ترغب بنشر مسار تعليمي؟ اضغط هنا

An Early Stopping Bayesian Data Assimilation Approach for Mixed-Logit Estimation

73   0   0.0 ( 0 )
 نشر من قبل Shanshan Xie
 تاريخ النشر 2021
والبحث باللغة English




اسأل ChatGPT حول البحث

The mixed-logit model is a flexible tool in transportation choice analysis, which provides valuable insights into inter and intra-individual behavioural heterogeneity. However, applications of mixed-logit models are limited by the high computational and data requirements for model estimation. When estimating on small samples, the Bayesian estimation approach becomes vulnerable to over and under-fitting. This is problematic for investigating the behaviour of specific population sub-groups or market segments with low data availability. Similar challenges arise when transferring an existing model to a new location or time period, e.g., when estimating post-pandemic travel behaviour. We propose an Early Stopping Bayesian Data Assimilation (ESBDA) simulator for estimation of mixed-logit which combines a Bayesian statistical approach with Machine Learning methodologies. The aim is to improve the transferability of mixed-logit models and to enable the estimation of robust choice models with low data availability. This approach can provide new insights into choice behaviour where the traditional estimation of mixed-logit models was not possible due to low data availability, and open up new opportunities for investment and planning decisions support. The ESBDA estimator is benchmarked against the Direct Application approach, a basic Bayesian simulator with random starting parameter values and a Bayesian Data Assimilation (BDA) simulator without early stopping. The ESBDA approach is found to effectively overcome under and over-fitting and non-convergence issues in simulation. Its resulting models clearly outperform those of the reference simulators in predictive accuracy. Furthermore, models estimated with ESBDA tend to be more robust, with significant parameters with signs and values consistent with behavioural theory, even when estimated on small samples.



قيم البحث

اقرأ أيضاً

In spatial statistics, it is often assumed that the spatial field of interest is stationary and its covariance has a simple parametric form, but these assumptions are not appropriate in many applications. Given replicate observations of a Gaussian sp atial field, we propose nonstationary and nonparametric Bayesian inference on the spatial dependence. Instead of estimating the quadratic (in the number of spatial locations) entries of the covariance matrix, the idea is to infer a near-linear number of nonzero entries in a sparse Cholesky factor of the precision matrix. Our prior assumptions are motivated by recent results on the exponential decay of the entries of this Cholesky factor for Matern-type covariances under a specific ordering scheme. Our methods are highly scalable and parallelizable. We conduct numerical comparisons and apply our methodology to climate-model output, enabling statistical emulation of an expensive physical model.
We propose a framework for Bayesian non-parametric estimation of the rate at which new infections occur assuming that the epidemic is partially observed. The developed methodology relies on modelling the rate at which new infections occur as a functi on which only depends on time. Two different types of prior distributions are proposed namely using step-functions and B-splines. The methodology is illustrated using both simulated and real datasets and we show that certain aspects of the epidemic such as seasonality and super-spreading events are picked up without having to explicitly incorporate them into a parametric model.
Model uncertainty quantification is an essential component of effective data assimilation. Model errors associated with sub-grid scale processes are often represented through stochastic parameterizations of the unresolved process. Many existing Stoch astic Parameterization schemes are only applicable when knowledge of the true sub-grid scale process or full observations of the coarse scale process are available, which is typically not the case in real applications. We present a methodology for estimating the statistics of sub-grid scale processes for the more realistic case that only partial observations of the coarse scale process are available. Model error realizations are estimated over a training period by minimizing their conditional sum of squared deviations given some informative covariates (e.g. state of the system), constrained by available observations and assuming that the observation errors are smaller than the model errors. From these realizations a conditional probability distribution of additive model errors given these covariates is obtained, allowing for complex non-Gaussian error structures. Random draws from this density are then used in actual ensemble data assimilation experiments. We demonstrate the efficacy of the approach through numerical experiments with the multi-scale Lorenz 96 system using both small and large time scale separations between slow (coarse scale) and fast (fine scale) variables. The resulting error estimates and forecasts obtained with this new method are superior to those from two existing methods.
291 - Yunbo Ouyang , Feng Liang 2017
A nonparametric Bayes approach is proposed for the problem of estimating a sparse sequence based on Gaussian random variables. We adopt the popular two-group prior with one component being a point mass at zero, and the other component being a mixture of Gaussian distributions. Although the Gaussian family has been shown to be suboptimal for this problem, we find that Gaussian mixtures, with a proper choice on the means and mixing weights, have the desired asymptotic behavior, e.g., the corresponding posterior concentrates on balls with the desired minimax rate. To achieve computation efficiency, we propose to obtain the posterior distribution using a deterministic variational algorithm. Empirical studies on several benchmark data sets demonstrate the superior performance of the proposed algorithm compared to other alternatives.
We introduce a numerically tractable formulation of Bayesian joint models for longitudinal and survival data. The longitudinal process is modelled using generalised linear mixed models, while the survival process is modelled using a parametric genera l hazard structure. The two processes are linked by sharing fixed and random effects, separating the effects that play a role at the time scale from those that affect the hazard scale. This strategy allows for the inclusion of non-linear and time-dependent effects while avoiding the need for numerical integration, which facilitates the implementation of the proposed joint model. We explore the use of flexible parametric distributions for modelling the baseline hazard function which can capture the basic shapes of interest in practice. We discuss prior elicitation based on the interpretation of the parameters. We present an extensive simulation study, where we analyse the inferential properties of the proposed models, and illustrate the trade-off between flexibility, sample size, and censoring. We also apply our proposal to two real data applications in order to demonstrate the adaptability of our formulation both in univariate time-to-event data and in a competing risks framework. The methodology is implemented in rstan.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا