Related papers: Estimating Fisher Information Matrix in Latent Var…
This paper studies the asymptotic behavior of the Fisher information for a Levy process discretely sampled at an increasing frequency. We show that it is possible to distinguish not only the continuous part of the process from its jumps…
In this paper the stochastic complexity criterion is applied to estimation of the order in AR and ARMA models. The power of the criterion for short strings is illustrated by simulations. It requires an integral of the square root of Fisher…
Estimation of model parameters in a dynamic system can be significantly improved with the choice of experimental trajectory. For general, nonlinear dynamic systems, finding globally "best" trajectories is typically not feasible; however,…
Dynamic factor models are often estimated by point-estimation methods, disregarding parameter uncertainty. We propose a method accounting for parameter uncertainty by means of posterior approximation, using variational inference. Our…
Missing data is common in applied data science, particularly for tabular data sets found in healthcare, social sciences, and natural sciences. Most supervised learning methods only work on complete data, thus requiring preprocessing such as…
Stochastic modeling and simulation provide powerful predictive methods for the intrinsic understanding of fundamental mechanisms in complex biochemical networks. Typically, such mathematical models involve networks of coupled jump…
The Fisher information matrix (FIM) plays an essential role in statistics and machine learning as a Riemannian metric tensor or a component of the Hessian matrix of loss functions. Focusing on the FIM and its variants in deep neural…
The semivarying coefficient models are widely used in the application of finance, economics, medical science and many other areas. The functional coefficients are commonly estimated by local smoothing methods, e.g. local linear estimator.…
The Fisher Information Metric (FIM) and the associated Cram\'er-Rao Bound (CRB) are fundamental tools in statistical signal processing, which inform the efficient design of experiments and algorithms for estimating the underlying…
In some multivariate problems with missing data, pairs of variables exist that are never observed together. For example, some modern biological tools can produce data of this form. As a result of this structure, the covariance matrix is…
This paper presents some results on the maximum likelihood (ML) estimation from incomplete data. Finite sample properties of conditional observed information matrices are established. They possess positive definiteness and the same Loewner…
Motivated by the growing interest in quantum machine learning, in particular quantum neural networks (QNNs), we study how recently introduced evaluation metrics based on the Fisher information matrix (FIM) are effective for predicting their…
For linear mixed models with co-variance matrices which are not linearly dependent on variance component parameters, we prove that the average of the observed information and the Fisher information can be split into two parts. The essential…
Mimicking the maximum likelihood estimator, we construct first order Cramer-Rao efficient and explicitly computable estimators for the scale parameter $\sigma^2$ in the model $Z_{i,n}=\sigma n^{-\beta}X_i+Y_i,i=1,\ldots,n,\beta>0$ with…
The Bayesian decision-theoretic approach to design of experiments involves specifying a design (values of all controllable variables) to maximise the expected utility function (expectation with respect to the distribution of responses and…
Posterior probabilistic statistical inference without priors is an important but so far elusive goal. Fisher's fiducial inference, Dempster-Shafer theory of belief functions, and Bayesian inference with default priors are attempts to…
Fisher Information is a key notion in the whole field of quantum metrology. It allows for a direct quantification of maximal achievable precision of estimation of parameters encoded in quantum states using the most general quantum…
A generic, fast and asymptotically efficient method for parametric estimation is described. It is based on the projected stochastic gradient descent on the log-likelihood function corrected by a single step of the Fisher scoring algorithm.…
The inferential model (IM) framework provides valid prior-free probabilistic inference by focusing on predicting unobserved auxiliary variables. But, efficient IM-based inference can be challenging when the auxiliary variable is of higher…
This paper presents state estimation and stochastic optimal control gathered in one global optimization problem generating dual effect i.e. the control can improve the future estimation. As the optimal policy is impossible to compute, a…