scholarly journals A robust and efficient algorithm to find profile likelihood confidence intervals

2021 ◽  
Vol 31 (4) ◽  
Author(s):  
Samuel M. Fischer ◽  
Mark A. Lewis
Keyword(s):  
Confidence Intervals ◽  
Likelihood Function ◽  
Profile Likelihood ◽  
Asymptotic Properties ◽  
Trust Region ◽  
Benchmark Problems ◽  
Success Rates ◽  
Wide Range ◽  
Local Approximations ◽  
Model Predictions

AbstractProfile likelihood confidence intervals are a robust alternative to Wald’s method if the asymptotic properties of the maximum likelihood estimator are not met. However, the constrained optimization problem defining profile likelihood confidence intervals can be difficult to solve in these situations, because the likelihood function may exhibit unfavorable properties. As a result, existing methods may be inefficient and yield misleading results. In this paper, we address this problem by computing profile likelihood confidence intervals via a trust-region approach, where steps computed based on local approximations are constrained to regions where these approximations are sufficiently precise. As our algorithm also accounts for numerical issues arising if the likelihood function is strongly non-linear or parameters are not estimable, the method is applicable in many scenarios where earlier approaches are shown to be unreliable. To demonstrate its potential in applications, we apply our algorithm to benchmark problems and compare it with 6 existing approaches to compute profile likelihood confidence intervals. Our algorithm consistently achieved higher success rates than any competitor while also being among the quickest methods. As our algorithm can be applied to compute both confidence intervals of parameters and model predictions, it is useful in a wide range of scenarios.

scholarly journals Dwarf spheroidal J-factor likelihoods for generalized NFW profiles

2019 ◽  
Vol 488 (2) ◽  
pp. 2616-2628 ◽  
Author(s):  
A Chiappo ◽  
J Cohen-Tanugi ◽  
J Conrad ◽  
L E Strigari
Keyword(s):  
Likelihood Function ◽  
Profile Likelihood ◽  
Indirect Detection ◽  
Maximum Likelihood Estimates ◽  
Large Area ◽  
Bayesian Techniques ◽  
Upper Limits ◽  
Model Predictions ◽  
Profile Likelihoods ◽  
Detection Strategies

ABSTRACT Indirect detection strategies of particle dark matter (DM) in Dwarf spheroidal satellite galaxies (dSphs) typically entail searching for annihilation signals above the astrophysical background. To robustly compare model predictions with the observed fluxes of product particles, most analyses of astrophysical data – which are generally frequentist – rely on estimating the abundance of DM by calculating the so-called J factor. This quantity is usually inferred from the kinematic properties of the stellar population of a dSph using the Jeans equation, commonly by means of Bayesian techniques that entail the presence (and additional systematic uncertainty) of prior choice. Here, extending earlier work, we develop a scheme to derive the profile likelihood for J factors of dwarf spheroidals for models with five or more free parameters. We validate our method on a publicly available simulation suite, released by the Gaia Challenge, finding satisfactory statistical properties for bias and probability coverage. We present the profile likelihood function and maximum likelihood estimates for the J-factor of 10 dSphs. As an illustration, we apply these profile likelihoods to recently published analyses of γ-ray data with the Fermi Large Area Telescope to derive new, consistent upper limits on the DM annihilation cross-section. We do this for a subset of systems, generally referred to as classical dwarfs. The implications of these findings for DM searches are discussed, together with future improvements and extensions of this technique.

scholarly journals Monte Carlo profile confidence intervals for dynamic systems

2017 ◽  
Vol 14 (132) ◽  
pp. 20170126 ◽  
Author(s):  
E. L. Ionides ◽  
C. Breto ◽  
J. Park ◽  
R. A. Smith ◽  
A. A. King
Keyword(s):  
Time Series ◽  
Monte Carlo ◽  
Confidence Intervals ◽  
Latent Variable ◽  
Dynamic Models ◽  
Likelihood Function ◽  
Profile Likelihood ◽  
Theory And Practice ◽  
Standard Theory ◽  
Series Data

Monte Carlo methods to evaluate and maximize the likelihood function enable the construction of confidence intervals and hypothesis tests, facilitating scientific investigation using models for which the likelihood function is intractable. When Monte Carlo error can be made small, by sufficiently exhaustive computation, then the standard theory and practice of likelihood-based inference applies. As datasets become larger, and models more complex, situations arise where no reasonable amount of computation can render Monte Carlo error negligible. We develop profile likelihood methodology to provide frequentist inferences that take into account Monte Carlo uncertainty. We investigate the role of this methodology in facilitating inference for computationally challenging dynamic latent variable models. We present examples arising in the study of infectious disease transmission, demonstrating our methodology for inference on nonlinear dynamic models using genetic sequence data and panel time-series data. We also discuss applicability to nonlinear time-series and spatio-temporal data.

