Null Probabilities Research Articles

Survival analysis with censored data: a further twist on ignorability conditions

A key assumption for the application of methods concerning censored data is that the random nature of the censoring mechanism should be ignorable when making likelihood-based inferences. The constant-sum property is an ignorability assumption that is critical for the correct use of a simplified version of the likelihood function and for the identifiability of the survival function [Oller R, Gómez G, Calle ML. Interval censoring: identifiability and the constant-sum property. Biometrika. 2007;94(1):61–70]. It has been proven to be weaker than the assumption of independence between the lifetime variable and the assessment process that leads to censored data. An important caveat is that the theoretical framework established in the class of constant-sum censoring models requires full knowledge of the support of the lifetime variable. In the present work we investigate the consequences of a wrong specification of the support. One might naively expect that this information is not necessary and that, for instance, the estimation of the survival function would assign null or almost null probabilities to regions outside the support. We reveal via examples that this premise is generally true but there are also several exceptions. To shed light on this issue, we introduce a new ignorability condition that extends the constant-sum property and removes the knowledge of the support from the equation. We also show that the independence assumption is stronger than the new extended constant-sum condition.

Adjusting for gene-specific covariates to improve RNA-seq analysis.

This paper suggests a novel positive false discovery rate (pFDR) controlling method for testing gene-specific hypotheses using a gene-specific covariate variable, such as gene length. We suppose the null probability depends on the covariate variable. In this context, we propose a rejection rule that accounts for heterogeneity among tests by employing two distinct types of null probabilities. We establish a pFDR estimator for a given rejection rule by following Storey's q-value framework. A condition on a type 1 error posterior probability is provided that equivalently characterizes our rejection rule. We also present a suitable procedure for selecting a tuning parameter through cross-validation that maximizes the expected number of hypotheses declared significant. A simulation study demonstrates that our method is comparable to or better than existing methods across realistic scenarios. In data analysis, we find support for our method's premise that the null probability varies with a gene-specific covariate variable. Online supplementary material includes proofs of theorems, results of additional simulation and data analysis.

Insiders and Their Free Lunches: The Role of Short Positions

Given a stock price process, we analyse the potential of arbitrage by insiders in a context of short-selling prohibitions. We introduce the notion of minimal supermartingale measure, and we analyse its properties in connection to the minimal martingale measure. In particular, we establish conditions when both fail to exist. These correspond to the case when the insider's information set includes some non null events that are perceived as having null probabilities by the uninformed market investors. These results may have different applications, such as in problems related to the local risk-minimisation for insiders whenever strategies are implemented without short selling.

Bayesian tests of symmetry for the generalized Von Mises distribution

Bayesian tests on the symmetry of the generalized von Mises model for planar directions (Gatto and Jammalamadaka in Stat Methodol 4(3):341–353, 2007) are introduced. The generalized von Mises distribution is a flexible model that can be axially symmetric or asymmetric, unimodal or bimodal. A characterization of axial symmetry is provided and taken as null hypothesis for one of the proposed Bayesian tests. The Bayesian tests are obtained by the technique of probability perturbation. The prior probability measure is perturbed so to give a positive prior probability to the null hypothesis, which would be null otherwise. This allows for the derivation of simple computational formulae for the Bayes factors. Numerical results reveal that, whenever the simulation scheme of the samples supports the null hypothesis, the null posterior probabilities appear systematically larger than their prior counterpart.

Second-order refinements for [formula omitted]-ratios with many instruments

This paper studies second-order properties of the many instruments robust t-ratios based on the limited information maximum likelihood and Fuller estimators for instrumental variable regression models with homoskedastic errors under the many instruments asymptotics, where the number of instruments may increase proportionally with the sample size n, and proposes second-order refinements to the t-ratios to improve the size and power properties. Based on asymptotic expansions of the null and non-null distributions of the t-ratios derived under the many instruments asymptotics, we show that the second-order terms of those expansions may have non-trivial impacts on the size as well as the power properties. Furthermore, we propose adjusted t-ratios whose approximation errors for the null rejection probabilities are of order O(n−1) in contrast to the ones for the unadjusted t-ratios of order O(n−1/2), and show that these adjustments induce some desirable power properties in terms of the local maximinity. Although these results are derived under homoskedastic errors, we also establish a stochastic expansion for a heteroskedasticity robust t-ratio, and propose an analogous adjustment under slight deviations from homoskedasticity.

