Estimating parameters from data is a fundamental problem, which is customarily done by minimizing a loss function between a model and observed statistics. In this talk, we discuss another paradigm termed the ab initio uncertainty quantification (AIUQ) method, for improving loss-minimization estimation in two steps. In step one, we define a probabilistic generative model from the beginning of data processing, and show the equivalence between loss-minimization estimation and a statistical estimator. In step two, we develop better models or estimators, such as the maximum marginal likelihood or Bayesian estimators by marginalizing out random components to improve estimation. Furthermore, we develop scalable methods for computing large matrix multiplication and inversion, to overcome the primary computational bottleneck of efficient estimation in science. To illustrate, we introduce two approaches to estimate dynamical systems, one in Fourier analysis of microscopy videos, and the other in inversely estimating the particle interaction kernel from trajectory. In the first approach, we utilized the Fast Fourier transform and generalized Schur method, and in the second approach, we developed a new method called the inverse Kalman filter and integrated it into the conjugate gradient algorithm for accelerating the computation. We achieved pseudolinear computational complexity with respect to the number of observations, with nearly no approximation in both approaches. These new approaches outline a wide range of applications, such as probing optically dense systems, automated determination of gelation time, and estimating cellular interaction and alignment dynamics for fibroblasts on liquid-crystalline substrates.