scholarly journals Sensitivity analysis of Wasserstein distributionally robust optimization problems

2021 ◽  
Vol 477 (2256) ◽  
Author(s):  
Daniel Bartl ◽  
Samuel Drapeau ◽  
Jan Obłój ◽  
Johannes Wiesel
Keyword(s):  
Model Uncertainty ◽  
Optimization Problems ◽  
Order Approximation ◽  
Mathematical Finance ◽  
Ordinary Least Squares ◽  
Linear Constraints ◽  
Least Squares Regression ◽  
Lasso Regression ◽  
First Order ◽  
Non Parametric

We consider sensitivity of a generic stochastic optimization problem to model uncertainty. We take a non-parametric approach and capture model uncertainty using Wasserstein balls around the postulated model. We provide explicit formulae for the first-order correction to both the value function and the optimizer and further extend our results to optimization under linear constraints. We present applications to statistics, machine learning, mathematical finance and uncertainty quantification. In particular, we provide an explicit first-order approximation for square-root LASSO regression coefficients and deduce coefficient shrinkage compared to the ordinary least-squares regression. We consider robustness of call option pricing and deduce a new Black–Scholes sensitivity, a non-parametric version of the so-called Vega. We also compute sensitivities of optimized certainty equivalents in finance and propose measures to quantify robustness of neural networks to adversarial examples.

scholarly journals First-order sensitivity of the optimal value in a Markov decision model with respect to deviations in the transition probability function

2020 ◽  
Vol 92 (1) ◽  
pp. 165-197 ◽  
Author(s):  
Patrick Kern ◽  
Axel Simroth ◽  
Henryk Zähle
Keyword(s):  
Optimization Problems ◽  
Transition Probabilities ◽  
Broad Class ◽  
Transition Probability ◽  
Mathematical Finance ◽  
Model Complexity ◽  
First Order ◽  
Optimal Value ◽  
Markov Decision ◽  
Markov Decision Model

Abstract Markov decision models (MDM) used in practical applications are most often less complex than the underlying ‘true’ MDM. The reduction of model complexity is performed for several reasons. However, it is obviously of interest to know what kind of model reduction is reasonable (in regard to the optimal value) and what kind is not. In this article we propose a way how to address this question. We introduce a sort of derivative of the optimal value as a function of the transition probabilities, which can be used to measure the (first-order) sensitivity of the optimal value w.r.t. changes in the transition probabilities. ‘Differentiability’ is obtained for a fairly broad class of MDMs, and the ‘derivative’ is specified explicitly. Our theoretical findings are illustrated by means of optimization problems in inventory control and mathematical finance.

Improved first-order approximation of eigenvalues and eigenvectors

AIAA Journal ◽  
1998 ◽  
Vol 36 ◽  
pp. 1721-1727
Author(s):  
Prasanth B. Nair ◽  
Andrew J. Keane ◽  
Robin S. Langley
Keyword(s):  
Order Approximation ◽  
Eigenvalues And Eigenvectors ◽  
First Order ◽  
First Order Approximation

scholarly journals Least Likely Observations in Regression Models for Categorical Outcomes

2002 ◽  
Vol 2 (3) ◽  
pp. 296-300 ◽  
Author(s):  
Jeremy Freese
Keyword(s):  
Logistic Regression ◽  
Regression Models ◽  
Binary Logistic Regression ◽  
Positive Outcome ◽  
Ordinary Least Squares ◽  
Parameter Estimates ◽  
Least Squares Regression ◽  
Binary Logistic Regression Model ◽  
Ordered Logistic Regression ◽  
Negative Outcome

This article presents a method and program for identifying poorly fitting observations for maximum-likelihood regression models for categorical dependent variables. After estimating a model, the program leastlikely will list the observations that have the lowest predicted probabilities of observing the value of the outcome category that was actually observed. For example, when run after estimating a binary logistic regression model, leastlikely will list the observations with a positive outcome that had the lowest predicted probabilities of a positive outcome and the observations with a negative outcome that had the lowest predicted probabilities of a negative outcome. These can be considered the observations in which the outcome is most surprising given the values of the independent variables and the parameter estimates and, like observations with large residuals in ordinary least squares regression, may warrant individual inspection. Use of the program is illustrated with examples using binary and ordered logistic regression.

Home Health Agencies: Empirical Evidence on the Patient-Driven Groupings Model’s Expected Effects on Agency Reimbursements

2021 ◽  
pp. 108482232199038
Author(s):  
Elizabeth Plummer ◽  
William F. Wempe
Keyword(s):  
Ordinary Least Squares ◽  
Process Quality ◽  
Home Health ◽  
Least Squares Regression ◽  
Residual Variation ◽  
Health Agencies ◽  
Dual Eligible ◽  
Home Health Agencies ◽  
Seriously Ill Patients ◽  
Seriously Ill

Beginning January 1, 2020, Medicare’s Patient-Driven Groupings Model (PDGM) eliminated therapy as a direct determinant of Home Health Agencies’ (HHAs’) reimbursements. Instead, PDGM advances Medicare’s shift toward value-based payment models by directly linking HHAs’ reimbursements to patients’ medical conditions. We use 3 publicly-available datasets and ordered logistic regression to examine the associations between HHAs’ pre-PDGM provision of therapy and their other agency, patient, and quality characteristics. Our study therefore provides evidence on PDGM’s likely effects on HHA reimbursements assuming current patient populations and service levels do not change. We find that PDGM will likely increase payments to rural and facility-based HHAs, as well as HHAs serving greater proportions of non-white, dual-eligible, and seriously ill patients. Payments will also increase for HHAs scoring higher on quality surveys, but decrease for HHAs with higher outcome and process quality scores. We also use ordinary least squares regression to examine residual variation in HHAs’ expected reimbursement changes under PDGM, after accounting for any expected changes related to their pre-PDGM levels of therapy provision. We find that larger and rural HHAs will likely experience residual payment increases under PDGM, as will HHAs with greater numbers of seriously ill, younger, and non-white patients. HHAs with higher process quality, but lower outcome quality, will similarly benefit from PDGM. Understanding how PDGM affects HHAs is crucial as policymakers seek ways to increase equitable access to safe and affordable non-facility-provided healthcare that provides appropriate levels of therapy, nursing, and other care.

