scholarly journals Phylogenetic effective sample size

2015 ◽  
Author(s):  
Krzysztof Bartoszek
Keyword(s):  
Brownian Motion ◽  
Mutual Information ◽  
Sample Size ◽  
Simulation Study ◽  
Effective Sample Size ◽  
Normal Process ◽  
Effective Number ◽  
Number Of Species ◽  
The Mean ◽  
Definition Of

AbstractIn this paper I address the question — how large is a phylogenetic sample? I propose a definition of a phylogenetic effective sample size for Brownian motion and Ornstein–Uhlenbeck processes — the regression effective sample size. I discuss how mutual information can be used to define an effective sample size in the non-normal process case and compare these two definitions to an already present concept of effective sample size (the mean effective sample size). Through a simulation study I find that the AICc is robust if one corrects for the number of species or effective number of species. Lastly I discuss how the concept of the phylogenetic effective sample size can be useful for biodiversity quantification, identification of interesting clades and deciding on the importance of phylogenetic correlations.

scholarly journals Quasi-reliable estimates of effective sample size

2020 ◽  
Author(s):  
Youhan Fang ◽  
Yudong Cao ◽  
Robert D Skeel
Keyword(s):  
Sample Size ◽  
Dimensional Subspace ◽  
Monte Carlo Algorithm ◽  
Finite Dimensional Subspace ◽  
Effective Sample Size ◽  
Finite Dimensional ◽  
Adequate Sampling ◽  
Autocorrelation Time ◽  
The Mean ◽  
The Cost

Abstract The efficiency of a Markov chain Monte Carlo algorithm for estimating the mean of a function of interest might be measured by the cost of generating one independent sample, or equivalently, the total cost divided by the effective sample size, defined in terms of the integrated autocorrelation time. To ensure the reliability of such an estimate, it is suggested that there be an adequate sampling of state space— to the extent that this can be determined from the available samples. A sufficient condition for adequate sampling is derived in terms of the supremum of all possible integrated autocorrelation times, which leads to a more stringent condition for adequate sampling than that simply obtained from integrated autocorrelation times for functions of interest. A method for estimating the supremum of all integrated autocorrelation times, based on approximation in a finite-dimensional subspace, is derived and evaluated empirically.

A mutual information estimator with exponentially decaying bias

2015 ◽  
Vol 14 (3) ◽  
Author(s):  
Zhiyi Zhang ◽  
Lukun Zheng
Keyword(s):  
Maximum Likelihood ◽  
Mutual Information ◽  
Asymptotic Normality ◽  
Sample Size ◽  
Maximum Likelihood Estimator ◽  
Simulation Study ◽  
Type I Error ◽  
Type I ◽  
Nonparametric Estimator ◽  
Likelihood Estimator

AbstractA nonparametric estimator of mutual information is proposed and is shown to have asymptotic normality and efficiency, and a bias decaying exponentially in sample size. The asymptotic normality and the rapidly decaying bias together offer a viable inferential tool for assessing mutual information between two random elements on finite alphabets where the maximum likelihood estimator of mutual information greatly inflates the probability of type I error. The proposed estimator is illustrated by three examples in which the association between a pair of genes is assessed based on their expression levels. Several results of simulation study are also provided.

The Theoretical Relationship between Sample Size and Expected Predictive Precision for EQ-5D Valuation Studies: A Mathematical Exploration and Simulation Study

2020 ◽  
Vol 40 (3) ◽  
pp. 339-347 ◽  
Author(s):  
Kelvin K. W. Chan ◽  
Eleanor M. Pullenayegum
Keyword(s):  
Sample Size ◽  
Least Squares ◽  
Closed Form ◽  
Random Effects ◽  
Simulation Study ◽  
Ordinary Least Squares ◽  
Health States ◽  
Data Set ◽  
The Mean ◽  
Closed Form Formula

