scholarly journals Bayesian inference of stellar parameters based on 1D stellar models coupled with 3D envelopes

2019 ◽  
Vol 490 (2) ◽  
pp. 2890-2904 ◽  
Author(s):  
Andreas Christ Sølvsten Jørgensen ◽  
George C Angelou
Keyword(s):  
Bayesian Inference ◽  
Structural Changes ◽  
Energy Transport ◽  
Parameter Estimates ◽  
Mixing Length ◽  
Milky Way Galaxy ◽  
3D Simulations ◽  
Robust Parameter ◽  
Stellar Models ◽  
Oscillation Frequencies

ABSTRACT Stellar models utilizing 1D, heuristic theories of convection fail to adequately describe the energy transport in superadiabatic layers. The improper modelling leads to well-known discrepancies between observed and predicted oscillation frequencies for stars with convective envelopes. Recently, 3D hydrodynamic simulations of stellar envelopes have been shown to facilitate a realistic depiction of superadiabatic convection in 1D stellar models. The resulting structural changes of the boundary layers have been demonstrated to impact not only the predicted oscillation spectra but evolution tracks as well. In this paper, we quantify the consequences that the change in boundary conditions has for stellar parameter estimates of main-sequence stars. For this purpose, we investigate two benchmark stars, Alpha Centauri A and B, using Bayesian inference. We show that the improved treatment of turbulent convection makes the obtained 1D stellar structures nearly insensitive to the mixing length parameter. By using 3D simulations in 1D stellar models, we hence overcome the degeneracy between the mixing length parameter and other stellar parameters. By lifting this degeneracy, the inclusion of 3D simulations has the potential to yield more robust parameter estimates. In this way, a more realistic depiction of superadiabatic convection has important implications for any field that relies on stellar models, including the study of the chemical evolution of the Milky Way Galaxy and exoplanet research.

scholarly journals New Theory of Stellar Convection without the mixing-length parameter: new stellar atmosphere models

2015 ◽  
Vol 11 (A29B) ◽  
pp. 154-155
Author(s):  
Stefano Pasetto ◽  
Cesare Chiosi ◽  
Mark Cropper
Keyword(s):  
Energy Transport ◽  
Surrounding Medium ◽  
Time Dependent ◽  
Length Scale ◽  
The Sun ◽  
Mixing Length ◽  
Local Pressure ◽  
Stellar Convection ◽  
Non Local ◽  
Stellar Models

AbstractStellar convection is customarily described by the mixing-length theory, which makes use of the mixing-length scale to express the convective flux, velocity, and temperature gradients of the convective elements and stellar medium. The mixing-length scale is taken to be proportional to the local pressure scale height, and the proportionality factor (the mixing-length parameter) must be determined by comparing the stellar models to some calibrator, usually the Sun. No strong arguments exist to suggest that the mixing-length parameter is the same in all stars and all evolutionary phases. Because of this, all stellar models in the literature are hampered by this basic uncertainty.In a recent paper (Pasettoet al.2014) we presented a new theory that does not require the mixing length parameter. Our self-consistent analytical formulation of stellar convection determines all the properties of stellar convection as a function of the physical behavior of the convective elements themselves and the surrounding medium. The new theory of stellar convection is formulated starting from a conventional solution of the Navier-Stokes/Euler equations, i.e. the Bernoulli equation for a perfect fluid, but expressed in a non-inertial reference frame co-moving with the convective elements. In our formalism, the motion of stellar convective cells inside convective-unstable layers is fully determined by a new system of equations for convection in a non-local and time-dependent formalism.We obtained an analytical, non-local, time-dependent solution for the convective energy transport that does not depend on any free parameter. The predictions of the new theory are compared with those from the standard mixing-length paradigm with positive results for atmosphere models of the Sun and all the stars in the Hertzsprung-Russell diagram.

scholarly journals Theory of stellar convection: removing the mixing-length parameter

2015 ◽  
Vol 11 (A29B) ◽  
pp. 608-613
Author(s):  
Stefano Pasetto ◽  
Cesare Chiosi ◽  
Mark Cropper ◽  
Eva K. Grebel
Keyword(s):  
Energy Transport ◽  
Surrounding Medium ◽  
Time Dependent ◽  
Length Scale ◽  
The Sun ◽  
Mixing Length ◽  
Local Pressure ◽  
Stellar Convection ◽  
Non Local ◽  
Stellar Models

