scholarly journals A Monte Carlo method to estimate cell population heterogeneity

2019 ◽  
Author(s):  
Ben Lambert ◽  
David J. Gavaghan ◽  
Simon Tavener
Keyword(s):  
Monte Carlo ◽  
Cell Population ◽  
A Priori ◽  
Biological Systems ◽  
Population Heterogeneity ◽  
Model Parameters ◽  
Cellular Processes ◽  
Laboratory Techniques ◽  
Hierarchical Bayesian Methods ◽  
Cell Variation

1AbstractVariation is characteristic of all living systems. Laboratory techniques such as flow cytometry can probe individual cells, and, after decades of experimentation, it is clear that even members of genetically identical cell populations can exhibit differences. To understand whether variation is biologically meaningful, it is essential to discern its source. Mathematical models of biological systems are tools that can be used to investigate causes of cell-to-cell variation. From mathematical analysis and simulation of these models, biological hypotheses can be posed and investigated, then parameter inference can determine which of these is compatible with experimental data. Data from laboratory experiments often consist of “snapshots” representing distributions of cellular properties at different points in time, rather than individual cell trajectories. These data are not straightforward to fit using hierarchical Bayesian methods, which require the number of cell population clusters to be chosen a priori. Here, we introduce a computational sampling method named “Contour Monte Carlo” for estimating mathematical model parameters from snapshot distributions, which is straightforward to implement and does not require cells be assigned to predefined categories. Our method is appropriate for systems where observed variation is mostly due to variability in cellular processes rather than experimental measurement error, which may be the case for many systems due to continued improvements in resolution of laboratory techniques. In this paper, we apply our method to quantify cellular variation for three biological systems of interest and provide Julia code enabling others to use this method.

Transdimensional seismic inversion using the reversible jump Hamiltonian Monte Carlo algorithm

Geophysics ◽  
2017 ◽  
Vol 82 (3) ◽  
pp. R119-R134 ◽  
Author(s):  
Mrinal K. Sen ◽  
Reetam Biswas
Keyword(s):  
Monte Carlo ◽  
A Priori ◽  
Seismic Inversion ◽  
Monte Carlo Algorithm ◽  
Model Parameters ◽  
Reversible Jump ◽  
Step Method ◽  
Acceptance Probability ◽  
Hamiltonian Monte Carlo ◽  
Impedance Inversion

Prestack or angle stack gathers are inverted to estimate pseudologs at every surface location for building reservoir models. Recently, several methods have been proposed to increase the resolution of the inverted models. All of these methods, however, require that the total number of model parameters be fixed a priori. We have investigated an alternate approach in which we allow the data themselves to choose model parameterization. In other words, in addition to the layer properties, the number of layers is also treated as a variable in our formulation. Such transdimensional inverse problems are generally solved by using the reversible jump Markov chain Monte Carlo (RJMCMC) approach, which is a tool for model exploration and uncertainty quantification. This method, however, has very low acceptance. We have developed a two-step method by combining RJMCMC with a fixed-dimensional MCMC called Hamiltonian Monte Carlo, which makes use of gradient information to take large steps. Acceptance probability for such a transition is also derived. We call this new method “reversible jump Hamiltonian Monte Carlo (RJHMC).” We have applied this technique to poststack acoustic impedance inversion and to prestack (angle stack) AVA inversion for estimating acoustic and shear impedance profiles. We have determined that the marginal posteriors estimated by RJMCMC and RJHMC are in good agreement. Our results demonstrate that RJHMC converges faster than RJMCMC, and it therefore can be a practical tool for inverting seismic data when the gradient can be computed efficiently.

