Related papers: Likelihood inference for incompletely observed sto…
When dealing with incomplete data in statistical learning, or incomplete observations in probabilistic inference, one needs to distinguish the fact that a certain event is observed from the fact that the observed event has happened. Since…
We study the problem of ignorability in likelihood-based inference from incomplete categorical data. Two versions of the coarsened at random assumption (car) are distinguished, their compatibility with the parameter distinctness assumption…
When data are incomplete, a random vector Y for the data process together with a binary random vector R for the process that causes missing data, are modelled jointly. We review conditions under which R can be ignored for drawing likelihood…
This paper provides further insight into the key concept of missing at random (MAR) in incomplete data analysis. Following the usual selection modelling approach we envisage two models with separable parameters: a model for the response of…
We offer a natural and extensible measure-theoretic treatment of missingness at random. Within the standard missing data framework, we give a novel characterisation of the observed data as a stopping-set sigma algebra. We demonstrate that…
We consider first the mixed discrete-continuous scheme of observation in multistate models; this is a classical pattern in epidemiology because very often clinical status is assessed at discrete visit times while times of death or other…
Taking a rigorous formal approach, we consider sequential decision problems involving observable variables, unobservable variables, and action variables. We can typically assume the property of extended stability, which allows…
Many non-equilibrium, active processes are observed at a coarse-grained level, where different microscopic configurations are projected onto the same observable state. Such "lumped" observables display memory, and in many cases the…
During the past few decades, missing-data problems have been studied extensively, with a focus on the ignorable missing case, where the missing probability depends only on observable quantities. By contrast, research into non-ignorable…
Sequential decision-making systems routinely operate with missing or incomplete data. Classical reinforcement learning theory, which is commonly used to solve sequential decision problems, assumes Markovian observability, which may not hold…
Multi-state models are frequently applied for representing processes evolving through a discrete set of state. Important classes of multi-state models arise when transitions between states may depend on the time since entry into the current…
Stochastic processes defined on integer valued state spaces are popular within the physical and biological sciences. These models are necessary for capturing the dynamics of small systems where the individual nature of the populations…
We study the dynamics of a class of two dimensional stochastic processes, depending on two parameters, which may be interpreted as two different temperatures, respectively associated to interfacial and to bulk noise. Special lines in the…
This paper generalizes the notion of stochastic order to a relation between probability measures over arbitrary measurable spaces. This generalization is motivated by the observation that for the stochastic ordering of two stationary Markov…
We present a method to analyze sensitivity of frequentist inferences to potential nonignorability of the missingness mechanism. Rather than starting from the selection model, as is typical in such analyses, we assume that the missingness…
This paper is concerned with a characterization of the observability for a continuous-time hidden Markov model where the state evolves as a general continuous-time Markov process and the observation process is modeled as nonlinear function…
In problems with large amounts of missing data one must model two distinct data generating processes: the outcome process which generates the response and the missing data mechanism which determines the data we observe. Under the…
Missing data problems arise in many applied research studies. They may jeopardize statistical inference of the model of interest, if the missing mechanism is nonignorable, that is, the missing mechanism depends on the missing values…
Lancaster (2002} proposes an estimator for the dynamic panel data model with homoskedastic errors and zero initial conditions. In this paper, we show this estimator is invariant to orthogonal transformations, but is inefficient because it…
We address the problem of estimating unknown model parameters and state variables in stochastic reaction processes when only sparse and noisy measurements are available. Using an asymptotic system size expansion for the backward equation we…