AbstractStellar convection is customarily described by the mixing-length theory, which makes use of the mixing-length scale to express the convective flux, velocity, and temperature gradients of the convective elements and stellar medium. The mixing-length scale is taken to be proportional to the local pressure scale height, and the proportionality factor (the mixing-length parameter) must be determined by comparing the stellar models to some calibrator, usually the Sun. No strong arguments exist to suggest that the mixing-length parameter is the same in all stars and all evolutionary phases. Because of this, all stellar models in the literature are hampered by this basic uncertainty.In a recent paper (Pasettoet al.2014) we presented a new theory that does not require the mixing length parameter. Our self-consistent analytical formulation of stellar convection determines all the properties of stellar convection as a function of the physical behaviour of the convective elements themselves and the surrounding medium. The new theory of stellar convection is formulated starting from a conventional solution of the Navier-Stokes/Euler equations, i.e. the Bernoulli equation for a perfect fluid, but expressed in a non-inertial reference frame co-moving with the convective elements. In our formalism, the motion of stellar convective cells inside convective-unstable layers is fully determined by a new system of equations for convection in a non-local and time-dependent formalism.We obtained an analytical, non-local, time-dependent solution for the convective energy transport that does not depend on any free parameter. The predictions of the new theory are compared with those from the standard mixing-length paradigm with positive results for atmosphere models of the Sun and all the stars in the Hertzsprung-Russell diagram.

scholarly journals Coupling 1D stellar evolution with 3D-hydrodynamical simulations on-the-fly II: stellar evolution and asteroseismic applications

2019 ◽  
Vol 491 (1) ◽  
pp. 1160-1173 ◽  
Author(s):  
Jakob Rørsted Mosumgaard ◽  
Andreas Christ Sølvsten Jørgensen ◽  
Achim Weiss ◽  
Víctor Silva Aguirre ◽  
Jørgen Christensen-Dalsgaard
Keyword(s):  
Stellar Evolution ◽  
Surface Effect ◽  
Stellar Structure ◽  
Red Giants ◽  
3D Simulations ◽  
Stellar Models ◽  
Red Giant ◽  
Hydrodynamical Simulations ◽  
Indispensable Tool ◽  
Oscillation Frequencies

ABSTRACT Models of stellar structure and evolution are an indispensable tool in astrophysics, yet they are known to incorrectly reproduce the outer convective layers of stars. In the first paper of this series, we presented a novel procedure to include the mean structure of 3D hydrodynamical simulations on-the-fly in stellar models, and found it to significantly improve the outer stratification and oscillation frequencies of a standard solar model. In this work, we extend the analysis of the method; specifically how the transition point between envelope and interior affects the models. We confirm the versatility of our method by successfully repeating the entire procedure for a different grid of 3D hydrosimulations. Furthermore, the applicability of the procedure was investigated across the HR diagram and an accuracy comparable to the solar case was found. Moreover, we explored the implications on stellar evolution and find that the red-giant branch is shifted about $40\, \mathrm{K}$ to higher effective temperatures. Finally, we present for the first time an asteroseismic analysis based on stellar models fully utilizing the stratification of 3D simulations on-the-fly. These new models significantly reduce the asteroseismic surface term for the two selected stars in the Kepler field. We extend the analysis to red giants and characterize the shape of the surface effect in this regime. Lastly, we stress that the interpolation required by our method would benefit from new 3D simulations, resulting in a finer sampling of the grid.

scholarly journals Marketing Mix Modeling Using PLS-SEM, Bootstrapping the Model Coefficients

Mathematics ◽  
2021 ◽  
Vol 9 (15) ◽  
pp. 1832
Author(s):  
Mariano Méndez-Suárez
Keyword(s):  
Time Series ◽  
Structural Changes ◽  
Marketing Mix ◽  
Structural Equations ◽  
Superior Performance ◽  
Parameter Estimates ◽  
Significance Analysis ◽  
Autocorrelation Structure ◽  
Multichannel Retailing ◽  
Black Friday

Partial least squares structural equations modeling (PLS-SEM) uses sampling bootstrapping to calculate the significance of the model parameter estimates (e.g., path coefficients and outer loadings). However, when data are time series, as in marketing mix modeling, sampling bootstrapping shows inconsistencies that arise because the series has an autocorrelation structure and contains seasonal events, such as Christmas or Black Friday, especially in multichannel retailing, making the significance analysis of the PLS-SEM model unreliable. The alternative proposed in this research uses maximum entropy bootstrapping (meboot), a technique specifically designed for time series, which maintains the autocorrelation structure and preserves the occurrence over time of seasonal events or structural changes that occurred in the original series in the bootstrapped series. The results showed that meboot had superior performance than sampling bootstrapping in terms of the coherence of the bootstrapped data and the quality of the significance analysis.

scholarly journals Development of the reproduction number from coronavirus SARS-CoV-2 case data in Germany and implications for political measures

BMC Medicine ◽  
2021 ◽  
Vol 19 (1) ◽  
Author(s):  
Sahamoddin Khailaie ◽  
Tanmay Mitra ◽  
Arnab Bandyopadhyay ◽  
Marta Schips ◽  
Pietro Mascheroni ◽  
...  
Keyword(s):  
Structural Changes ◽  
Reproduction Number ◽  
National Level ◽  
Transmission Dynamics ◽  
Federal State ◽  
Parameter Estimates ◽  
Time Varying ◽  
Short Term ◽  
Robert Koch Institute ◽  
Federal States

