scholarly journals Empirical Priors and Posterior Concentration Rates for a Monotone Density

Sankhya A ◽  
2018 ◽  
Vol 81 (2) ◽  
pp. 493-509 ◽  
Author(s):  
Ryan Martin
Keyword(s):  
Empirical Priors ◽  
Posterior Concentration ◽  
Monotone Density

scholarly journals Comparing the use of aggregate data and various methods of integrating individual patient data to network meta-analysis and its application to first-line ART

2021 ◽  
Vol 21 (1) ◽  
Author(s):  
Steve Kanters ◽  
Mohammad Ehsanul Karim ◽  
Kristian Thorlund ◽  
Aslam H. Anis ◽  
Michael Zoratti ◽  
...  
Keyword(s):  
Meta Analysis ◽  
Evidence Base ◽  
Aggregate Data ◽  
World Health ◽  
Coefficient Estimates ◽  
Two Stage ◽  
Individual Patient Level ◽  
One Stage ◽  
Meta Regression ◽  
Empirical Priors

Abstract Background The 2018 World Health Organization HIV guidelines were based on the results of a network meta-analysis (NMA) of published trials. This study employed individual patient-level data (IPD) and aggregate data (AgD) and meta-regression methods to assess the evidence supporting the WHO recommendations and whether they needed any refinements. Methods Access to IPD from three trials was granted through ClinicalStudyDataRequest.com (CSDR). Seven modelling approaches were applied and compared: 1) Unadjusted AgD network meta-analysis (NMA) – the original analysis; 2) AgD-NMA with meta-regression; 3) Two-stage IPD-AgD NMA; 4) Unadjusted one-stage IPD-AgD NMA; 5) One-stage IPD-AgD NMA with meta-regression (one-stage approach); 6) Two-stage IPD-AgD NMA with empirical-priors (empirical-priors approach); 7) Hierarchical meta-regression IPD-AgD NMA (HMR approach). The first two were the models used previously. Models were compared with respect to effect estimates, changes in the effect estimates, coefficient estimates, DIC and model fit, rankings and between-study heterogeneity. Results IPD were available for 2160 patients, representing 6.5% of the evidence base and 3 of 24 edges. The aspect of the model affected by the choice of modeling appeared to differ across outcomes. HMR consistently generated larger intervals, often with credible intervals (CrI) containing the null value. Discontinuations due to adverse events and viral suppression at 96 weeks were the only two outcomes for which the unadjusted AgD NMA would not be selected. For the first, the selected model shifted the principal comparison of interest from an odds ratio of 0.28 (95% CrI: 10.17, 0.44) to 0.37 (95% CrI: 0.23, 0.58). Throughout all outcomes, the regression estimates differed substantially between AgD and IPD methods, with the latter being more often larger in magnitude and statistically significant. Conclusions Overall, the use of IPD often impacted the coefficient estimates, but not sufficiently as to necessitate altering the final recommendations of the 2018 WHO Guidelines. Future work should examine the features of a network where adjustments will have an impact, such as how much IPD is required in a given size of network.

scholarly journals Posterior Concentration Rates for Counting Processes with Aalen Multiplicative Intensities

2017 ◽  
Vol 12 (1) ◽  
pp. 53-87
Author(s):  
Sophie Donnet ◽  
Vincent Rivoirard ◽  
Judith Rousseau ◽  
Catia Scricciolo
Keyword(s):  
Counting Processes ◽  
Posterior Concentration

scholarly journals Optimal Control with Absolutely Continuous Strategies for Spectrally Negative Lévy Processes

2012 ◽  
Vol 49 (01) ◽  
pp. 150-166 ◽  
Author(s):  
Andreas E. Kyprianou ◽  
Ronnie Loeffen ◽  
José-Luis Pérez
Keyword(s):  
Control Problem ◽  
Optimal Strategy ◽  
Lévy Process ◽  
Control Strategies ◽  
Levy Process ◽  
Lévy Measure ◽  
Absolutely Continuous ◽  
Completely Monotone ◽  
Hamilton Jacobi Bellman ◽  
Monotone Density

In the last few years there has been renewed interest in the classical control problem of de Finetti (1957) for the case where the underlying source of randomness is a spectrally negative Lévy process. In particular, a significant step forward was made by Loeffen (2008), who showed that a natural and very general condition on the underlying Lévy process which allows one to proceed with the analysis of the associated Hamilton-Jacobi-Bellman equation is that its Lévy measure is absolutely continuous, having completely monotone density. In this paper we consider de Finetti's control problem, but with the restriction that control strategies are absolutely continuous with respect to the Lebesgue measure. This problem has been considered by Asmussen and Taksar (1997), Jeanblanc-Picqué and Shiryaev (1995), and Boguslavskaya (2006) in the diffusive case, and Gerber and Shiu (2006) for the case of a Cramér-Lundberg process with exponentially distributed jumps. We show the robustness of the condition that the underlying Lévy measure has a completely monotone density and establish an explicit optimal strategy for this case that envelopes the aforementioned existing results. The explicit optimal strategy in question is the so-called refraction strategy.

scholarly journals Empirical Bayes posterior concentration in sparse high-dimensional linear models

Bernoulli ◽  
2017 ◽  
Vol 23 (3) ◽  
pp. 1822-1847 ◽  
Author(s):  
Ryan Martin ◽  
Raymond Mess ◽  
Stephen G. Walker
Keyword(s):  
Empirical Bayes ◽  
Linear Models ◽  
High Dimensional ◽  
Posterior Concentration

scholarly journals The horseshoe estimator: Posterior concentration around nearly black vectors

2014 ◽  
Vol 8 (2) ◽  
pp. 2585-2618 ◽  
Author(s):  
S. L. van der Pas ◽  
B. J. K. Kleijn ◽  
A. W. van der Vaart
Keyword(s):  
Posterior Concentration

scholarly journals Finite sample posterior concentration in high-dimensional regression

2014 ◽  
Vol 4 (1) ◽  
pp. 77-77
Author(s):  
N. Strawn ◽  
A. Armagan ◽  
R. Saab ◽  
L. Carin ◽  
D. Dunson
Keyword(s):  
High Dimensional ◽  
Finite Sample ◽  
High Dimensional Regression ◽  
Posterior Concentration

Sharp Bounds for Sums of Dependent Risks

2013 ◽  
Vol 50 (01) ◽  
pp. 42-53 ◽  
Author(s):  
Giovanni Puccetti ◽  
Ludger Rüschendorf
Keyword(s):  
Random Variables ◽  
Dependence Structure ◽  
Homogeneous Case ◽  
Marginal Distributions ◽  
Sharp Bounds ◽  
Duality Result ◽  
Dependent Risks ◽  
Monotone Densities ◽  
Monotone Density ◽  
Dual Bounds

Sharp tail bounds for the sum of d random variables with given marginal distributions and arbitrary dependence structure have been known since Makarov (1981) and Rüschendorf (1982) for d=2 and, in some examples, for d≥3. Based on a duality result, dual bounds have been introduced in Embrechts and Puccetti (2006b). In the homogeneous case, F 1=···=F n , with monotone density, sharp tail bounds were recently found in Wang and Wang (2011). In this paper we establish the sharpness of the dual bounds in the homogeneous case under general conditions which include, in particular, the case of monotone densities and concave densities. We derive the corresponding optimal couplings and also give an effective method to calculate the sharp bounds.

scholarly journals A Bayesian framework for inter-cellular information sharing improves dscRNA-seq quantification

2020 ◽  
Author(s):  
Avi Srivastava ◽  
Laraib Malik ◽  
Hirak Sarkar ◽  
Rob Patro
Keyword(s):  
Information Sharing ◽  
Target Genes ◽  
Expression Patterns ◽  
Sampling Bias ◽  
Bayesian Framework ◽  
Accurate Estimation ◽  
Multiple Modalities ◽  
Gene Level ◽  
Candidate Target ◽  
Empirical Priors

AbstractMotivationDroplet based single cell RNA-seq (dscRNA-seq) data is being generated at an unprecedented pace, and the accurate estimation of gene level abundances for each cell is a crucial first step in most dscRNA-seq analyses. When preprocessing the raw dscRNA-seq data to generate a count matrix, care must be taken to account for the potentially large number of multi-mapping locations per read. The sparsity of dscRNA-seq data, and the strong 3’ sampling bias, makes it difficult to disambiguate cases where there is no uniquely mapping read to any of the candidate target genes.ResultsWe introduce a Bayesian framework for information sharing across cells within a sample, or across multiple modalities of data using the same sample, to improve gene quantification estimates for dscRNA-seq data. We use an anchor-based approach to connect cells with similar gene expression patterns, and learn informative, empirical priors which we provide to alevin’s gene multi-mapping resolution algorithm. This improves the quantification estimates for genes with no uniquely mapping reads (i.e. when there is no unique intra-cellular information). We show our new model improves the per cell gene level estimates and provides a principled framework for information sharing across multiple modalities. We test our method on a combination of simulated and real datasets under various setups.AvailabilityThe information sharing model is included in alevin and is implemented in C++14. It is available as open-source software, under GPL v3, at https://github.com/COMBINE-lab/salmon as of version [email protected], [email protected]

scholarly journals Two distinct mechanisms localise cyclin B transcripts in syncytial Drosophila embryos

Development ◽  
1990 ◽  
Vol 110 (4) ◽  
pp. 1249-1261 ◽  
Author(s):  
J.W. Raff ◽  
W.G. Whitfield ◽  
D.M. Glover
Keyword(s):  
Cell Cycle ◽  
Distribution Pattern ◽  
Actin Filaments ◽  
Posterior Pole ◽  
Cyclin B ◽  
Polar Granules ◽  
Posterior Concentration ◽  
Microtubular Structures ◽  
Drosophila Embryos

We demonstrate that two independent mechanisms act on maternally derived cyclin B transcripts to concentrate the transcripts at the posterior pole of the Drosophila oocyte and at the cortex of the syncytial embryo. The cortical accumulation occurs because the cyclin B transcript is concentrated around nuclei and comigrates with them to the cortex. The perinuclear localisation of the transcript is blocked by inhibitors of microtubule polymerisation and the transcript colocalises with microtubular structures during the cell cycle, suggesting that the transcript is associated either directly or indirectly with microtubules. Neither microtubules nor actin filaments are required to maintain the posterior concentration of cyclin B transcripts. Instead, this seems to depend on the association of the transcripts with a component of the posterior cytoplasm. The distribution pattern of the transcript at the posterior pole throughout embryogenesis and in a variety of mutant embryos suggests that this component is associated with polar granules.

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