scholarly journals Pairwise meta-analysis of aggregate data using metaan in Stata

2020 ◽  
Vol 20 (3) ◽  
pp. 680-705
Author(s):  
Evangelos Kontopantelis ◽  
David Reeves
Keyword(s):  
Maximum Likelihood ◽  
Random Effects ◽  
Likelihood Function ◽  
Profile Likelihood ◽  
Meta Analysis ◽  
Aggregate Data ◽  
Wide Range ◽  
New Models ◽  
Analysis Models ◽  
Likelihood Profile

A few years ago, we developed metaan, a package to perform fixedor random-effects meta-analysis. In terms of random-effects meta-analysis, it offered a wide choice of models, including maximum likelihood, profile likelihood, or restricted maximum-likelihood, in addition to the established DerSimonian–Laird method available in metan or Cochrane’s RevMan software. Other unique features included a wide range of reported heterogeneity measures and a plot of the maximum likelihood function. Since then, metaan has been continuously updated to offer improved graphics, more options, and more meta-analysis models. In this necessary update, we describe these additions and discuss the new models and the evidence behind them.

scholarly journals A Method for Confidence Intervals of High Quantiles

Entropy ◽  
2021 ◽  
Vol 23 (1) ◽  
pp. 70
Author(s):  
Mei Ling Huang ◽  
Xiang Raney-Yan
Keyword(s):  
Confidence Intervals ◽  
Computational Algorithm ◽  
Geometric Mean ◽  
Asymptotic Properties ◽  
Quantile Estimation ◽  
Heavy Tailed Distributions ◽  
High Quantiles ◽  
High Quantile ◽  
Heavy Tailed ◽  
Infinite Moments

The high quantile estimation of heavy tailed distributions has many important applications. There are theoretical difficulties in studying heavy tailed distributions since they often have infinite moments. There are also bias issues with the existing methods of confidence intervals (CIs) of high quantiles. This paper proposes a new estimator for high quantiles based on the geometric mean. The new estimator has good asymptotic properties as well as it provides a computational algorithm for estimating confidence intervals of high quantiles. The new estimator avoids difficulties, improves efficiency and reduces bias. Comparisons of efficiencies and biases of the new estimator relative to existing estimators are studied. The theoretical are confirmed through Monte Carlo simulations. Finally, the applications on two real-world examples are provided.

scholarly journals Trust-Region Based Penalty Barrier Algorithm for Constrained Nonlinear Programming Problems: An Application of Design of Minimum Cost Canal Sections

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1551
Author(s):  
Bothina El-Sobky ◽  
Yousria Abo-Elnaga ◽  
Abd Allah A. Mousa ◽  
Mohamed A. El-Shorbagy
Keyword(s):  
Nonlinear Programming ◽  
Global Convergence ◽  
Programming Problem ◽  
Trust Region ◽  
Convergence Theory ◽  
Benchmark Problems ◽  
Nonlinear Programming Problem ◽  
Barrier Method ◽  
Starting Point ◽  
Constrained Nonlinear Programming

In this paper, a penalty method is used together with a barrier method to transform a constrained nonlinear programming problem into an unconstrained nonlinear programming problem. In the proposed approach, Newton’s method is applied to the barrier Karush–Kuhn–Tucker conditions. To ensure global convergence from any starting point, a trust-region globalization strategy is used. A global convergence theory of the penalty–barrier trust-region (PBTR) algorithm is studied under four standard assumptions. The PBTR has new features; it is simpler, has rapid convergerce, and is easy to implement. Numerical simulation was performed on some benchmark problems. The proposed algorithm was implemented to find the optimal design of a canal section for minimum water loss for a triangle cross-section application. The results are promising when compared with well-known algorithms.

Near-Wall Microlayer Evaporation Analysis and Experimental Study of Nucleate Pool Boiling on Inclined Surfaces

1998 ◽  
Vol 120 (3) ◽  
pp. 641-653 ◽  
Author(s):  
G. F. Naterer ◽  
W. Hendradjit ◽  
K. J. Ahn ◽  
J. E. S. Venart
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Heating Surface ◽  
Nucleate Boiling ◽  
Inclined Surfaces ◽  
Wide Range ◽  
Model Predictions ◽  
Microlayer Evaporation ◽  
Near Wall

Boiling heat transfer from inclined surfaces is examined and an analytical model of bubble growth and nucleate boiling is presented. The model predicts the average heat flux during nucleate boiling by considering alternating near-wall liquid and vapor periods. It expresses the heat flux in terms of the bubble departure diameter, frequency and duration of contact with the heating surface. Experiments were conducted over a wide range of upward and downward-facing surface orientations and the results were compared to model predictions. More active microlayer agitation and mixing along the surface as well as more frequent bubble sweeps along the heating surface provide the key reasons for more effective heat transfer with downward facing surfaces as compared to upward facing cases. Additional aspects of the role of surface inclination on boiling dynamics are quantified and discussed.