Abstract Background SARS-CoV-2 has induced a worldwide pandemic and subsequent non-pharmaceutical interventions (NPIs) to control the spread of the virus. As in many countries, the SARS-CoV-2 pandemic in Germany has led to a consecutive roll-out of different NPIs. As these NPIs have (largely unknown) adverse effects, targeting them precisely and monitoring their effectiveness are essential. We developed a compartmental infection dynamics model with specific features of SARS-CoV-2 that allows daily estimation of a time-varying reproduction number and published this information openly since the beginning of April 2020. Here, we present the transmission dynamics in Germany over time to understand the effect of NPIs and allow adaptive forecasts of the epidemic progression. Methods We used a data-driven estimation of the evolution of the reproduction number for viral spreading in Germany as well as in all its federal states using our model. Using parameter estimates from literature and, alternatively, with parameters derived from a fit to the initial phase of COVID-19 spread in different regions of Italy, the model was optimized to fit data from the Robert Koch Institute. Results The time-varying reproduction number (Rt) in Germany decreased to <1 in early April 2020, 2–3 weeks after the implementation of NPIs. Partial release of NPIs both nationally and on federal state level correlated with moderate increases in Rt until August 2020. Implications of state-specific Rt on other states and on national level are characterized. Retrospective evaluation of the model shows excellent agreement with the data and usage of inpatient facilities well within the healthcare limit. While short-term predictions may work for a few weeks, long-term projections are complicated by unpredictable structural changes. Conclusions The estimated fraction of immunized population by August 2020 warns of a renewed outbreak upon release of measures. A low detection rate prolongs the delay reaching a low case incidence number upon release, showing the importance of an effective testing-quarantine strategy. We show that real-time monitoring of transmission dynamics is important to evaluate the extent of the outbreak, short-term projections for the burden on the healthcare system, and their response to policy changes.

scholarly journals Convective motions as an indicator of solar structure

1984 ◽  
Vol 105 ◽  
pp. 71-74
Author(s):  
R. Van der Borght ◽  
P. Fox
Keyword(s):  
Energy Transport ◽  
Turbulent Energy ◽  
Stellar Structure ◽  
Mixing Length ◽  
Theoretical Formulation ◽  
Solar Structure ◽  
Convective Motions

Most stars contain regions which are convectively unstable and one of the more daunting tasks facing astrophysics today is to find a satisfactory theoretical formulation of turbulent energy transport in stars. Various theories have been proposed, such as the mixing-length formalism and its extensions, and it would be most useful if one could test the accuracy of such models in view of their importance in the theory of stellar structure and evolution.

scholarly journals Bayesian inference of distributed time delay in transcriptional and translational regulation

2019 ◽  
Vol 36 (2) ◽  
pp. 586-593
Author(s):  
Boseung Choi ◽  
Yu-Yu Cheng ◽  
Selahattin Cinar ◽  
William Ott ◽  
Matthew R Bennett ◽  
...  
Keyword(s):  
Bayesian Inference ◽  
Stochastic Systems ◽  
Imaging Techniques ◽  
Reaction Rates ◽  
Biochemical Networks ◽  
Supplementary Information ◽  
Mcmc Methods ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Cell Functions

Abstract Motivation Advances in experimental and imaging techniques have allowed for unprecedented insights into the dynamical processes within individual cells. However, many facets of intracellular dynamics remain hidden, or can be measured only indirectly. This makes it challenging to reconstruct the regulatory networks that govern the biochemical processes underlying various cell functions. Current estimation techniques for inferring reaction rates frequently rely on marginalization over unobserved processes and states. Even in simple systems this approach can be computationally challenging, and can lead to large uncertainties and lack of robustness in parameter estimates. Therefore we will require alternative approaches to efficiently uncover the interactions in complex biochemical networks. Results We propose a Bayesian inference framework based on replacing uninteresting or unobserved reactions with time delays. Although the resulting models are non-Markovian, recent results on stochastic systems with random delays allow us to rigorously obtain expressions for the likelihoods of model parameters. In turn, this allows us to extend MCMC methods to efficiently estimate reaction rates, and delay distribution parameters, from single-cell assays. We illustrate the advantages, and potential pitfalls, of the approach using a birth–death model with both synthetic and experimental data, and show that we can robustly infer model parameters using a relatively small number of measurements. We demonstrate how to do so even when only the relative molecule count within the cell is measured, as in the case of fluorescence microscopy. Availability and implementation Accompanying code in R is available at https://github.com/cbskust/DDE_BD. Supplementary information Supplementary data are available at Bioinformatics online.

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