Related papers: Estimation for general birth-death processes

In this paper, we develop a computational approach for computing most likely trajectories describing rare events that correspond to the emergence of non-dominant genotypes. This work is based on the large deviations approach for discrete…

Predictability of behavior has emerged an an important characteristic in many fields including biology, medicine, and marketing. Behavior can be recorded as a sequence of actions performed by an individual over a given time period. This…

Many applications require that we learn the parameters of a model from data. EM is a method used to learn the parameters of probabilistic models for which the data for some of the variables in the models is either missing or hidden. There…

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 consider a bilateral birth-death process characterized by a constant transition rate $\lambda$ from even states and a possibly different transition rate $\mu$ from odd states. We determine the probability generating functions of the even…

Jump Markov linear models consists of a finite number of linear state space models and a discrete variable encoding the jumps (or switches) between the different linear models. Identifying jump Markov linear models makes for a challenging…

Decentralized partially observable Markov decision process (DEC-POMDP) models sequential decision making problems by a team of agents. Since the planning of DEC-POMDP can be interpreted as the maximum likelihood estimation for the latent…

The expectation--maximization (EM) algorithm combines global monotonicity, local linear convergence, and strong practical robustness, but these features are usually analyzed separately. Global descent is nonlinear, whereas local convergence…

Birth-death processes form a natural class where ideas and results on large deviations can be tested. In this paper, we derive a large deviation principle under the assumption that the rate of a jump down (death) is growing asymptotically…

Positron Emission Particle Tracking (PEPT) is an imaging method that tracks individual radioactive particles. PEPT relies on the detection of back-to-back photon pairs emitted by positron annihilation. It requires an algorithm to locate the…

We consider infinite-horizon Markov Decision Processes where parameters, such as transition probabilities, are unknown and estimated from data. The popular distributionally robust approach to addressing the parameter uncertainty can…

Computing optimal conditional reachability probabilities in Markov decision processes (MDPs) is tractable by a reduction to reachability probabilities. Yet, this reduction yields cyclic, challenging MDPs that are often notoriously hard to…

The edge partition model (EPM) is a generative model for extracting an overlapping community structure from static graph-structured data. In the EPM, the gamma process (GaP) prior is adopted to infer the appropriate number of latent…

In this paper, we consider statistical estimation of time-inhomogeneous aggregate Markov models. Unaggregated models, which corresponds to Markov chains, are commonly used in multi-state life insurance to model the biometric states of an…

The Expectation-Maximization (EM) algorithm is an iterative method to maximize the log-likelihood function for parameter estimation. Previous works on the convergence analysis of the EM algorithm have established results on the asymptotic…

We present the first PAC optimal algorithm for Bayes-Adaptive Markov Decision Processes (BAMDPs) in continuous state and action spaces, to the best of our knowledge. The BAMDP framework elegantly addresses model uncertainty by incorporating…

Markov decision processes (MDPs) are a fundamental model for decision making under uncertainty. They exhibit non-deterministic choice as well as probabilistic uncertainty. Traditionally, verification algorithms assume exact knowledge of the…

Models of biological systems often have many unknown parameters that must be determined in order for model behavior to match experimental observations. Commonly-used methods for parameter estimation that return point estimates of the…

Spatial birth and death processes are obtained as solutions of a system of stochastic equations. The processes are required to be locally finite, but may involve an infinite population over the full (noncompact) type space. Conditions are…

Markov chains provide a foundational framework for modeling sequential stochastic processes, with the transition probability matrix characterizing the dynamics of state evolution. While classical estimation methods such as maximum…