Influence of body mass, sociality, and movement behavior on improved detection probabilities when using a second camera trap

Maximizing detection probability is a common goal for occupancy studies using camera traps for data collection. Placing additional cameras at a survey station may improve precision of occupancy and detection estimates. However, these benefits are situational and potentially influenced by species' physical characteristics and behavior. We estimated null occupancy and detection probabilities for 20 mammalian species with >10 detections at multiple sites from one- and two-camera data sets from 63 stations set in a commercial forest reserve in Sabah, Malaysian Borneo during October–December 2015. We used a cross-validated absolute shrinkage and selection operator approach to model the effects of species’ body mass, social behavior, dietary niche, and foot posture on detection probability using one- and two-camera designs. The number of species detections, sites where species were detected, detection probability estimates, and precision of model parameter estimates for all species improved using two cameras. Our results showed that unguligrade species were associated with both high detection probability estimates with one camera and also the greatest improvements using the two-camera design in detection probability compared to all other species. Greater improvements in precision of model parameter estimates from two-camera designs were observed in species detected less frequently. Our data suggests that camera designs need to be adapted based on the focal species and we suggest that future occupancy studies collect preliminary information to maximize effectiveness of camera effort and ensure that data collection is efficient and meets project needs.

Improving weighted least squares inference

These days, it is common practice to base inference about the coefficients in a hetoskedastic linear model on the ordinary least squares estimator in conjunction with using heteroskedasticity consistent standard errors. Even when the true form of heteroskedasticity is unknown, heteroskedasticity consistent standard errors can also used to base valid inference on a weighted least squares estimator and using such an estimator can provide large gains in efficiency over the ordinary least squares estimator. However, intervals based on asymptotic approximations with plug-in standard errors often have coverage that is below the nominal level, especially for small sample sizes. Similarly, tests can have null rejection probabilities that are above the nominal level. It is shown that under unknown hereroskedasticy, a bootstrap approximation to the sampling distribution of the weighted least squares estimator is valid, which allows for inference with improved finite-sample properties. For testing linear constraints, permutations tests are proposed which are exact when the error distribution is symmetric and is asymptotically valid otherwise. Another concern that has discouraged the use of weighting is that the weighted least squares estimator may be less efficient than the ordinary least squares estimator when the model used to estimate the unknown form of the heteroskedasticity is misspecified. To address this problem, a new estimator is proposed that is asymptotically at least as efficient as both the ordinary and the weighted least squares estimator. Simulation studies demonstrate the attractive finite-sample properties of this new estimator as well as the improvements in performance realized by bootstrap confidence intervals.

Análisis Costo-Utilidad Del Uso De Adalimumab, Etanercept E Infliximab Para El Tratamiento De La Artritis Psoriásica En Uruguay

ObjectiveTo support an evidence-based decision regarding the inclusion of the anti TNFʼs adalimumab, etanercept or infliximab to the National Formulary of Uruguay for the treatment of psoriatic arthritis, in patients who did not respond to first-line treatment. MethodsWe perform a cost-utility evaluation using a Markov model, to estimate the incremental costs and quality-adjusted life years (QALY) gained with each of these biologic drugs compared with palliative care only. The model considered the perspective of the National Health System, with a time horizon of 40 years. ResultsUnder base-case assumptions, infliximab results in an incremental cost-effectiveness ratio (ICER) of United States Dollars (USD) 47,294 compared to palliative care only. Adalimumab was extendedly dominated and etanercept was dominated. However, infliximab requires intravenous administration which could significantly reduce access to treatment, thus producing inequities for patients from different regions. The probabilistic sensitivity analysis shows that all biologics had null probabilities of being cost-effective considering a willingness-to-pay (WTP) threshold of one time the gross domestic product per capita of Uruguay per QALY. ConclusionsIn our analysis from the perspective of the National Health System, the use of biologic drug treatments for psoriatic arthritis results in an ICER above the WTP ceiling proposed by the World Health Organization. Reduction of drug prices could bring more favorable cost-effectiveness results.

