scholarly journals Sampling bias minimization in disease frequency estimates

2021 ◽  
Author(s):  
oshrit shtossel ◽  
yoram louzoun
Keyword(s):  
Explicit Solution ◽  
Total Population ◽  
Sampling Bias ◽  
Accurate Estimate ◽  
Time Dependent ◽  
Bayesian Estimator ◽  
Total Probability ◽  
Sampling Depth ◽  
Alternative Method ◽  
Dependent Probability

An accurate estimate of the number of infected individuals in any disease is crucial. Current estimates are mainly based on the fraction of positive samples or the total number of positive samples. However, both methods are biased and sensitive to the sampling depth. We here propose an alternative method to use the attributes of each sample to estimate the change in the total number of positive patients in the total population. We present a Bayesian estimator assuming a combination of condition and time-dependent probability of being positive, and mixed implicit-explicit solution for the probability of a person with conditions i at time t of being positive. We use this estimate to predict the total probability of being positive at a given day t. We show that these estimate results are smooth and not sensitive to the properties of the samples. Moreover, these results are a better predictor of future mortality.

Time-Dependent Reliability Analysis of Vibratory Systems With Random Parameters

2016 ◽  
Vol 138 (3) ◽  
Author(s):  
Zissimos P. Mourelatos ◽  
Monica Majcher ◽  
Vasileios Geroulas
Keyword(s):  
Large Scale ◽  
Probability Of Failure ◽  
Time Dependent ◽  
Total Probability ◽  
Conditional Probabilities ◽  
Random Parameters ◽  
Random Vibrations ◽  
Input Parameters ◽  
Total Probability Theorem ◽  
Dependent Probability

The field of random vibrations of large-scale systems with millions of degrees-of-freedom (DOF) is of significant importance in many engineering disciplines. In this paper, we propose a method to calculate the time-dependent reliability of linear vibratory systems with random parameters excited by nonstationary Gaussian processes. The approach combines principles of random vibrations, the total probability theorem, and recent advances in time-dependent reliability using an integral equation involving the upcrossing and joint upcrossing rates. A space-filling design, such as optimal symmetric Latin hypercube (OSLH) sampling, is first used to sample the input parameter space. For each design point, the corresponding conditional time-dependent probability of failure is calculated efficiently using random vibrations principles to obtain the statistics of the output process and an efficient numerical estimation of the upcrossing and joint upcrossing rates. A time-dependent metamodel is then created between the input parameters and the output conditional probabilities allowing us to estimate the conditional probabilities for any set of input parameters. The total probability theorem is finally applied to calculate the time-dependent probability of failure. The proposed method is demonstrated using a vibratory beam example.

Time-Dependent Reliability Analysis of Vibratory Systems With Random Parameters

2015 ◽  
Author(s):  
Zissimos P. Mourelatos ◽  
Monica Majcher ◽  
Vasileios Geroulas
Keyword(s):  
Large Scale ◽  
Probability Of Failure ◽  
Time Dependent ◽  
Total Probability ◽  
Conditional Probabilities ◽  
Random Parameters ◽  
Random Vibrations ◽  
Input Parameters ◽  
Total Probability Theorem ◽  
Dependent Probability

The field of random vibrations of large-scale systems with millions of degrees of freedom is of significant importance in many engineering disciplines. In this paper, we propose a method to calculate the time-dependent reliability of linear vibratory systems with random parameters excited by non-stationary Gaussian processes. The approach combines principles of random vibrations, the total probability theorem and recent advances in time-dependent reliability using an integral equation involving the up-crossing and joint up-crossing rates. A space-filling design, such as optimal symmetric Latin hypercube sampling, is first used to sample the input parameter space. For each design point, the corresponding conditional time-dependent probability of failure is calculated efficiently using random vibrations principles to obtain the statistics of the output process and an efficient numerical estimation of the up-crossing and joint up-crossing rates. A time-dependent metamodel is then created between the input parameters and the output conditional probabilities allowing us to estimate the conditional probabilities for any set of input parameters. The total probability theorem is finally applied to calculate the time-dependent probability of failure. The proposed method is demonstrated using a vibratory beam example.

A Random Process Metamodel Approach for Time-Dependent Reliability

2015 ◽  
Vol 138 (1) ◽  
Author(s):  
Dorin Drignei ◽  
Igor Baseski ◽  
Zissimos P. Mourelatos ◽  
Ervisa Kosova
Keyword(s):  
Random Process ◽  
Kriging Model ◽  
Random Processes ◽  
Time Dependent ◽  
Total Probability ◽  
Sampling Distributions ◽  
Input And Output ◽  
System Input ◽  
Total Probability Theorem ◽  
Dependent Probability

A new metamodeling approach is proposed to characterize the output (response) random process of a dynamic system with random variables, excited by input random processes. The metamodel is then used to efficiently estimate the time-dependent reliability. The input random processes are decomposed using principal components, and a few simulations are used to estimate the distributions of the decomposition coefficients. A similar decomposition is performed on the output random process. A Kriging model is then built between the input and output decomposition coefficients and is used subsequently to quantify the output random process. The innovation of our approach is that the system input is not deterministic but random. We establish, therefore, a surrogate model between the input and output random processes. To achieve this goal, we use an integral expression of the total probability theorem to estimate the marginal distribution of the output decomposition coefficients. The integral is efficiently estimated using a Monte Carlo (MC) approach which simulates from a mixture of sampling distributions with equal mixing probabilities. The quantified output random process is finally used to estimate the time-dependent probability of failure. The proposed method is illustrated with a corroding beam example.