Identification, Prediction and Data Analysis of Noncoding RNAs: A Review

2019 ◽  
Vol 15 (3) ◽  
pp. 216-230 ◽  
Author(s):  
Abbasali Emamjomeh ◽  
Javad Zahiri ◽  
Mehrdad Asadian ◽  
Mehrdad Behmanesh ◽  
Barat A. Fakheri ◽  
...  
Keyword(s):  
Computational Methods ◽  
State Of The Art ◽  
Noncoding Rnas ◽  
Research Field ◽  
Design Strategies ◽  
Structural Prediction ◽  
Computational Costs ◽  
Cellular Processes ◽  
Laboratory Techniques ◽  
Fast Prediction

Background:Noncoding RNAs (ncRNAs) which play an important role in various cellular processes are important in medicine as well as in drug design strategies. Different studies have shown that ncRNAs are dis-regulated in cancer cells and play an important role in human tumorigenesis. Therefore, it is important to identify and predict such molecules by experimental and computational methods, respectively. However, to avoid expensive experimental methods, computational algorithms have been developed for accurately and fast prediction of ncRNAs.Objective:The aim of this review was to introduce the experimental and computational methods to identify and predict ncRNAs structure. Also, we explained the ncRNA’s roles in cellular processes and drugs design, briefly.Method:In this survey, we will introduce ncRNAs and their roles in biological and medicinal processes. Then, some important laboratory techniques will be studied to identify ncRNAs. Finally, the state-of-the-art models and algorithms will be introduced along with important tools and databases.Results:The results showed that the integration of experimental and computational approaches improves to identify ncRNAs. Moreover, the high accurate databases, algorithms and tools were compared to predict the ncRNAs.Conclusion:ncRNAs prediction is an exciting research field, but there are different difficulties. It requires accurate and reliable algorithms and tools. Also, it should be mentioned that computational costs of such algorithm including running time and usage memory are very important. Finally, some suggestions were presented to improve computational methods of ncRNAs gene and structural prediction.

scholarly journals Statistical Analysis of Tritium Breeding Ratio Deviations in the DEMO Due to Nuclear Data Uncertainties

2021 ◽  
Vol 11 (11) ◽  
pp. 5234
Author(s):  
Jin Hun Park ◽  
Pavel Pereslavtsev ◽  
Alexandre Konobeev ◽  
Christian Wegmann
Keyword(s):  
Monte Carlo ◽  
Fusion Reactor ◽  
Nuclear Data ◽  
Data File ◽  
Nuclear Model ◽  
Model Parameters ◽  
Tritium Breeding ◽  
Tritium Breeding Ratio ◽  
Nuclear Data Library ◽  
Breeding Ratio

For the stable and self-sufficient functioning of the DEMO fusion reactor, one of the most important parameters that must be demonstrated is the Tritium Breeding Ratio (TBR). The reliable assessment of the TBR with safety margins is a matter of fusion reactor viability. The uncertainty of the TBR in the neutronic simulations includes many different aspects such as the uncertainty due to the simplification of the geometry models used, the uncertainty of the reactor layout and the uncertainty introduced due to neutronic calculations. The last one can be reduced by applying high fidelity Monte Carlo simulations for TBR estimations. Nevertheless, these calculations have inherent statistical errors controlled by the number of neutron histories, straightforward for a quantity such as that of TBR underlying errors due to nuclear data uncertainties. In fact, every evaluated nuclear data file involved in the MCNP calculations can be replaced with the set of the random data files representing the particular deviation of the nuclear model parameters, each of them being correct and valid for applications. To account for the uncertainty of the nuclear model parameters introduced in the evaluated data file, a total Monte Carlo (TMC) method can be used to analyze the uncertainty of TBR owing to the nuclear data used for calculations. To this end, two 3D fully heterogeneous geometry models of the helium cooled pebble bed (HCPB) and water cooled lithium lead (WCLL) European DEMOs were utilized for the calculations of the TBR. The TMC calculations were performed, making use of the TENDL-2017 nuclear data library random files with high enough statistics providing a well-resolved Gaussian distribution of the TBR value. The assessment was done for the estimation of the TBR uncertainty due to the nuclear data for entire material compositions and for separate materials: structural, breeder and neutron multipliers. The overall TBR uncertainty for the nuclear data was estimated to be 3~4% for the HCPB and WCLL DEMOs, respectively.