Abstract 18743: Bayesian Comparative Analysis for Prevention of Stroke and Net Clinical Benefit of Novel Oral Anticoagulants in Non-Valvular Atrial Fibrillation

Background: The recent emergence of novel oral anticoagulants dabigatran, rivaroxaban and apixaban for prevention of stroke and systemic embolization in atrial fibrillation are attractive alternatives to warfarin. Despite this, the differences in efficacy and bleeding events between these medications remains unclear. To compare differential benefit, we performed a Bayesian analysis comparing the efficacy and safety parameters of the 3 novel agents. Methods: Using data from the 3 major trials investigating the novel oral anticoagulants, we conducted a Bayesian analysis using null prior probabilities, which is particularly suited to indirect comparisons. The primary endpoints of stroke and systemic embolization were assessed, along with safety endpoints of major bleeding. A Bayesian analysis was performed on each group, defining probabilities of benefit for the posterior probability. From this data, net clinical benefit calculations were performed and posterior probabilities were obtained. Results: Posterior probabilities for stroke and systemic embolization indicate the apixaban, rivaroxaban and dabigatran have an 87.3%, 88.7%, and 66.3% probability of benefit over warfarin, respectively. Major bleeding events were found to have a 98.6%, 88.0% and 55.0% probability of benefit over warfarin. Net clinical benefit analysis indicates benefit with apixaban and rivaroxaban that was greater than dabigatran. Conclusions: Using Bayesian analytic techniques, all of the novel oral anticoagulants were found to be non-inferior to warfarin. However, the effectiveness in prevention of stroke suggests that both apixaban and rivaroxaban significantly outperform dabigatran. Net clinic benefit and safety endpoints support the use of apixaban as opposed to rivaroxaban and dabigatran. While more data emerges investigating the differential benefit of these new medications, Bayesian techniques offer novel comparative statistics which can guide clinical decision making.

SECOND-ORDER REFINEMENT OF EMPIRICAL LIKELIHOOD FOR TESTING OVERIDENTIFYING RESTRICTIONS

This paper studies second-order properties of the empirical likelihood overidentifying restriction test to check the validity of moment condition models. We show that the empirical likelihood test is Bartlett correctable and suggest second-order refinement methods for the test based on the empirical Bartlett correction and adjusted empirical likelihood. Our second-order analysis supplements the one in Chen and Cui (2007, Journal of Econometrics141, 492–516) who considered parameter hypothesis testing for overidentified models. In simulation studies we find that the empirical Bartlett correction and adjusted empirical likelihood assisted by bootstrapping provide reasonable improvements for the properties of the null rejection probabilities.

GEL statistics under weak identification

The central concern of this paper is the provision in a time series moment condition framework of practical recommendations of confidence regions for parameters whose coverage probabilities are robust to the strength or weakness of identification. To this end we develop Pearson-type test statistics based on GEL implied probabilities formed from general kernel smoothed versions of the moment indicators. We also modify the statistics suggested in Guggenberger and Smith (2008) for a general kernel smoothing function. Importantly for our conclusions, we provide GEL time series counterparts to GMM and GEL conditional likelihood ratio statistics given in Kleibergen (2005) and Smith (2007). Our analysis not only demonstrates that these statistics are asymptotically (conditionally) pivotal under both classical asymptotic theory and weak instrument asymptotics of Stock and Wright (2000) but also provides asymptotic power results in the weakly identified time series context. Consequently, the empirical null rejection probabilities of the associated tests and, thereby, the coverage probabilities of the corresponding confidence regions, should not be affected greatly by the strength or otherwise of identification. A comprehensive Monte Carlo study indicates that a number of the tests proposed here represent very competitive choices in comparison with those suggested elsewhere in the literature.

