<b>TMB</b>: Automatic Differentiation and Laplace Approximation

Kristensen, Kasper; Nielsen, Anders; Berg, Casper Willestofte; Skaug, Hans J.; Bell, Brad

doi:10.18637/jss.v070.i05

Cited by 700 publications

(620 citation statements)

References 15 publications

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“…Small area estimation was carried out in R version 3.2.4 statistical software (R Foundation for Statistical Computing). Models were fit using the Template Model Builder Package in R. 25 …”

Section: Methodsmentioning

confidence: 99%

US County-Level Trends in Mortality Rates for Major Causes of Death, 1980-2014

Dwyer-Lindgren

Bertozzi‐Villa

Stubbs

et al. 2016

JAMA

221

192

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IMPORTANCECounty-level patterns in mortality rates by cause have not been systematically described but are potentially useful for public health officials, clinicians, and researchers seeking to improve health and reduce geographic disparities.OBJECTIVES To demonstrate the use of a novel method for county-level estimation and to estimate annual mortality rates by US county for 21 mutually exclusive causes of death from 1980 through 2014. DESIGN, SETTING, AND PARTICIPANTSRedistribution methods for garbage codes (implausible or insufficiently specific cause of death codes) and small area estimation methods (statistical methods for estimating rates in small subpopulations) were applied to death registration data from the National Vital Statistics System to estimate annual county-level mortality rates for 21 causes of death. These estimates were raked (scaled along multiple dimensions) to ensure consistency between causes and with existing national-level estimates. Geographic patterns in the age-standardized mortality rates in 2014 and in the change in the age-standardized mortality rates between 1980 and 2014 for the 10 highest-burden causes were determined. EXPOSURE County of residence.MAIN OUTCOMES AND MEASURES Cause-specific age-standardized mortality rates.RESULTS A total of 80 412 524 deaths were recorded from January 1, 1980, through December 31, 2014, in the United States. Of these, 19.4 million deaths were assigned garbage codes. Mortality rates were analyzed for 3110 counties or groups of counties. Large between-county disparities were evident for every cause, with the gap in age-standardized mortality rates between counties in the 90th and 10th percentiles varying from 14.0 deaths per 100 000 population (cirrhosis and chronic liver diseases) to 147.0 deaths per 100 000 population (cardiovascular diseases). Geographic regions with elevated mortality rates differed among causes: for example, cardiovascular disease mortality tended to be highest along the southern half of the Mississippi River, while mortality rates from self-harm and interpersonal violence were elevated in southwestern counties, and mortality rates from chronic respiratory disease were highest in counties in eastern Kentucky and western West Virginia. Counties also varied widely in terms of the change in cause-specific mortality rates between 1980 and 2014. For most causes (eg, neoplasms, neurological disorders, and self-harm and interpersonal violence), both increases and decreases in county-level mortality rates were observed. CONCLUSIONS AND RELEVANCEIn this analysis of US cause-specific county-level mortality rates from 1980 through 2014, there were large between-county differences for every cause of death, although geographic patterns varied substantially by cause of death. The approach to county-level analyses with small area models used in this study has the potential to provide novel insights into US disease-specific mortality time trends and their differences across geographic regions.

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“…Small area estimation was carried out in R version 3.2.4 statistical software (R Foundation for Statistical Computing). Models were fit using the Template Model Builder Package in R. 25 …”

Section: Methodsmentioning

confidence: 99%

US County-Level Trends in Mortality Rates for Major Causes of Death, 1980-2014

Dwyer-Lindgren

Bertozzi‐Villa

Stubbs

et al. 2016

JAMA

221

192

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“…The package is built via the R-Package Template Model Builder (TMB) [29], which is a tool to construct complex state-space models using Automatic Differentiation and the Laplace approximation to obtain accurate and stable optimization [30]. The package offers the user the possibility to easily estimate robust water levels.…”

Section: Methods and Data Processingmentioning

confidence: 99%

The Performance and Potentials of the CryoSat-2 SAR and SARIn Modes for Lake Level Estimation

Nielsen

Stenseng

Andersen

et al. 2017

Water

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Abstract:Over the last few decades, satellite altimetry has proven to be valuable for monitoring lake levels. With the new generation of altimetry missions, CryoSat-2 and Sentinel-3, which operate in Synthetic Aperture Radar (SAR) and SAR Interferometric (SARIn) modes, the footprint size is reduced to approximately 300 m in the along-track direction. Here, the performance of these new modes is investigated in terms of uncertainty of the estimated water level from CryoSat-2 data and the agreement with in situ data. The data quality is compared to conventional low resolution mode (LRM) altimetry products from Envisat, and the performance as a function of the lake area is tested. Based on a sample of 145 lakes with areas ranging from a few to several thousand km 2 , the CryoSat-2 results show an overall superior performance. For lakes with an area below 100 km 2 , the uncertainty of the lake levels is only half of that of the Envisat results. Generally, the CryoSat-2 lake levels also show a better agreement with the in situ data. The lower uncertainty of the CryoSat-2 results entails a more detailed description of water level variations.

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“…lacking the corrections that we have mentioned in Section 3.2. Therefore, we have used the package TMB (Kristensen et al , 2016) which provides the corrections and has the added flexibility to accomodate the RWLB.…”

Section: Methodsmentioning

confidence: 99%

Bootstrap estimation of uncertainty in prediction for generalized linear mixed models

Flores-Agreda

Cantoni

2019

Computational Statistics & Data Analysis

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In this article, we focus on the estimation of the Mean Squared Error for the Predictors (MSEP) of Random Effects (RE) in Generalized Linear Mixed Models (GLMM) by means of non-parametric bootstrap methods. In the frequentist paradigm, the MSEP is used as a measure of the uncertainty in prediction and has been shown to be affected by the estimation of the model parameters. In the particular case of linear mixed models (LMM), two solutions are provided to practitioners: on one hand, secondorder correct approximations which yield estimators of this quantity and, on the other hand, several Parametric Bootstrap algorithms. We propose a non-parametric bootstrap scheme, consisting of an adaptation of the Random Weighted Laplace Bootstrap (RWLB) that can be used in the entire class of GLMM. On a first stage, the RWLB is used to generate bootstrap replicates of the parameters while, on a second stage, simulation is used to generate bootstrap samples of standardized RE. We conduct a first simulation study in the framework of Gaussian LMM to contrast the quality of our approach with respect to: (i) analytical estimators of MSEP based on approximations, (ii) Conditional Variances obtained with a Bayesian representation and (iii) other bootstrap schemes, on the grounds of their relative bias, relative efficiency and the coverage ratios of resulting prediction intervals. A second simulation study serves the purpose to illustrate the use and benefits of our proposal against other feasible alternatives in a pure, Non-Gaussian, GLMM setting.

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TMB: Automatic Differentiation and Laplace Approximation

Cited by 700 publications

References 15 publications

US County-Level Trends in Mortality Rates for Major Causes of Death, 1980-2014

US County-Level Trends in Mortality Rates for Major Causes of Death, 1980-2014

The Performance and Potentials of the CryoSat-2 SAR and SARIn Modes for Lake Level Estimation

Bootstrap estimation of uncertainty in prediction for generalized linear mixed models

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