefulness and applicability of the proposed Lindley-Cox model is given

Performance Evaluation of Judgmental Directional Exchange Rate Predictions

Cataloged from PDF version of article.A procedure is proposed for examining different aspects of performance for judgemental directional probability predictions of exchange rate movements. In particular, a range of new predictive performance measures is identified to highlight specific expressions of strengths and weaknesses in judgemental directional forecasts. Proposed performance qualifiers extend the existing accuracy measures, enabling detailed comparisons of probability forecasts with ex-post empirical probabilities that are derived from changes in the logarithms of the series. This provides a multi-faceted evaluation that is straightforward for practitioners to implement, while affording the flexibility of being used in situations where the time intervals between the predictions have variable lengths. The proposed procedure is illustrated via an application to a set of directional probability exchange rate forecasts for the US Dollar/Swiss Franc from 23/7/96 to 7/12/99 and the findings are discussed. D 2005 International Institute of Forecasters. Published by Elsevier B.V. All rights reserved

A Statistical Analysis of the Change in Age Distribution of Spawning Hatchery Salmon

Declines in salmon sizes have been reported primarily as a result of younger maturation rates. This change in age distribution poses serious threats to salmon-dependent peoples and ecological systems. We perform a statistical analysis to examine the change in age structure of spawning Alaskan chum salmon Oncorhynchus keta and Chinook salmon O. tshawytscha using 30 years of hatchery data. To highlight the impacts of this change, we investigate the average number of fry/smolt that each age of spawning chum/Chinook salmon produce. Our findings demonstrate an increase in younger hatchery salmon populations returning to spawn, and fewer amounts of fry produced by younger salmon compared to older salmon. These results suggest the potential risks associated with younger spawning salmon and aim to help better understand salmon behavior in order to sustain and protect healthy salmon populations

Evaluating predictive performance of judgemental extrapolations from simulated currency series

Cataloged from PDF version of article.Judgemental forecasting of exchange rates is critical for ®nancial decision-making. Detailed investigations of the potential e ects of time-series characteristics on judgemental currency forecasts demand the use of simulated series where the form of the signal and probability distribution of noise are known. The accuracy measures Mean Absolute Error (MAE) and Mean Squared Error (MSE) are frequently applied quantities in assessing judgemental predictive performance on actual exchange rate data. This paper illustrates that, in applying these measures to simulated series with Normally distributed noise, it may be desirable to use their expected values after standardising the noise variance. A method of calculating the expected values for the MAE and MSE is set out, and an application to ®nancial experts' judgemental currency forecasts is presented. Ó 1999 Elsevier Science B.V. All rights reserved