scholarly journals Parameter stability and consistency in an alongshore-current model determined with Markov chain Monte Carlo

2008 ◽  
Vol 10 (2) ◽  
pp. 153-162 ◽  
Author(s):  
B. G. Ruessink
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Parameter Stability ◽  
Small Uncertainty ◽  
Best Fit ◽  
Stability And Consistency

When a numerical model is to be used as a practical tool, its parameters should preferably be stable and consistent, that is, possess a small uncertainty and be time-invariant. Using data and predictions of alongshore mean currents flowing on a beach as a case study, this paper illustrates how parameter stability and consistency can be assessed using Markov chain Monte Carlo. Within a single calibration run, Markov chain Monte Carlo estimates the parameter posterior probability density function, its mode being the best-fit parameter set. Parameter stability is investigated by stepwise adding new data to a calibration run, while consistency is examined by calibrating the model on different datasets of equal length. The results for the present case study indicate that various tidal cycles with strong (say, >0.5 m/s) currents are required to obtain stable parameter estimates, and that the best-fit model parameters and the underlying posterior distribution are strongly time-varying. This inconsistent parameter behavior may reflect unresolved variability of the processes represented by the parameters, or may represent compensational behavior for temporal violations in specific model assumptions.

scholarly journals COSMIC COVARIANCE AND THE LOW QUADRUPOLE ANISOTROPY IN THE WMAP DATA

2008 ◽  
Vol 23 (17n20) ◽  
pp. 1489-1497 ◽  
Author(s):  
LUNG-YIH CHIANG ◽  
PAVEL D. NASELSKY ◽  
PETER COLES
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
A Priori ◽  
Gaussian Random Field ◽  
Minimum Variance ◽  
Microwave Background ◽  
Data Release ◽  
Intrinsic Correlation ◽  
Wmap Data ◽  
Cmb Temperature

Low quadrupole power in the cosmic microwave background (CMB) temperature anisotropies has been a puzzle since WMAP data release. In this talk I will demonstrate that the minimum variance optimization (MVO), a methodology used by many authors including the WMAP science team to separate the CMB from foreground contamination, serves not only to extract the CMB, but to subtract the “cosmic covariance”, an intrinsic correlation between the CMB and the foregrounds. Such subtraction induces low variance in the signal via MVO, which in turn propagates into the multipoles, causing a quadrupole deficit with more than 90% CL. As we do not know the CMB and the foregrounds a priori, and their correlation is subtracted by the MVO in any case, there is therefore an unknown error in the quadrupole power even before the cosmic variance interpretation. We combine the MVO and Monte Carlo simulations, assuming CMB is a Gaussian random field, and the estimated quadrupole power falls in [308.13, 401.97] μ K 2 (at 1 − σ level).

Probabilistic Assessment of Wind Farm Active Power Based on Monte-Carlo Simulation

2013 ◽  
Vol 291-294 ◽  
pp. 536-540 ◽  
Author(s):  
Xin Wei Wang ◽  
Jian Hua Zhang ◽  
Cheng Jiang ◽  
Lei Yu
Keyword(s):  
Monte Carlo ◽  
Power Output ◽  
Wind Farm ◽  
Active Power ◽  
Assessment Methods ◽  
Probabilistic Methods ◽  
Model Parameters ◽  
Probability Assessment ◽  
Reliability Models ◽  
Reliability Parameters

The conventional deterministic methods have been unable to accurately assess the active power output of the wind farm being the random and intermittent of wind power, and the probabilistic methods commonly used to solve this problem. In this paper the multi-state fault model is built considering run, outage and derating state of wind turbine, and then the reliability model of the wind farm is established considering the randomness of the wind speed, the wind farm wake effects and turbine failure. The active wind farm output probability assessment methods and processes based on the Monte Carlo method. The related programs are written in MATLAB, and the probability assessment for active power output of a wind farm in carried out, the effectiveness and adaptability of built reliability models and assessment methods are illustrated by analysis of the effects of reliability parameters and model parameters on assessment results.