Uncertainty in Collapse Strength Prediction of Sandwich Pipelines

2021 ◽  
Author(s):  
U. Bhardwaj ◽  
A. P. Teixeira ◽  
C. Guedes Soares
Keyword(s):  
Probabilistic Models ◽  
Uncertainty Propagation ◽  
Simulation Method ◽  
External Pressure ◽  
Design Parameters ◽  
Collapse Strength ◽  
Parameters Uncertainty ◽  
Wide Range ◽  
Model Predictions ◽  
Strength Models

Abstract This paper assesses the uncertainty in the collapse strength of sandwich pipelines under external pressure predicted by various strength models in three categories based on interlayer adhesion conditions. First, the validity of the strength models is verified by comparing their predictions with sandwich pipeline collapse test data and the corresponding model uncertainty factors are derived. Then, a parametric analysis of deterministic collapse strength predictions by models is conducted, illustrating insights of models’ behaviour for a wide range of design configurations. Furthermore, the uncertainty among different model predictions is perceived at different configurations of outer and inner pipes and core thicknesses. A case study of a realistic sandwich pipeline is developed, and probabilistic models are defined to basic design parameters. Uncertainty propagation of models’ predictions is assessed by the Monte Carlo simulation method. Finally, the strength model predictions of sandwich pipelines are compared to that of an equivalent single walled pipe.

scholarly journals Characterizing global expansion evolution of the ionized matter in planetary nebulae

2016 ◽  
Vol 12 (S323) ◽  
pp. 352-353
Author(s):  
J. A. López ◽  
M. G. Richer ◽  
M. Pereyra ◽  
M. T. García-Díaz
Keyword(s):  
Galactic Halo ◽  
Evolutionary Rate ◽  
Planetary Nebulae ◽  
Central Star ◽  
Global Expansion ◽  
Kinematic Evolution ◽  
Wide Range ◽  
Model Predictions ◽  
First Time ◽  
Highly Evolved

AbstractBulk outflow or global expansion velocities are presented for a large number of planetary nebulae (PNe) that span a wide range of evolutionary stages and different stellar populations. The sample comprises 133 PNe from the Galactic bulge, 100 mature and highly evolved PNe from the disk, 11 PNe from the Galactic halo and 15 PNe with very low central star masses and low metallicities, for a total of 259 PNe. These results reveal from a statistical perspective the kinematic evolution of the expansion velocities of PNe in relation to changing characteristics of the central star’s wind and ionizing luminosity and as a function of the evolutionary rate determined by the central (CS) mass. The large number of PNe utilized in this work for each group of PNe under study and the homogeneity of the data provide for the first time a solid benchmark form observations for model predictions, as has been described by López et al. (2016).

Comparison of Four Friction Models: Feature Prediction

2015 ◽  
Vol 11 (3) ◽  
Author(s):  
Yun-Hsiang Sun ◽  
Tao Chen ◽  
Christine Qiong Wu ◽  
Cyrus Shafai
Keyword(s):  
Numerical Model ◽  
Viscous Friction ◽  
Friction Model ◽  
Dynamic Features ◽  
Numerical Predictions ◽  
Wide Range ◽  
Model Predictions ◽  
Friction Models ◽  
Parameter Identifications ◽  
Model Structures

In this paper, we provide not only key knowledge for friction model selection among candidate models but also experimental friction features compared with numerical predictions reproduced by the candidate models. A motor-driven one-dimensional sliding block has been designed and fabricated in our lab to carry out a wide range of control tasks for the friction feature demonstrations and the parameter identifications of the candidate models. Besides the well-known static features such as break-away force and viscous friction, our setup experimentally demonstrates subtle dynamic features that characterize the physical behavior. The candidate models coupled with correct parameters experimentally obtained from our setup are taken to simulate the features of interest. The first part of this work briefly introduces the candidate friction models, the friction features of interest, and our experimental approach. The second part of this work is dedicated to the comparisons between the experimental features and the numerical model predictions. The discrepancies between the experimental features and the numerical model predictions help researchers to judge the accuracy of the models. The relation between the candidate model structures and their numerical friction feature predictions is investigated and discussed. A table that summarizes how to select the most optimal friction model among a variety of engineering applications is presented at the end of this paper. Such comprehensive comparisons have not been reported in previous literature.

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