scholarly journals Computing Accurate Probabilistic Estimates of One-D Entropy from Equiprobable Random Samples

Entropy ◽  
2021 ◽  
Vol 23 (6) ◽  
pp. 740
Author(s):  
Hoshin V. Gupta ◽  
Mohammad Reza Ehsani ◽  
Tirthankar Roy ◽  
Maria A. Sans-Fuentes ◽  
Uwe Ehret ◽  
...  
Keyword(s):  
Sample Size ◽  
Parameter Tuning ◽  
Gaussian Mixture ◽  
Optimal Number ◽  
Small Sample ◽  
Random Samples ◽  
Data Points ◽  
Probability Mass ◽  
Entropy Estimate ◽  
Log Normal

We develop a simple Quantile Spacing (QS) method for accurate probabilistic estimation of one-dimensional entropy from equiprobable random samples, and compare it with the popular Bin-Counting (BC) and Kernel Density (KD) methods. In contrast to BC, which uses equal-width bins with varying probability mass, the QS method uses estimates of the quantiles that divide the support of the data generating probability density function (pdf) into equal-probability-mass intervals. And, whereas BC and KD each require optimal tuning of a hyper-parameter whose value varies with sample size and shape of the pdf, QS only requires specification of the number of quantiles to be used. Results indicate, for the class of distributions tested, that the optimal number of quantiles is a fixed fraction of the sample size (empirically determined to be ~0.25–0.35), and that this value is relatively insensitive to distributional form or sample size. This provides a clear advantage over BC and KD since hyper-parameter tuning is not required. Further, unlike KD, there is no need to select an appropriate kernel-type, and so QS is applicable to pdfs of arbitrary shape, including those with discontinuous slope and/or magnitude. Bootstrapping is used to approximate the sampling variability distribution of the resulting entropy estimate, and is shown to accurately reflect the true uncertainty. For the four distributional forms studied (Gaussian, Log-Normal, Exponential and Bimodal Gaussian Mixture), expected estimation bias is less than 1% and uncertainty is low even for samples of as few as 100 data points; in contrast, for KD the small sample bias can be as large as -10% and for BC as large as -50%. We speculate that estimating quantile locations, rather than bin-probabilities, results in more efficient use of the information in the data to approximate the underlying shape of an unknown data generating pdf.

scholarly journals Accurate and Practical Energy Detection over α-μ Fading Channels

Sensors ◽  
2020 ◽  
Vol 20 (3) ◽  
pp. 754 ◽  
Author(s):  
Kaitian Cao ◽  
Ping Qian ◽  
Jing An ◽  
Li Wang
Keyword(s):  
Sample Size ◽  
Fading Channels ◽  
Small Sample Size ◽  
Energy Detection ◽  
Mass Function ◽  
Detection Performance ◽  
Small Sample ◽  
Closed Form Expression ◽  
Probability Mass Function ◽  
Probability Mass

In this study, a novel and exact closed-form expression for detection probability of energy detection (ED) in terms of Meijer’s G-function over α-μ generalized fading channels was derived. It is more accurate and practical than the existing exact expressions and has wide application prospects in the performance evaluations in various areas of wireless communications, especially in the wireless sensor network (WSN) and the cognitive radio network (CRN). Furthermore, an exact and simple analytical solution for the sample size meeting the desired detection performance in terms of the probability mass function of a Poisson distribution was also solved. Simulations verified the detection performance and accuracy of our derived expressions with a small sample size compared to the existing exact expressions and approximations.

scholarly journals Efficient Greedy Learning of Gaussian Mixture Models

2003 ◽  
Vol 15 (2) ◽  
pp. 469-485 ◽  
Author(s):  
J. J. Verbeek ◽  
N. Vlassis ◽  
B. Kröse
Keyword(s):  
Mixture Models ◽  
Density Estimation ◽  
Expectation Maximization ◽  
State Of The Art ◽  
Gaussian Mixture Models ◽  
Gaussian Mixture ◽  
Optimal Number ◽  
Gaussian Mixtures ◽  
Data Points ◽  
Time Linear

This article concerns the greedy learning of gaussian mixtures. In the greedy approach, mixture components are inserted into the mixture one aftertheother.We propose a heuristic for searching for the optimal component to insert. In a randomized manner, a set of candidate new components is generated. For each of these candidates, we find the locally optimal new component and insert it into the existing mixture. The resulting algorithm resolves the sensitivity to initialization of state-of-the-art methods, like expectation maximization, and has running time linear in the number of data points and quadratic in the (final) number of mixture components. Due to its greedy nature, the algorithm can be particularly useful when the optimal number of mixture components is unknown. Experimental results comparing the proposed algorithm to other methods on density estimation and texture segmentation are provided.