Background. Scoring algorithms of multi-attribute utility instruments (MAUI) are developed in valuation studies and are hence estimated subject to uncertainty. Valuation studies need to be designed to achieve reasonable accuracy. We aim to provide the first closed-form mathematical formula for the mean square error (MSE) of an additive MAUI as a function of sample size that acknowledges that the MAUI model for the mean utility is not a perfect fit. Methods. Based on the design of the EQ-5D valuation study, we derived our closed-form formula in terms of sample size and number of directly valued health states overall and per subject. We validated our formula by conducting a simulation study using the US EQ-5D-3L valuation data set and examined the effect of using a random-effects versus an ordinary least-squares model and the effect of heteroscedasticity. We explored the effect of sample size and number of valued health states. Results. The simulation study validated our MSE-based closed-form formula regardless of whether assuming a random-effects model versus an ordinary least squares model or heteroscedasticity versus homoscedasticity. As the sample size approaches infinity, the MSE does not approach zero but levels off asymptotically. The improvement based on increasing sample is more prominent when the sample is small. When the sample size is greater than 300 to 500, further increases do not meaningfully improve the MSE, while increasing the number of health states can further improve the MSE. Conclusion. We have derived a closed-form formula to calculate the MSE of an additive MAUI scoring algorithm based on sample size and number of health states, which will enable the developers of MAUI valuation studies to calculate the required sample size for their desired predictive precision.

Comparison of Fluorine(18)-fluorodeoxyglucose and Gallium(68)-citrate PET/CT in patients with tuberculosis

2019 ◽  
Vol 58 (05) ◽  
pp. 371-378
Author(s):  
Alfred O. Ankrah ◽  
Ismaheel O. Lawal ◽  
Tebatso M.G. Boshomane ◽  
Hans C. Klein ◽  
Thomas Ebenhan ◽  
...  
Keyword(s):  
Tracer Uptake ◽  
Pet Ct ◽  
The Mean ◽  
18F Fdg ◽  
Definition Of ◽  
Gallium 68 ◽  
Attending Physician ◽  
Pet Scans ◽  
The Brain

Abstract 18F-FDG and 68Ga-citrate PET/CT have both been shown to be useful in the management of tuberculosis (TB). We compared the abnormal PET findings of 18F-FDG- and 68Ga-citrate-PET/CT in patients with TB. Methods Patients with TB on anti-TB therapy were included. Patients had a set of PET scans consisting of both 18F-FDG and 68Ga-citrate. Abnormal lesions were identified, and the two sets of scans were compared. The scan findings were correlated to the clinical data as provided by the attending physician. Results 46 PET/CT scans were performed in 18 patients, 11 (61 %) were female, and the mean age was 35.7 ± 13.5 years. Five patients also had both studies for follow-up reasons during the use of anti-TB therapy. Thirteen patients were co-infected with HIV. 18F-FDG detected more lesions than 68Ga-citrate (261 vs. 166, p < 0.0001). 68Ga-citrate showed a better definition of intracerebral lesions due to the absence of tracer uptake in the brain. The mean SUVmax was higher for 18F-FDG compared to 68Ga-citrate (5.73 vs. 3.01, p < 0.0001). We found a significant correlation between the SUVmax of lesions that were determined by both tracers (r = 0.4968, p < 0.0001). Conclusion Preliminary data shows 18F-FDG-PET detects more abnormal lesions in TB compared to 68Ga-citrate. However, 68Ga-citrate has better lesion definition in the brain and is therefore especially useful when intracranial TB is suspected.

scholarly journals The Sankara Nethralaya Tamil Nadu Essilor Myopia (STEM) Study—Defining a Threshold for Non-Cycloplegic Myopia Prevalence in Children

2021 ◽  
Vol 10 (6) ◽  
pp. 1215
Author(s):  
Aparna Gopalakrishnan ◽  
Jameel Rizwana Hussaindeen ◽  
Viswanathan Sivaraman ◽  
Meenakshi Swaminathan ◽  
Yee Ling Wong ◽  
...  
Keyword(s):  
Open Field ◽  
Tamil Nadu ◽  
Mean Difference ◽  
School Vision ◽  
Elite School ◽  
Prevalence Estimates ◽  
The Mean ◽  
Clinically Significant ◽  
Set Up ◽  
Definition Of