scholarly journals Predicting presenteeism using measures of health status

2021 ◽  
Author(s):  
Cheryl Jones ◽  
Katherine Payne ◽  
Alexander Thompson ◽  
Suzanne M. M. Verstappen
Keyword(s):  
Health Status ◽  
Online Survey ◽  
Activity Index ◽  
Work Productivity ◽  
Rank Correlation ◽  
Ordinary Least Squares ◽  
Statistical Correlation ◽  
Least Squares Regression ◽  
Mapping Algorithm ◽  
Spearman’S Rank Correlation

Abstract Objectives To identify whether it is feasible to develop a mapping algorithm to predict presenteeism using multiattribute measures of health status. Methods Data were collected using a bespoke online survey in a purposive sample (n = 472) of working individuals with a self-reported diagnosis of Rheumatoid arthritis (RA). Survey respondents were recruited using an online panel company (ResearchNow). This study used data captured using two multiattribute measures of health status (EQ5D-5 level; SF6D) and a measure of presenteeism (WPAI, Work Productivity Activity Index). Statistical correlation between the WPAI and the two measures of health status (EQ5D-5 level; SF6D) was assessed using Spearman’s rank correlation. Five regression models were estimated to quantify the relationship between WPAI and predict presenteeism using health status. The models were specified based in index and domain scores and included covariates (age; gender). Estimated and observed presenteeism were compared using tenfold cross-validation and evaluated using Root mean square error (RMSE). Results A strong and negative correlation was found between WPAI and: EQ5D-5 level and WPAI (r = − 0.64); SF6D (r =− 0.60). Two models, using ordinary least squares regression were identified as the best performing models specifying health status using: SF6D domains with age interacted with gender (RMSE = 1.7858); EQ5D-5 Level domains and age interacted with gender (RMSE = 1.7859). Conclusions This study provides indicative evidence that two existing measures of health status (SF6D and EQ5D-5L) have a quantifiable relationship with a measure of presenteeism (WPAI) for an exemplar application of working individuals with RA. A future study should assess the external validity of the proposed mapping algorithms.

From Measures of Association to Multilevel Models: Sociology Journals and the Quantitative Literacy Gap

2020 ◽  
pp. 0092055X2098042
Author(s):  
Thomas J. Linneman
Keyword(s):  
Multilevel Models ◽  
Ordinary Least Squares ◽  
Quantitative Literacy ◽  
Least Squares Regression ◽  
Journal Articles ◽  
Measures Of Association ◽  
Chi Square ◽  
Literacy Gap ◽  
Statistics Course ◽  
Sociology Journals

While most sociology majors must take a statistics course, the content of this course varies widely across departments. Starting from the assumption that sociology students should be able to engage effectively with the sociological literature, this article examines the statistical techniques used in 2,804 journal articles—from four generalist sociology journals from 1990 to 2019 and 11 additional sociology journals from 2019—in order to assess which techniques have risen or fallen in prevalence. Although stalwarts such as ordinary least squares regression, chi-square tests, and t tests maintain strong presences, the rise of logistic regression, interaction effects, and multilevel models has been dramatic. After assessing the proportion of articles students hypothetically could understand given various levels of statistical training, the article ends with suggestions for how to revamp the statistics course to help our students become more numerate citizens, both in their sociology courses and in the world at large.

Analytical solution for unsteady flow behind ionizing shock wave in a rotational axisymmetric non-ideal gas with azimuthal or axial magnetic field

2021 ◽  
Vol 76 (3) ◽  
pp. 265-283
Author(s):  
G. Nath
Keyword(s):  
Magnetic Field ◽  
Shock Wave ◽  
Analytical Solution ◽  
Axial Magnetic Field ◽  
Order Approximation ◽  
Ideal Gas ◽  
Field Region ◽  
First Order ◽  
First Order Approximation ◽  
Flow Variables

Abstract The approximate analytical solution for the propagation of gas ionizing cylindrical blast (shock) wave in a rotational axisymmetric non-ideal gas with azimuthal or axial magnetic field is investigated. The axial and azimuthal components of fluid velocity are taken into consideration and these flow variables, magnetic field in the ambient medium are assumed to be varying according to the power laws with distance from the axis of symmetry. The shock is supposed to be strong one for the ratio C 0 V s 2 ${\left(\frac{{C}_{0}}{{V}_{s}}\right)}^{2}$ to be a negligible small quantity, where C 0 is the sound velocity in undisturbed fluid and V S is the shock velocity. In the undisturbed medium the density is assumed to be constant to obtain the similarity solution. The flow variables in power series of C 0 V s 2 ${\left(\frac{{C}_{0}}{{V}_{s}}\right)}^{2}$ are expanded to obtain the approximate analytical solutions. The first order and second order approximations to the solutions are discussed with the help of power series expansion. For the first order approximation the analytical solutions are derived. In the flow-field region behind the blast wave the distribution of the flow variables in the case of first order approximation is shown in graphs. It is observed that in the flow field region the quantity J 0 increases with an increase in the value of gas non-idealness parameter or Alfven-Mach number or rotational parameter. Hence, the non-idealness of the gas and the presence of rotation or magnetic field have decaying effect on shock wave.

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