Generalised DOPs with Consideration of the Influence Function of Signal-in-Space Errors

2011 ◽  
Vol 64 (S1) ◽  
pp. S3-S18 ◽  
Author(s):  
Yuanxi Yang ◽  
Jinlong Li ◽  
Junyi Xu ◽  
Jing Tang
Keyword(s):  
Least Squares ◽  
Stochastic Models ◽  
Influence Function ◽  
A Priori ◽  
Functional Model ◽  
Global Navigation Satellite Systems ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Integrated Navigation ◽  
Satellite Systems

Integrated navigation using multiple Global Navigation Satellite Systems (GNSS) is beneficial to increase the number of observable satellites, alleviate the effects of systematic errors and improve the accuracy of positioning, navigation and timing (PNT). When multiple constellations and multiple frequency measurements are employed, the functional and stochastic models as well as the estimation principle for PNT may be different. Therefore, the commonly used definition of “dilution of precision (DOP)” based on the least squares (LS) estimation and unified functional and stochastic models will be not applicable anymore. In this paper, three types of generalised DOPs are defined. The first type of generalised DOP is based on the error influence function (IF) of pseudo-ranges that reflects the geometry strength of the measurements, error magnitude and the estimation risk criteria. When the least squares estimation is used, the first type of generalised DOP is identical to the one commonly used. In order to define the first type of generalised DOP, an IF of signal–in-space (SIS) errors on the parameter estimates of PNT is derived. The second type of generalised DOP is defined based on the functional model with additional systematic parameters induced by the compatibility and interoperability problems among different GNSS systems. The third type of generalised DOP is defined based on Bayesian estimation in which the a priori information of the model parameters is taken into account. This is suitable for evaluating the precision of kinematic positioning or navigation. Different types of generalised DOPs are suitable for different PNT scenarios and an example for the calculation of these DOPs for multi-GNSS systems including GPS, GLONASS, Compass and Galileo is given. New observation equations of Compass and GLONASS that may contain additional parameters for interoperability are specifically investigated. It shows that if the interoperability of multi-GNSS is not fulfilled, the increased number of satellites will not significantly reduce the generalised DOP value. Furthermore, the outlying measurements will not change the original DOP, but will change the first type of generalised DOP which includes a robust error IF. A priori information of the model parameters will also reduce the DOP.

scholarly journals Modelling the spread of American foulbrood in honeybees

2013 ◽  
Vol 10 (88) ◽  
pp. 20130650 ◽  
Author(s):  
Samik Datta ◽  
James C. Bull ◽  
Giles E. Budge ◽  
Matt J. Keeling
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Control Strategies ◽  
Sir Model ◽  
Model Parameters ◽  
American Foulbrood ◽  
Inspection Period ◽  
Stochastic Sir ◽  
Stochastic Sir Model ◽  
The Impact

We investigate the spread of American foulbrood (AFB), a disease caused by the bacterium Paenibacillus larvae , that affects bees and can be extremely damaging to beehives. Our dataset comes from an inspection period carried out during an AFB epidemic of honeybee colonies on the island of Jersey during the summer of 2010. The data include the number of hives of honeybees, location and owner of honeybee apiaries across the island. We use a spatial SIR model with an underlying owner network to simulate the epidemic and characterize the epidemic using a Markov chain Monte Carlo (MCMC) scheme to determine model parameters and infection times (including undetected ‘occult’ infections). Likely methods of infection spread can be inferred from the analysis, with both distance- and owner-based transmissions being found to contribute to the spread of AFB. The results of the MCMC are corroborated by simulating the epidemic using a stochastic SIR model, resulting in aggregate levels of infection that are comparable to the data. We use this stochastic SIR model to simulate the impact of different control strategies on controlling the epidemic. It is found that earlier inspections result in smaller epidemics and a higher likelihood of AFB extinction.

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