Regularized Regression for Reserving and Mortality Models

2018 ◽  
Vol 13 (2) ◽  
Author(s):  
Gary Venter
Keyword(s):  
Goodness Of Fit ◽  
Linear Models ◽  
Model Parameters ◽  
Regularized Regression ◽  
Linear Modeling ◽  
Estimation Errors ◽  
Smooth Curves ◽  
Lower Estimation ◽  
Mortality Models ◽  
Loss Reserving

Abstract Bayesian regularization, a relatively new method for estimating model parameters, shrinks estimates towards the overall mean by shrinking the parameters. It has been proven to lower estimation and prediction variances from those of MLE for linear models, such as regression or GLM. It has a goodness-of-fit measure, and can readily be applied using available software. This can be used for any type of actuarial linear modeling, but it is slightly more complicated for mortality and loss reserving models that use row, column, and diagonal effects for array data. These are called age-period-cohort, or APC models by statisticians. The problem is that the row, column and diagonal effects are not what should be shrunk. These models can easily become over-parameterized, and actuaries often reduce parameters with smooth curves or cubic splines. We discuss an alternative smoothing method that uses regularization, with its reduction in estimation errors, and illustrate both its classical and Bayesian forms and their application to APC modeling. Typical actuarial models and some generalizations are used as examples.

Estimation and Inference Are Missing Data Problems: Unifying Social Science Statistics via Bayesian Simulation

2000 ◽  
Vol 8 (4) ◽  
pp. 307-332 ◽  
Author(s):  
Simon Jackman
Keyword(s):  
Missing Data ◽  
Social Science ◽  
Goodness Of Fit ◽  
Linear Models ◽  
Likelihood Estimation ◽  
Model Parameters ◽  
Data Sampling ◽  
Fit Statistics ◽  
Bill Cosponsorship ◽  
Bayesian Simulation

Bayesian simulation is increasingly exploited in the social sciences for estimation and inference of model parameters. But an especially useful (if often overlooked) feature of Bayesian simulation is that it can be used to estimate any function of model parameters, including “auxiliary” quantities such as goodness-of-fit statistics, predicted values, and residuals. Bayesian simulation treats these quantities as if they were missing data, sampling from their implied posterior densities. Exploiting this principle also lets researchers estimate models via Bayesian simulation where maximum-likelihood estimation would be intractable. Bayesian simulation thus provides a unified solution for quantitative social science. I elaborate these ideas in a variety of contexts: these include generalized linear models for binary responses using data on bill cosponsorship recently reanalyzed in Political Analysis, item—response models for the measurement of respondent's levels of political information in public opinion surveys, the estimation and analysis of legislators' ideal points from roll-call data, and outlier-resistant regression estimates of incumbency advantage in U.S. Congressional elections

Algorithm 1017

2021 ◽  
Vol 47 (3) ◽  
pp. 1-18
Author(s):  
Pavel Škrabánek ◽  
Natália Martínková
Keyword(s):  
Linear Regression ◽  
Goodness Of Fit ◽  
Fuzzy Numbers ◽  
Linear Models ◽  
Total Error ◽  
Estimation Method ◽  
Fuzzy Regression ◽  
Model Parameters ◽  
Statistical Regression ◽  
Fuzzy Linear Regression

Fuzzy regression provides an alternative to statistical regression when the model is indefinite, the relationships between model parameters are vague, the sample size is low, or the data are hierarchically structured. Such cases allow to consider the choice of a regression model based on the fuzzy set theory. In fuzzyreg, we implement fuzzy linear regression methods that differ in the expectations of observational data types, outlier handling, and parameter estimation method. We provide a wrapper function that prepares data for fitting fuzzy linear models with the respective methods from a syntax established in R for fitting regression models. The function fuzzylm thus provides a novel functionality for R through standardized operations with fuzzy numbers. Additional functions allow for conversion of real-value variables to be fuzzy numbers, printing, summarizing, model plotting, and calculation of model predictions from new data using supporting functions that perform arithmetic operations with triangular fuzzy numbers. Goodness of fit and total error of the fit measures allow model comparisons. The package contains a dataset named bats with measurements of temperatures of hibernating bats and the mean annual surface temperature reflecting the climate at the sampling sites. The predictions from fuzzy linear models fitted to this dataset correspond well to the observed biological phenomenon. Fuzzy linear regression has great potential in predictive modeling where the data structure prevents statistical analysis and the modeled process exhibits inherent fuzziness.