Application of Ultrasound Elastography for Assessing Intestinal Fibrosis in Inflammatory Bowel Disease: Fiction or Reality?

2020 ◽  
Vol 21 ◽  
Author(s):  
Roberto Gabbiadini ◽  
Eirini Zacharopoulou ◽  
Federica Furfaro ◽  
Vincenzo Craviotto ◽  
Alessandra Zilli ◽  
...  
Keyword(s):  
Inflammatory Bowel Disease ◽  
Sample Size ◽  
Bowel Disease ◽  
Small Sample Size ◽  
Shear Wave Elastography ◽  
Small Sample ◽  
Ultrasound Elastography ◽  
Invasive Technique ◽  
Intestinal Fibrosis ◽  
Inflammatory Bowel

Background: Intestinal fibrosis and subsequent strictures represent an important burden in inflammatory bowel disease (IBD). The detection and evaluation of the degree of fibrosis in stricturing Crohn’s disease (CD) is important to address the best therapeutic strategy (medical anti-inflammatory therapy, endoscopic dilation, surgery). Ultrasound elastography (USE) is a non-invasive technique that has been proposed in the field of IBD for evaluating intestinal stiffness as a biomarker of intestinal fibrosis. Objective: The aim of this review is to discuss the ability and current role of ultrasound elastography in the assessment of intestinal fibrosis. Results and Conclusion: Data on USE in IBD are provided by pilot and proof-of-concept studies with small sample size. The first type of USE investigated was strain elastography, while shear wave elastography has been introduced lately. Despite the heterogeneity of the methods of the studies, USE has been proven to be able to assess intestinal fibrosis in patients with stricturing CD. However, before introducing this technique in current practice, further studies with larger sample size and homogeneous parameters, testing reproducibility, and identification of validated cut-off values are needed.

MHealth Applications for People with Cognitive Impairment and Their Caregivers: A Scoping Review (Preprint)

2020 ◽  
Author(s):  
Qing Zhao ◽  
Pei Chen ◽  
Yu Zhang ◽  
Haining Liu ◽  
Xianwen Li
Keyword(s):  
Cognitive Impairment ◽  
Sample Size ◽  
Research Design ◽  
Scoping Review ◽  
Life Support ◽  
Small Sample ◽  
Mobile Technologies ◽  
Control Group ◽  
Caregiver Support ◽  
The Impact

BACKGROUND Mobile health application has become an important tool for healthcare systems. One such tool is the delivery of assisting in people with cognitive impairment and their caregivers. OBJECTIVE This scoping review aims to explore and evaluate the existing evidence and challenges on the use of mHealth applications that assisting in people with cognitive impairment and their caregivers. METHODS Nine databases, including PubMed, EMBASE, Cochrane, PsycARTICLES, CINAHL, Web of Science, Applied Science & Technology Source, IEEE Xplore and the ACM Digital Library were searched from inception through June 2020 for the studies of mHealth applications on people with cognitive impairment and their caregivers. Two reviewers independently extracted, checked synthesized data independently. RESULTS Of the 6101 studies retrieved, 64 studies met the inclusion criteria. Three categories emerged from this scoping review. These categories are ‘application functionality’, ‘evaluation strategies’, ‘barriers and challenges’. All the included studies were categorized into 7 groups based on functionality: (1) cognitive assessment; (2) cognitive training; (3) life support; (4) caregiver support; (5) symptom management; (6) reminiscence therapy; (7) exercise intervention. The included studies were broadly categorized into four types: (1) Usability testing; (2) Pilot and feasibility studies; (3) Validation studies; and (4) Efficacy or Effectiveness design. These studies had many defects in research design such as: (1) small sample size; (2) deficiency in active control group; (3) deficiency in analyzing the effectiveness of intervention components; (4) lack of adverse reactions and economic evaluation; (5) lack of consideration about the education level, electronic health literacy and smartphone proficiency of the participants; (6) deficiency in assessment tool; (7) lack of rating the quality of mHealth application. Some progress should be improved in the design of smartphone application functionality, such as: (1) the design of cognitive measurements and training game need to be differentiated; (2) reduce the impact of the learning effect. Besides this, few studies used health behavior theory and performed with standardized reporting. CONCLUSIONS Preliminary results show that mobile technologies facilitate the assistance in people with cognitive impairment and their caregivers. The majority of mHealth application interventions incorporated usability outcome and health outcomes. However, these studies have many defects in research design that limit the extrapolation of research. The content of mHealth application is urgently improved to adapt to demonstrate the real effect. In addition, further research with strong methodological rigor and adequate sample size are needed to examine the feasibility, effectiveness, and cost-effectiveness of mHealth applications for people with cognitive impairment and their caregivers.