The aim of this study was to investigate the agreement between cycloplegic and non-cycloplegic autorefraction with an open-field auto refractor in a school vision screening set up, and to define a threshold for myopia that agrees with the standard cycloplegic refraction threshold. The study was conducted as part of the Sankara Nethralaya Tamil Nadu Essilor Myopia (STEM) study, which investigated the prevalence, incidence, and risk factors for myopia among children in South India. Children from two schools aged 5 to 15 years, with no ocular abnormalities and whose parents gave informed consent for cycloplegic refraction were included in the study. All the children underwent visual acuity assessment (Pocket Vision Screener, Elite school of Optometry, India), followed by non-cycloplegic and cycloplegic (1% tropicamide) open-field autorefraction (Grand Seiko, WAM-5500). A total of 387 children were included in the study, of whom 201 were boys. The mean (SD) age of the children was 12.2 (±2.1) years. Overall, the mean difference between cycloplegic and non-cycloplegic spherical equivalent (SE) open-field autorefraction measures was 0.34 D (limits of agreement (LOA), 1.06 D to −0.38 D). For myopes, the mean difference between cycloplegic and non-cycloplegic SE was 0.13 D (LOA, 0.63D to −0.36D). The prevalence of myopia was 12% (95% CI, 8% to 15%) using the threshold of cycloplegic SE ≤ −0.50 D, and was 14% (95% CI, 11% to 17%) with SE ≤ −0.50 D using non-cycloplegic refraction. When myopia was defined as SE of ≤−0.75 D under non-cycloplegic conditions, there was no difference between cycloplegic and non-cycloplegic open-field autorefraction prevalence estimates (12%; 95% CI, 8% to 15%; p = 1.00). Overall, non-cycloplegic refraction underestimates hyperopia and overestimates myopia; but for subjects with myopia, this difference is minimal and not clinically significant. A threshold of SE ≤ −0.75 D agrees well for the estimation of myopia prevalence among children when using non-cycloplegic refraction and is comparable with the standard definition of cycloplegic myopic refraction of SE ≤ −0.50 D.

scholarly journals Conditional Rényi Entropy and the Relationships between Rényi Capacities

Entropy ◽  
2020 ◽  
Vol 22 (5) ◽  
pp. 526
Author(s):  
Gautam Aishwarya ◽  
Mokshay Madiman
Keyword(s):  
Mutual Information ◽  
Renyi Entropy ◽  
Rényi Entropy ◽  
Basic Properties ◽  
Reference Measure ◽  
Definition Of ◽  
Discrete Setting

The analogues of Arimoto’s definition of conditional Rényi entropy and Rényi mutual information are explored for abstract alphabets. These quantities, although dependent on the reference measure, have some useful properties similar to those known in the discrete setting. In addition to laying out some such basic properties and the relations to Rényi divergences, the relationships between the families of mutual informations defined by Sibson, Augustin-Csiszár, and Lapidoth-Pfister, as well as the corresponding capacities, are explored.

Changes in the legal environment and enforcement of firearm transfer laws in Pennsylvania and Maryland

2018 ◽  
Vol 25 (Suppl 1) ◽  
pp. i2-i4 ◽  
Author(s):  
Cassandra K Crifasi ◽  
Molly Merrill-Francis ◽  
Daniel W Webster ◽  
Garen J Wintemute ◽  
Jon S Vernick
Keyword(s):  
Court Decision ◽  
Annual Number ◽  
Legal Environment ◽  
Background Check ◽  
The Mean ◽  
Definition Of

The effectiveness of laws depends on circumstances affecting their enforcement. To assess such circumstances for comprehensive background check (CBC) and straw purchase laws for firearm sales, we examined prosecutions for CBC and straw purchase violations in Pennsylvania and CBC violations in Maryland. We generated pre-post variables and conducted t-tests to assess differences in the mean number of prosecutions filed following changes to the legal environments. The annual number of prosecutions for straw purchase violations increased significantly in Pennsylvania following the passage of a law that strengthened penalties for these violations (difference in means = +1310.86, P=0.003). The annual number of prosecutions for CBC violations decreased significantly in Maryland following a court decision that narrowed the definition of a firearm transfer making enforcement more difficult (difference in means = −20.52, P=0.026). Our findings suggest enforcement is likely influenced by the penalties associated with violating these laws and the interpretation of the language of the laws.

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