Evaluating the Goodness of Fit of Stochastic Mortality Models

2009 ◽  
Author(s):  
Kevin Dowd ◽  
Andrew J. G. Cairns ◽  
David P. Blake ◽  
Guy Coughlan ◽  
David Epstein ◽  
...  
Keyword(s):  
Goodness Of Fit ◽  
Stochastic Mortality ◽  
Stochastic Mortality Models ◽  
Mortality Models

Behavioral Referents for Molar Ratings of Heterosocial Skill

1982 ◽  
Vol 50 (1) ◽  
pp. 139-146 ◽  
Author(s):  
W. Stephen Royce
Keyword(s):  
Multiple Regression ◽  
Linear Models ◽  
Eye Contact ◽  
Regression Analyses ◽  
Linear Modeling ◽  
Hand Gestures ◽  
Men And Women ◽  
Behavioral Cues ◽  
Wide Range ◽  
Highly Skilled

A linear modeling technique was used to identify valid behavioral referents of molar heterosocial skill ratings in both men and women. Videotapes of the heterosocial interactions of 30 men and 30 women representing a wide range of skill were shown to untrained peers who made molar heterosocial skill ratings and supplied lists of the behavioral cues they believed to be useful in discriminating skillful and unskillful subjects. The most widely endorsed cues were then scored for their rates of occurrence in the target subjects' interactions, and multiple regression analyses were used to construct linear models of behavioral referents for the molar heterosocial skill ratings. Highly skilled men were those who kept their gaze up, asked questions, and used appropriate hand gestures. Highly skilled women were those who kept their gaze up, made eye contact, and avoided speaking too softly.

scholarly journals Evaluating performances of simplified physically based models for landslide susceptibility

2015 ◽  
Vol 12 (12) ◽  
pp. 13217-13256 ◽  
Author(s):  
G. Formetta ◽  
G. Capparelli ◽  
P. Versace
Keyword(s):  
Landslide Susceptibility ◽  
Goodness Of Fit ◽  
Shallow Landslides ◽  
Model Parameters ◽  
Test Case ◽  
Susceptibility Analysis ◽  
Physically Based ◽  
Private And Public ◽  
Physically Based Models

Abstract. Rainfall induced shallow landslides cause loss of life and significant damages involving private and public properties, transportation system, etc. Prediction of shallow landslides susceptible locations is a complex task that involves many disciplines: hydrology, geotechnical science, geomorphology, and statistics. Usually to accomplish this task two main approaches are used: statistical or physically based model. Reliable models' applications involve: automatic parameters calibration, objective quantification of the quality of susceptibility maps, model sensitivity analysis. This paper presents a methodology to systemically and objectively calibrate, verify and compare different models and different models performances indicators in order to individuate and eventually select the models whose behaviors are more reliable for a certain case study. The procedure was implemented in package of models for landslide susceptibility analysis and integrated in the NewAge-JGrass hydrological model. The package includes three simplified physically based models for landslides susceptibility analysis (M1, M2, and M3) and a component for models verifications. It computes eight goodness of fit indices by comparing pixel-by-pixel model results and measurements data. Moreover, the package integration in NewAge-JGrass allows the use of other components such as geographic information system tools to manage inputs-output processes, and automatic calibration algorithms to estimate model parameters. The system was applied for a case study in Calabria (Italy) along the Salerno-Reggio Calabria highway, between Cosenza and Altilia municipality. The analysis provided that among all the optimized indices and all the three models, the optimization of the index distance to perfect classification in the receiver operating characteristic plane (D2PC) coupled with model M3 is the best modeling solution for our test case.

scholarly journals Estimation of baseflow parameters of variable infiltration capacity model with soil and topography properties for predictions in ungauged basins

2011 ◽  
Vol 8 (4) ◽  
pp. 7017-7053 ◽  
Author(s):  
Z. Bao ◽  
J. Liu ◽  
J. Zhang ◽  
G. Fu ◽  
G. Wang ◽  
...  
Keyword(s):  
Goodness Of Fit ◽  
Model Simulation ◽  
Parameters Estimation ◽  
Model Parameters ◽  
Ungauged Basins ◽  
Variable Infiltration Capacity ◽  
Infiltration Capacity ◽  
Ungauged Catchments ◽  
Vic Model ◽  
Predictions In Ungauged Basins

Abstract. Equifinality is unavoidable when transferring model parameters from gauged catchments to ungauged catchments for predictions in ungauged basins (PUB). A framework for estimating the three baseflow parameters of variable infiltration capacity (VIC) model, directly with soil and topography properties is presented. When the new parameters setting methodology is used, the number of parameters needing to be calibrated is reduced from six to three, that leads to a decrease of equifinality and uncertainty. This is validated by Monte Carlo simulations in 24 hydro-climatic catchments in China. Using the new parameters estimation approach, model parameters become more sensitive and the extent of parameters space will be smaller when a threshold of goodness-of-fit is given. That means the parameters uncertainty is reduced with the new parameters setting methodology. In addition, the uncertainty of model simulation is estimated by the generalised likelihood uncertainty estimation (GLUE) methodology. The results indicate that the uncertainty of streamflow simulations, i.e., confidence interval, is lower with the new parameters estimation methodology compared to that used by original calibration methodology. The new baseflow parameters estimation framework could be applied in VIC model and other appropriate models for PUB.

scholarly journals Analytical and Numerical Connections between Fractional Fickian and Intravoxel Incoherent Motion Models of Diffusion MRI

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1963
Author(s):  
Jingting Yao ◽  
Muhammad Ali Raza Anjum ◽  
Anshuman Swain ◽  
David A. Reiter
Keyword(s):  
Skeletal Muscle ◽  
Goodness Of Fit ◽  
Numerical Models ◽  
Tissue Perfusion ◽  
Parametric Models ◽  
Intravoxel Incoherent Motion ◽  
Fickian Diffusion ◽  
Model Parameters ◽  
Mathematical Framework ◽  
Stretched Exponential

