scholarly journals From Blackwell Dominance in Large Samples to Rényi Divergences and Back Again

Econometrica ◽  
2021 ◽  
Vol 89 (1) ◽  
pp. 475-506
Author(s):  
Xiaosheng Mu ◽  
Luciano Pomatto ◽  
Philipp Strack ◽  
Omer Tamuz

We study repeated independent Blackwell experiments; standard examples include drawing multiple samples from a population, or performing a measurement in different locations. In the baseline setting of a binary state of nature, we compare experiments in terms of their informativeness in large samples. Addressing a question due to Blackwell (1951), we show that generically an experiment is more informative than another in large samples if and only if it has higher Rényi divergences. We apply our analysis to the problem of measuring the degree of dissimilarity between distributions by means of divergences. A useful property of Rényi divergences is their additivity with respect to product distributions. Our characterization of Blackwell dominance in large samples implies that every additive divergence that satisfies the data processing inequality is an integral of Rényi divergences.

2021 ◽  
Vol 19 (1) ◽  
pp. 21-29
Author(s):  
Itai Arieli ◽  
Yakov Babichenko ◽  
Fedor Sandomirskiy ◽  
Omer Tamuz

Through a sequence of examples, we survey the main results of "Feasible Joint Posterior Beliefs" [Arieli, Babichenko, Sandomirskiy, Tamuz 2021]. A group of agents share a common prior distribution regarding a binary state, and observe some information structure. What are the possible joint distributions of their posteriors? We discuss feasibility of product distributions, correlation of posteriors in feasible distributions, extreme feasible distributions and the characterization of feasibility in terms of a "no-trade" condition.


2019 ◽  
Author(s):  
Yuan Qi ◽  
Youhan Fang ◽  
David R. Sinclair ◽  
Shangqin Guo ◽  
Meritxell Alberich-Jorda ◽  
...  

AbstractA new computational framework for FLow cytometric Analysis of Rare Events (FLARE) has been developed specifically for fast and automatic identification of rare cell populations in very large samples generated by platforms like multi-parametric flow cytometry. Using a hierarchical Bayesian model and information-sharing via parallel computation, FLARE rapidly explores the high-dimensional marker-space to detect highly rare populations that are consistent across multiple samples. Further it can focus within specified regions of interest in marker-space to detect subpopulations with desired precision.


Microbiome ◽  
2021 ◽  
Vol 9 (1) ◽  
Author(s):  
Ina Maria Deutschmann ◽  
Gipsi Lima-Mendez ◽  
Anders K. Krabberød ◽  
Jeroen Raes ◽  
Sergio M. Vallina ◽  
...  

Abstract Background Ecological interactions among microorganisms are fundamental for ecosystem function, yet they are mostly unknown or poorly understood. High-throughput-omics can indicate microbial interactions through associations across time and space, which can be represented as association networks. Associations could result from either ecological interactions between microorganisms, or from environmental selection, where the association is environmentally driven. Therefore, before downstream analysis and interpretation, we need to distinguish the nature of the association, particularly if it is due to environmental selection or not. Results We present EnDED (environmentally driven edge detection), an implementation of four approaches as well as their combination to predict which links between microorganisms in an association network are environmentally driven. The four approaches are sign pattern, overlap, interaction information, and data processing inequality. We tested EnDED on networks from simulated data of 50 microorganisms. The networks contained on average 50 nodes and 1087 edges, of which 60 were true interactions but 1026 false associations (i.e., environmentally driven or due to chance). Applying each method individually, we detected a moderate to high number of environmentally driven edges—87% sign pattern and overlap, 67% interaction information, and 44% data processing inequality. Combining these methods in an intersection approach resulted in retaining more interactions, both true and false (32% of environmentally driven associations). After validation with the simulated datasets, we applied EnDED on a marine microbial network inferred from 10 years of monthly observations of microbial-plankton abundance. The intersection combination predicted that 8.3% of the associations were environmentally driven, while individual methods predicted 24.8% (data processing inequality), 25.7% (interaction information), and up to 84.6% (sign pattern as well as overlap). The fraction of environmentally driven edges among negative microbial associations in the real network increased rapidly with the number of environmental factors. Conclusions To reach accurate hypotheses about ecological interactions, it is important to determine, quantify, and remove environmentally driven associations in marine microbial association networks. For that, EnDED offers up to four individual methods as well as their combination. However, especially for the intersection combination, we suggest using EnDED with other strategies to reduce the number of false associations and consequently the number of potential interaction hypotheses.