scholarly journals Confirming known planetary trends using a photometrically selected Kepler sample

2020 ◽  
Author(s):  
Jonah T Hansen ◽  
Luca Casagrande ◽  
Michael J Ireland ◽  
Jane Lin
Keyword(s):  
Sample Size ◽  
Robust Statistics ◽  
Narrow Band ◽  
Small Sample Size ◽  
Small Sample ◽  
Fitting Algorithm ◽  
Statistical Studies ◽  
The Rich ◽  
Host Stars ◽  
High Metallicity

Abstract Statistical studies of exoplanets and the properties of their host stars have been critical to informing models of planet formation. Numerous trends have arisen in particular from the rich Kepler dataset, including that exoplanets are more likely to be found around stars with a high metallicity and the presence of a “gap” in the distribution of planetary radii at 1.9 R⊕. Here we present a new analysis on the Kepler field, using the APOGEE spectroscopic survey to build a metallicity calibration based on Gaia, 2MASS and Strömgren photometry. This calibration, along with masses and radii derived from a Bayesian isochrone fitting algorithm, is used to test a number of these trends with unbiased, photometrically derived parameters, albeit with a smaller sample size in comparison to recent studies. We recover that planets are more frequently found around higher metallicity stars; over the entire sample, planetary frequencies are 0.88 ± 0.12 percent for [Fe/H] < 0 and 1.37 ± 0.16 percent for [Fe/H] ≥ 0 but at two sigma we find that the size of exoplanets influences the strength of this trend. We also recover the planet radius gap, along with a slight positive correlation with stellar mass. We conclude that this method shows promise to derive robust statistics of exoplanets. We also remark that spectrophotometry from Gaia DR3 will have an effective resolution similar to narrow band filters and allow to overcome the small sample size inherent in this study.

scholarly journals The use of diversity indices for local assessment of marine sediment quality

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Shinya Hosokawa ◽  
Kyosuke Momota ◽  
Anthony A. Chariton ◽  
Ryoji Naito ◽  
Yoshiyuki Nakamura
Keyword(s):  
Community Structure ◽  
Sample Size ◽  
Small Sample Size ◽  
Benthic Communities ◽  
Sediment Quality ◽  
Diversity Indices ◽  
Small Sample ◽  
Species Density ◽  
Local Case ◽  
Two Indices

AbstractDiversity indices are commonly used to measure changes in marine benthic communities. However, the reliability (and therefore suitability) of these indices for detecting environmental change is often unclear because of small sample size and the inappropriate choice of communities for analysis. This study explored uncertainties in taxonomic density and two indices of community structure in our target region, Japan, and in two local areas within this region, and explored potential solutions. Our analysis of the Japanese regional dataset showed a decrease in family density and a dominance of a few species as sediment conditions become degraded. Local case studies showed that species density is affected by sediment degradation at sites where multiple communities coexist. However, two indices of community structure could become insensitive because of masking by community variability, and small sample size sometimes caused misleading or inaccurate estimates of these indices. We conclude that species density is a sensitive indicator of change in marine benthic communities, and emphasise that indices of community structure should only be used when the community structure of the target community is distinguishable from other coexisting communities and there is sufficient sample size.

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