Related papers: Maximum Likelihood Estimation for a Markov-Modulat…
Automated synthesis of provably correct controllers for cyber-physical systems is crucial for deployment in safety-critical scenarios. However, hybrid features and stochastic or unknown behaviours make this problem challenging. We propose a…
In various practical situations, we encounter data from stochastic processes which can be efficiently modelled by an appropriate parametric model for subsequent statistical analyses. Unfortunately, the most common estimation and inference…
The method of maximum likelihood estimation (MLE) is a widely used statistical approach for estimating the values of one or more unknown parameters of a probabilistic model based on observed data. In this tutorial, I briefly review the…
This article investigates a regime-switching investment strategy aimed at mitigating downside risk by reducing market exposure during anticipated unfavorable market regimes. We highlight the statistical jump model (JM) for market regime…
A fundamental question in the field of molecular computation is what computational tasks a biochemical system can carry out. In this work, we focus on the problem of finding the maximum likelihood estimate (MLE) for log-affine models. We…
This paper develops a unified estimation framework, the Maximum Ideal Likelihood Estimation (MILE), for general parametric models with latent variables. Unlike traditional approaches relying on the marginal likelihood of the observed data,…
Diffusion can be conceptualized, at microscopic scales, as the random hopping of particles between neighboring lattice sites. In the case of diffusion in inhomogeneous media, distinct spatial domains in the system may yield distinct…
Bayesian inference for Markov jump processes (MJPs) where available observations relate to either system states or jumps typically relies on data-augmentation Markov Chain Monte Carlo. State-of-the-art developments involve representing MJP…
Generative Artificial Intelligence (GenAI) models, with their powerful feature learning capabilities, have been applied in many fields. In mobile wireless communications, GenAI can dynamically optimize the network to enhance the user…
The finite state semi-Markov process is a generalization over the Markov chain in which the sojourn time distribution is any general distribution. In this article we provide a sufficient stochastic maximum principle for the optimal control…
This paper introduces a jump-diffusion pricing model specifically designed for algorithmic trading and high-frequency trading (HFT). The model incorporates independent jump and diffusion processes, providing a more precise representation of…
This paper studies an approximation method for the log-likelihood function of a nonlinear diffusion process using the bridge of the diffusion. The main result (Theorem \refthm:approx) shows that this approximation converges uniformly to the…
This paper deals with the problem of inference associated with linear fractional diffusion process with random effects in the drift. In particular we are concerned with the maximum likelihood estimators (MLE) of the random effect…
We study maximum likelihood estimation (MLE) in the generalized group orbit recovery model, where each observation is generated by applying a random group action and a known, fixed linear operator to an unknown signal, followed by additive…
We advocate for a practical Maximum Likelihood Estimation (MLE) approach towards designing loss functions for regression and forecasting, as an alternative to the typical approach of direct empirical risk minimization on a specific target…
The primary objective of this scholarly work is to develop two estimation procedures - maximum likelihood estimator (MLE) and method of trimmed moments (MTM) - for the mean and variance of lognormal insurance payment severity data sets…
In this paper we consider the problem of parameter inference for Markov jump process (MJP) representations of stochastic kinetic models. Since transition probabilities are intractable for most processes of interest yet forward simulation is…
We can directly sample from the conditional distribution of any log-affine model. The algorithm is a Markov chain on a bounded integer lattice, and its transition probability is the ratio of the UMVUE (uniformly minimum variance unbiased…
Markovian jump linear systems (MJLS) are an important class of dynamical systems that arise in many control applications. In this paper, we introduce the problem of controlling unknown (discrete-time) MJLS as a new benchmark for…
We formally introduce and study locally-balanced Markov jump processes (LBMJPs) defined on a general state space. These continuous-time stochastic processes with a user-specified limiting distribution are designed for sampling in settings…