Pollen-based climate reconstruction: Calibration of the vegetation–pollen processes

Palaeoclimate reconstructions are based on the relationship between climate and sediment pollen assemblages. This model is called the transfer function (TF). Process-based TF emerge as an opportunity to better quantify past climate changes. For example, when a process-based model of vegetation dynamics is part of the TF it allows to include atmospheric CO2 concentration and plant–plant interactions as factors affecting the reconstruction. We propose the missing piece for a fully process-based TF: the model linking, at a continental scale, vegetation model outputs and pollen sampled in sediments. We perform its calibration and we explore the quality of fit.The model represents the error of the vegetation model LPJ-GUESS and four main processes: pollen production, dispersal, accumulation and sampling. Accumulation and sampling processes are either modelled using a multinomial-Poisson (MP) or a multinomial-negative binomial (MNB) model, both models allowing for overdispersion and structural zeros in the sense of null multinomial probabilities. We perform inference for a European pollen dataset by parallelising a Monte Carlo Markov Chain algorithm.Model fitness diagnostics indicate that MP model is not supported by the European dataset. The MNB model is also detected inconsistent, but with a p-value of 0.014 and without stationarity nor overdispersion problems. At this stage, the MNB model is considered as a robust alternative to more complex models. We finally discuss the challenge of the TF inversion for palaeoclimate reconstruction and vegetation model re-calibration.

Second-Order Refinement of Empirical Likelihood for Testing Overidentifying Restrictions

This paper studies second-order properties of the empirical likelihood overidentifying restriction test to check the validity of moment condition models. We show that the empirical likelihood test is Bartlett correctable and suggest second-order refinement methods for the test based on the empirical Bartlett correction and adjusted empirical likelihood. Our second-order analysis supplements the one in Chen and Cui (2007) who considered parameter hypothesis testing for overidentified models. In simulation studies we find that the empirical Bartlett correction and adjusted empirical likelihood assisted by bootstrapping provide reasonable improvements for the properties of the null rejection probabilities.

A space-time generator for rainfall nowcasting: the PRAISEST model

Abstract. The paper introduces a stochastic technique for forecasting rainfall in space-time domain: the PRAISEST Model (Prediction of Rainfall Amount Inside Storm Events: Space and Time). The model is based on the assumption that the rainfall height H accumulated on an interval Δt between the instants iΔt and (i+1)Δt and on a spatial cell of size ΔxΔy is correlated either with a variable Z, representing antecedent precipitation at the same point, either with a variable W, representing simultaneous rainfall at neighbour cells. The mathematical background is given by a joined probability density fH,W,Z (h,w,z) in which the variables have a mixed nature, that is a finite probability for null value and infinitesimal probabilities for the positive values. As study area, the Calabria region, in Southern Italy, has been selected. The region has been discretised by 10 km×10 km cell grid, according to the raingauge network density in this area. Storm events belonging to 1990–2004 period were analyzed to test performances of the PRAISEST model.

Scaling Smoothed Language Models

In Continuous Speech Recognition (CSR) systems a Language Model (LM) is required to represent the syntactic constraints of the language. Then a smoothing technique needs to be applied to avoid null LM probabilities. Each smoothing technique leads to a different LM probability distribution. Test set perplexity is usually used to evaluate smoothing techniques but the relationship with acoustic models is not taken into account. In fact, it is well-known that to obtain optimum CSR performances a scaling exponential parameter must be applied over LMs in the Bayes’ rule. This scaling factor implies a new redistribution of smoothed LM probabilities. The shape of the final probability distribution is due to both the smoothing technique used when designing the language model and the scaling factor required to get the optimum system performance when integrating the LM into the CSR system. The main object of this work is to study the relationship between the two factors, which result in dependent effects. Experimental evaluation is carried out over two Spanish speech application tasks. Classical smoothing techniques representing very different degrees of smoothing are compared. A new proposal, Delimited discounting, is also considered. The results of the experiments showed a strong dependence between the amount of smoothing given by the smoothing technique and the way that the LM probabilities need to be scaled to get the best system performance, which is perplexity independent in many cases. This relationship is not independent of the task and available training data.