Impaired tissue perfusion underlies many chronic disease states and aging. Diffusion-weighted imaging (DWI) is a noninvasive MRI technique that has been widely used to characterize tissue perfusion. Parametric models based on DWI measurements can characterize microvascular perfusion modulated by functional and microstructural alterations in the skeletal muscle. The intravoxel incoherent motion (IVIM) model uses a biexponential form to quantify the incoherent motion of water molecules in the microvasculature at low b-values of DWI measurements. The fractional Fickian diffusion (FFD) model is a parsimonious representation of anomalous superdiffusion that uses the stretched exponential form and can be used to quantify the microvascular volume of skeletal muscle. Both models are established measures of perfusion based on DWI, and the prognostic value of model parameters for identifying pathophysiological processes has been studied. Although the mathematical properties of individual models have been previously reported, quantitative connections between IVIM and FFD models have not been examined. This work provides a mathematical framework for obtaining a direct, one-way transformation of the parameters of the stretched exponential model to those of the biexponential model. Numerical simulations are implemented, and the results corroborate analytical results. Additionally, analysis of in vivo DWI measurements in skeletal muscle using both biexponential and stretched exponential models is shown and compared with analytical and numerical models. These results demonstrate the difficulty of model selection based on goodness of fit to experimental data. This analysis provides a framework for better interpreting and harmonizing perfusion parameters from experimental results using these two different models.

scholarly journals Flight crew diagnostic using aviation simulator training data

2016 ◽  
Vol 9 (3) ◽  
pp. 118-137
Author(s):  
L.S. Kuravsky ◽  
P.A. Marmalyuk ◽  
G.A. Yuryev ◽  
O.B. Belyaeva ◽  
O.Yu. Prokopieva
Keyword(s):  
Continuous Time ◽  
Goodness Of Fit ◽  
Training Data ◽  
Simulator Training ◽  
Model Parameters ◽  
Flight Crew ◽  
Advantages And Disadvantages ◽  
Goodness Of Fit Tests ◽  
Flight Simulators ◽  
Discrete States

This paper describes a new concept of flight crew assessment based on flight simulators training result. It is based on representation of pilot gaze movement with the aid of continuous-time Markov processes with discrete states. Considered are both the procedure of model parameters identification provided with goodness-of-fit tests in use and the classifier-building technique, which makes it possible to estimate degree of correspondence between the observed gaze motion distribution under study and reference distributions identified for different diagnosed groups. The final assessing criterion is formed on the basis of integrated diagnostic parameters, which are determined by the parameters of the identified models. The article provides a description of the experiment, illustrations, and results of studies aimed at assessing the reliability of the developed models and criteria, as well as conclusions about the applicability of the approach, its advantages and disadvantages.

Abstract WMP85: Recovery Rate vs. Recovery Capacity: A Mathematical Model and its Implications for Rehabilitation

Stroke ◽  
2013 ◽  
Vol 44 (suppl_1) ◽  
Author(s):  
Adam B Schweber ◽  
Lauren E Dunn ◽  
Andrea R Lendaris ◽  
Brandon M Minzer ◽  
Ronald M Lazar ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Recovery Rate ◽  
Goodness Of Fit ◽  
Recovery Period ◽  
Stroke Onset ◽  
Motor Deficit ◽  
Model Parameters ◽  
Stroke Severity ◽  
Recovery Capacity ◽  
Rate Dynamic

INTRODUCTION: Recovery of most hemiparetic patients at 90 days can be well predicted as a fixed proportion (70%) of initial motor deficit. However, recent work has shown considerable variability in the rate of recovery among proportional recoverers, prompting consideration of whether rate of recovery and recovery capacity are independent and whether a single rate dynamic governs proportional recovery. HYPOTHESIS: Among proportional recoverers, recovery rate variability can be accounted for by a single mathematical model in which: 1) recovery rate is independent of recovery capacity and 2) recovery has a sigmoid trajectory parameterized only by initial stroke severity. METHODS: We studied 23 patients with first-ever unilateral hemiparetic stroke previously identified as proportional recoverers. Fugl-Meyer Upper Extremity Motor Exam (FM-UE) had been measured at <72h, 1 week, and 90 days. A non-linear model predicting patients’ FM-UE score at any time after stroke onset was posited and model parameters were estimated by regressing one-week FM-UE scores against initial scores. Statistical significance and goodness of fit were evaluated. RESULTS: The model accounted for 86% of variability in motor recovery achieved by patients at 1 week after stroke onset (pseudo-R 2 =0.863, F 23,21= 418.0, p <.0001) and predicted that more severely impaired patients will have a slower maximum recovery rate and a recovery period that is longer in duration and more delayed in onset. CONCLUSION: The model provides evidence that proportional recovery is governed by a single rate dynamic and that recovery rate is independent of recovery capacity. It provides a tool for predicting motor impairment at any time following stroke onset and suggests a framework for characterizing the biology of recovery and the role of therapeutic interventions as either capacity-enhancing or rate-enhancing.

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