scholarly journals Asymptotic consistency of loss‐calibrated variational Bayes

Stat ◽  
2020 ◽  
Vol 9 (1) ◽  
Author(s):  
Prateek Jaiswal ◽  
Harsha Honnappa ◽  
Vinayak A. Rao
Keyword(s):  
Variational Bayes ◽  
Asymptotic Consistency

scholarly journals Estimating Simultaneous Equation Models through an Entropy-Based Incremental Variational Bayes Learning Algorithm

Entropy ◽  
2021 ◽  
Vol 23 (4) ◽  
pp. 384
Author(s):  
Rocío Hernández-Sanjaime ◽  
Martín González ◽  
Antonio Peñalver ◽  
Jose J. López-Espín
Keyword(s):  
Statistical Theory ◽  
Learning Algorithm ◽  
Real Life ◽  
Simulated Data ◽  
Simultaneous Equation ◽  
Variational Bayes ◽  
Parameter Estimates ◽  
Step Method ◽  
The One ◽  
Simultaneous Equation Models

The presence of unaccounted heterogeneity in simultaneous equation models (SEMs) is frequently problematic in many real-life applications. Under the usual assumption of homogeneity, the model can be seriously misspecified, and it can potentially induce an important bias in the parameter estimates. This paper focuses on SEMs in which data are heterogeneous and tend to form clustering structures in the endogenous-variable dataset. Because the identification of different clusters is not straightforward, a two-step strategy that first forms groups among the endogenous observations and then uses the standard simultaneous equation scheme is provided. Methodologically, the proposed approach is based on a variational Bayes learning algorithm and does not need to be executed for varying numbers of groups in order to identify the one that adequately fits the data. We describe the statistical theory, evaluate the performance of the suggested algorithm by using simulated data, and apply the two-step method to a macroeconomic problem.

Comparing the usefulness of a new algorithm to measure visual field using the variational Bayes linear regression in glaucoma patients, in comparison to the Swedish interactive thresholding algorithm

2021 ◽  
pp. bjophthalmol-2020-318304
Author(s):  
Hiroshi Murata ◽  
Ryo Asaoka ◽  
Yuri Fujino ◽  
Masato Matsuura ◽  
Kazunori Hirasawa ◽  
...  
Keyword(s):  
Visual Field ◽  
Linear Regression ◽  
Open Angle Glaucoma ◽  
Variational Bayes ◽  
Mean Deviation ◽  
Test Duration ◽  
Field Analyser ◽  
Measurement Duration ◽  
Measurement Algorithm ◽  
Thresholding Algorithm

Background/aimsWe previously reported that the visual field (VF) prediction model using the variational Bayes linear regression (VBLR) is useful for accurately predicting VF progression in glaucoma (Invest Ophthalmol Vis Sci. 2014, 2018). We constructed a VF measurement algorithm using VBLR, and the purpose of this study was to investigate its usefulness.Method122 eyes of 73 patients with open-angle glaucoma were included in the current study. VF measurement was performed using the currently proposed VBLR programme with AP-7700 perimetry (KOWA). VF measurements were also conducted using the Swedish interactive thresholding algorithm (SITA) standard programme with Humphrey field analyser. VF measurements were performed using the 24–2 test grid. Visual sensitivities, test–retest reproducibility and measurement duration were compared between the two algorithms.ResultMean mean deviation (MD) values with SITA standard were −7.9 and −8.7 dB (first and second measurements), whereas those with VBLR-VF were −8.2 and −8.0 dB, respectively. There were no significant differences across these values. The correlation coefficient of MD values between the 2 algorithms was 0.97 or 0.98. Test–retest reproducibility did not differ between the two algorithms. Mean measurement duration with SITA standard was 6 min and 02 s or 6 min and 00 s (first or second measurement), whereas a significantly shorter duration was associated with VBLR-VF (5 min and 23 s or 5 min and 30 s).ConclusionVBLR-VF reduced test duration while maintaining the same accuracy as the SITA-standard.

Consistency of Sample Estimates of Risk Averse Stochastic Programs

2013 ◽  
Vol 50 (02) ◽  
pp. 533-541 ◽  
Author(s):  
Alexander Shapiro
Keyword(s):  
Stochastic Programming ◽  
Law Of Large Numbers ◽  
Risk Measures ◽  
Regularity Conditions ◽  
Distributed Data ◽  
Risk Averse ◽  
Asymptotic Consistency ◽  
Stochastic Programs ◽  
Large Numbers ◽  
Independent Identically Distributed

In this paper we study asymptotic consistency of law invariant convex risk measures and the corresponding risk averse stochastic programming problems for independent, identically distributed data. Under mild regularity conditions, we prove a law of large numbers and epiconvergence of the corresponding statistical estimators. This can be applied in a straightforward way to establish convergence with probability 1 of sample-based estimators of risk averse stochastic programming problems.

scholarly journals Variational Bayes on manifolds

2021 ◽  
Vol 31 (6) ◽  
Author(s):  
Minh-Ngoc Tran ◽  
Dang H. Nguyen ◽  
Duy Nguyen
Keyword(s):  
Variational Bayes
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