Generalized empirical likelihood tests in time series models with potential identification failure

We introduce test statistics based on generalized empirical likelihood methods that can be used to test simple hypotheses involving the unknown parameter vector in moment condition time series models. The test statistics generalize those in Guggenberger and Smith [2005. Generalized empirical likelihood estimators and tests under partial, weak and strong identification. Econometric Theory 21 (4), 667–709] from the i.i.d. to the time series context and are alternatives to those in Kleibergen [2005a. Testing parameters in GMM without assuming that they are identified. Econometrica 73 (4), 1103–1123] and Otsu [2006. Generalized empirical likelihood inference for nonlinear and time series models under weak identification. Econometric Theory 22 (3), 513–527]. The main feature of these tests is that their empirical null rejection probabilities are not affected much by the strength or weakness of identification. More precisely, we show that the statistics are asymptotically distributed as chi-square under both classical asymptotic theory and weak instrument asymptotics of Stock and Wright [2000. GMM with weak identification. Econometrica 68 (5), 1055–1096]. We also introduce a modification to Otsu's (2006) statistic that is computationally more attractive. A Monte Carlo study reveals that the finite-sample performance of the suggested tests is very competitive.

Testing Recursive Path Models With Correlated Errors Using D-Separation

This article shows how to extend the inferential test of Shipley (2000b), which is applicable to recursive path models without correlated errors (a directed acyclic graph [DAG] model), to a class of recursive path models that include correlated errors (a semi-Markov model). The path model is first converted to a partial ancestral graph (PAG) and then, for PAGs that do not require latent variables, an inducing path DAG is obtained that is equivalent in its conditional independence relations to the original path model. The null probabilities of the k tests of independence that are implied by this DAG are combined using Fisher's test statistic C = -2ΣLn(pi), which is distributed as a chi-square variate with 2k degrees of freedom.

On the distribution of a test for exponentiality based on progressively type-II right censored spacings

A test for exponentiality based on progressively Type-II right censored spacings has been proposed recently by Balakrishnan et al. (2002). They derived the asymptotic null distribution of the test statistic. In this work, we utilize the algorithm of Huffer and Lin (2001) to evaluate the exact null probabilities and the exact critical values of this test statistic.

Finitely additive conditional probabilities with values on a hyperstructure

In this paper we introduce a particular non standard algebraic hyperstructure ∑ with two hyperoperations called addition and multiplication that is an extension of the field of real numbers. After we define probabilities and conditional probabilities with values on ∑. In this way we can assign non null probabilities to events that have null standard probabilities. We prove that, with such hyperstructure, many problems about the conditional probability (e.g. coherence) can have easy and smart solutions. There-fore, with such generalized probability, we can assume that, in a generalized sense, the classical definition of conditional probability agrees with the one of de Finetti.

Testing exponentiality of the residual life, based on dynamic Kullback-Leibler information

This paper proposes a test-of-fit for exponentiality of the residual life (TF-ERL) based on the estimated dynamic Kullback-Leibler information. TF-ERL applies when the exponential parameter is or is not specified under the null hypothesis. Asymptotic properties of TF-ERL are discussed. In particular, the TF-ERL is shown to be a statistically consistent test of the null hypothesis for all alternatives. Small-sample null tail probabilities are derived; critical values are tabulated; and its use is shown in an example. Monte-Carlo simulation is used to compute the power of TF-ERL under various alternatives; it performs well in terms of its power.