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Both constrained and unconstrained optimization problems regularly appear in recursive tracking problems engineers currently address -- however, constraints are rarely exploited for these applications. We define the Kalman Filter and…
We consider the filtering problem with the partially observed Lorenz 96 model. Although the accuracy of the 3DVar filter in this problem has been established, the theoretical guarantee for the ensemble Kalman filter (EnKF) remains limited…
We study linear policy approximations for the risk-conscious operation of an industrial energy system with uncertain wind power, significant and variable electricity demand, and high thermal output, as found in a modern foundry. The system…
Labor productivity in Turkey, Spain, Belgium, Austria, Switzerland, and New Zealand has been analyzed and modeled. These counties extend the previously analyzed set of the US, UK, Japan, France, Italy, and Canada. Modelling is based on the…
This paper derives "scaling laws"--empirical relationships between the training compute of Large Language Models (LLMs) and their performance--for economic outcomes. In a preregistered online experiment, 300 professional translators…
We consider the nonlinear Kalman filtering problem using Kullback-Leibler (KL) and $\alpha$-divergence measures as optimization criteria. Unlike linear Kalman filters, nonlinear Kalman filters do not have closed form Gaussian posteriors…
The effectiveness of farmer loan policies is crucial for the high-quality development of agriculture and the orderly advancement of the rural revitalization strategy. Exploring the impact of farmers' borrowing behavior on agricultural…
Remittances have become one of the driving forces of development for countries all over the world, especially in lower-middle-income nations. This paper empirically investigates the association between remittance flows and financial…
Accurate state estimation using low-cost MEMS (Micro Electro- Mechanical Systems) sensors present on Commercial-off-the-shelf (COTS) drones is a challenging problem. Most UAV systems use a combination of a gyroscope, an accelerometer, and a…
For dynamical systems involving decision making, the success of the system greatly depends on its ability to make good decisions with incomplete and uncertain information. By leveraging the Koopman operator and its adjoint property, we…
This brief technical note elaborates three well-known state estimators, which are used extensively in practice. These are the rather old-fashioned extended Kalman filter (EKF) and the recently-designed cubature Kalman filtering (CKF) and…
This paper is concerned with the filtering problem in continuous-time. Three algorithmic solution approaches for this problem are reviewed: (i) the classical Kalman-Bucy filter which provides an exact solution for the linear Gaussian…
Data-driven models for nonlinear dynamical systems based on approximating the underlying Koopman operator or generator have proven to be successful tools for forecasting, feature learning, state estimation, and control. It has become well…
Kalman filtering and smoothing are the foundational mechanisms for efficient inference in Gauss-Markov models. However, their time and memory complexities scale prohibitively with the size of the state space. This is particularly…
This paper extends quantile factor analysis to a probabilistic variant that incorporates regularization and computationally efficient variational approximations. We establish through synthetic and real data experiments that the proposed…
Although wage inequality has evolved in advanced countries over recent decades, it remains unknown the extent to which changes in wage inequality and their differences across countries are attributable to specific capital and labor…
Research on productive structures has shown that economic complexity conditions economic growth. However, little is known about which type of complexity, e.g., export or industrial complexity, matters more for regional economic growth in a…
Recently, it has been demonstrated experimentally that adaptive estimation of a continuously varying optical phase provides superior accuracy in the phase estimate compared to static estimation. Here, we show that the mean-square error in…
We consider a model of optimal investment and consumption with both habit formation and partial observations in incomplete It\^{o} processes market. The investor chooses his consumption under the addictive habits constraint while only…
Large language models (LLMs) have rapidly evolved as the foundation of various natural language processing (NLP) applications. Despite their wide use cases, their understanding of culturally-related concepts and reasoning remains limited.…