Author(s):  
Xiangdong Xu ◽  
M Karlsson ◽  
K. Gaska ◽  
Stanislaw Gubanski ◽  
Henrik Hillborg ◽  
...  

<p>In this work, a measurement setup and an algorithm are introduced that allow for obtaining and processing the current data during standard measurements of electric conductivity in polymeric insulation materials. Robustness of this setup is demonstrated through dc conductivity measurements of low density polyethylene (LDPE) specimens that were prepared by two different techniques, i.e. compression molding and extrusion, at two independent laboratories (at Chalmers and KTH) from the same raw pellets. The results resented in this paper reveal that the implemented data processing algorithm allows for clear separation of the conduction current level and the external noise and thus for good differentiation between the conductivity levels in the investigated material specimens. In addition, a high reproducibility of the results is obtained for the independently manufactured specimens, suggesting the proposed measurement technique is well suitable for characterization of low conducting dielectrics.</p>


2022 ◽  
pp. 146906672110733
Author(s):  
Sean Sebastian Hughes ◽  
Marcus M. K. Hughes ◽  
Rasmus Voersaa Jonsbo ◽  
Carsten Uhd Nielsen ◽  
Frants Roager Lauritsen ◽  
...  

Beer is a complex mix of more than 7700 compounds, around 800 of which are volatile. While GC-MS has been actively employed in the analysis of the volatome of beer, this method is challenged by the complex nature of the sample. Herein, we explored the possible of using membrane-inlet mass spectrometry (MIMS) coupled to KNIME to characterize local Danish beers. KNIME stands for Konstanz Information Miner and is a free open-source data processing software which comes with several prebuilt nodes, that, when organized, result in data processing workflows allowing swift analysis of data with outputs that can be visualized in the desired format. KNIME has been shown to be promising in automation of large datasets and requires very little computing power. In fact, most of the computations can be carried out on a regular PC. Herein, we have utilized a KNIME workflow for data visualization of MIMS data to understand the global volatome of beers. Feature identification was not possible as of now but with a combination of MIMS and a KNIME workflow, we were able to distinguish beers from different micro-breweries located in Denmark, laying the foundation for the use of MIMS in future analysis of the beer volatome.


2011 ◽  
Vol 11 (3) ◽  
pp. 751-757 ◽  
Author(s):  
O. G. Terranova ◽  
P. Iaquinta

Abstract. Temporal properties of 152 575 rainfall events, recorded at time steps of 5 min, having different durations and occurring between 1989 and 2008 at 155 localities of Calabria (Italy), have been analysed in this paper. Samples from 45 533 storms have been selected to classify rainfall events as "significant" with regard to their contribution to soil erosion, flooding and/or other geo-hydrological processes. The samples are representative of a wide variety of situations in terms of duration, total rainfall, intensity, etc. The use of standardized rainfall profiles (SRP) is proposed to describe the within-storm temporal pattern. The main attraction of this method lies in the fact that it is based on actual data of regional precipitation. Its weak point is that large samples of data are required to obtain regional profiles. The research necessities for improving the use of Huff curves for storm disaggregation and its the potential use are summarized in this paper on the basis of the specific literature. A new criterion – based on the comparison of the areas A1, A2, A3 and A4 that underlie the four 25% of durations of a given SRP, and the corresponding four values of the "uniform" SRP (USRP), is suggested here with the aim of improving the use of the information content of SRP. Some interesting results concerning the sample frequency and the characterization of parameters for hydrological applications are commented on. The study conducted so far has produced important, albeit preliminary, results for different contexts of Calabria concerning the use of SRP among the methods for constructing design storm hyetographs.


2019 ◽  
Vol 32 (02) ◽  
pp. 2050005 ◽  
Author(s):  
Andreas Bluhm ◽  
Ángela Capel

In this work, we provide a strengthening of the data processing inequality for the relative entropy introduced by Belavkin and Staszewski (BS-entropy). This extends previous results by Carlen and Vershynina for the relative entropy and other standard [Formula: see text]-divergences. To this end, we provide two new equivalent conditions for the equality case of the data processing inequality for the BS-entropy. Subsequently, we extend our result to a larger class of maximal [Formula: see text]-divergences. Here, we first focus on quantum channels which are conditional expectations onto subalgebras and use the Stinespring dilation to lift our results to arbitrary quantum channels.


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