Quantifying electron transit in donor-bridge-acceptor systems using probabilistic confidence

2018 ◽  
Vol 17 (07) ◽  
pp. 1850046 ◽  
Author(s):  
Evan Curtin ◽  
Gloria Bazargan ◽  
Karl Sohlberg
Keyword(s):  
Charge Transport ◽  
Conditional Probability ◽  
Probabilistic Approach ◽  
Probability Analysis ◽  
Time Dependent ◽  
Quantum Particles ◽  
Transit Times ◽  
Conditional Probability Analysis ◽  
Insight Into ◽  
Dependent Probability

A probabilistic approach to characterizing transit times for quantum particles is generalized to a system of more than two spatial regions and applied to the transport of charge in donor-bridge-acceptor systems. The approach is based on applying conditional probability analysis to a discrete representation of the time-dependent probability density as generated by numerical solution of the time-dependent Schrödinger equation for an initially localized electron. To carry out this analysis, it is first necessary to cast the conditional probability analysis approach in matrix form. The results afford a quantification of the electron transit time and may provide a tool to gain insight into the mechanism of charge transport.

scholarly journals SIGNIFICANT EARTHQUAKES NEAR THE CITY OF THESSALONIKI (NORTHERN GREECE) AND PROBABILITY DISTRIBUTION ON FAULTS

2017 ◽  
Vol 50 (3) ◽  
pp. 1389
Author(s):  
P.M. Paradisopoulou ◽  
E.E. Papadimitriou ◽  
J. Mirek
Keyword(s):  
Stress Transfer ◽  
Time Dependent ◽  
Earthquake Catalog ◽  
Northern Greece ◽  
Earthquake Probability ◽  
Fault Segment ◽  
Probability Estimates ◽  
Macroseismic Intensities ◽  
The City ◽  
Dependent Probability

Stress triggering must be incorporated into quantitative earthquake probability estimate, given that faults are interacted though their stress field. Using time dependent probability estimates this work aims at the evaluation of the occurrence probability of anticipated earthquakes near the city of Thessaloniki, an urban center of 1 million people located in northern Greece, conditional to the time elapsed since the last stronger event on each fault segment of the study area. A method that calculates the macroseismic epicenter and magnitude according to macroseismic intensities is used to improve the existing earthquake catalog (from AD 1600 - 2013 with M≥6.0) in order to compute new interevent and elapsed time values which form the basis for time-dependent probability estimates. To investigate the effects of stress transfer to seismic hazard, the probabilistic calculations presented here employ detailed models of coseismic stress associated with the 20 June 1978 M=6.5 Thessaloniki which is the latest destructive earthquake in the area in the instrumental era. The combined 2015-2045 regional Poisson probability of M≥6.0 earthquakes is ~35% the regional time-dependent probability varies from 0% to 15% and incorporation of stress transfer from 0% to 20% for each fault segment.

scholarly journals Attack rate and the price of SARS-CoV-2 herd immunity in Brazil

2021 ◽  
Author(s):  
Tarcisio Rocha Filho ◽  
José Mendes ◽  
Carson Chow ◽  
James Phillips ◽  
Antônio Cordeiro ◽  
...  
Keyword(s):  
Attack Rate ◽  
Contact Structure ◽  
Compartmental Model ◽  
Total Population ◽  
Herd Immunity ◽  
Age Groups ◽  
Time Dependent ◽  
Contact Matrix ◽  
The City ◽  
Pharmaceutical Interventions

Abstract We introduce a compartmental model with age structure to study the dynamics of the SARS-COV−2 pandemic. The contagion matrix in the model is given by the product of a probability per contact with a contact matrix explicitly taking into account the contact structure among different age groups. The probability of contagion per contact is considered as time dependent to represent non-pharmaceutical interventions, and is fitted from the time series of deaths. The approach is used to study the evolution of the COVID−19 pandemic in the main Brazilian cities and compared to two good quality serological surveys. We also discuss with some detail the case of the city of Manaus which raised special attention due to a previous report of three-quarters attack rate by the end of 2020. We discuss estimates for Manaus and all Brazilian cities with a total population of more than one million. We also estimate the attack rate with respect to the total population, in each Brazilian state by January, 1 st 2021 and May, 23 2021.

Analysis of Feedback Retrial Queue with Starting Failure and Server Vacation

2016 ◽  
pp. 71-96
Author(s):  
K. Sathiya Thiyagarajan ◽  
G. Ayyappan
Keyword(s):  
Steady State ◽  
Performance Measures ◽  
Generating Functions ◽  
Retrial Queue ◽  
Laplace Transforms ◽  
Time Dependent ◽  
Steady State Analysis ◽  
Starting Failure ◽  
Dependent Probability ◽  
Bernoulli Vacation

In this chapter we discusses a batch arrival feedback retrial queue with Bernoulli vacation, where the server is subjected to starting failure. Any arriving batch finding the server busy, breakdown or on vacation enters an orbit. Otherwise one customer from the arriving batch enters a service immediately while the rest join the orbit. After the completion of each service, the server either goes for a vacation with probability or may wait for serving the next customer. Repair times, service times and vacation times are assumed to be arbitrarily distributed. The time dependent probability generating functions have been obtained in terms of their Laplace transforms. The steady state analysis and key performance measures of the system are also studied. Finally, some numerical illustrations are presented.

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