A tutorial on spatiotemporal partially observed Markov process models via the R package spatPomp

Partially observed Markov process (POMP) models, also known as hidden Markov models or state space models, are ubiquitous tools for time series analysis. The R package pomp provides a very flexible framework for Monte Carlo statistical investigations using nonlinear, non-Gaussian POMP models. A range of modern statistical methods for POMP models have been implemented in this framework including sequential Monte Carlo, iterated filtering, particle Markov chain Monte Carlo, approximate Bayesian computation, maximum synthetic likelihood estimation, nonlinear forecasting, and trajectory matching. In this paper, we demonstrate the application of these methodologies using some simple toy problems. We also illustrate the specification of more complex POMP models, using a nonlinear epidemiological model with a discrete population, seasonality, and extra-demographic stochasticity. We discuss the specification of user-defined models and the development of additional methods within the programmin …

Filter stability is a classical problem for partially observed Markov processes (POMP). For a POMP, an incorrectly initialized non-linear filter is said to be stable if the filter eventually corrects itself with the arrival of new measurement information. In the literature, studies on the stability of non-linear filters either focus on the ergodic properties on the hidden Markov process, or the observability of the measurement channel. While notions of observability exist in the literature, they are difficult to verify for many systems and specific examples of observable systems are mostly restricted to additive noise models. In this paper, we introduce a general definition of observability for stochastic non-linear dynamical systems and compare it with related findings in the literature. Our notion involves a functional characterization which is easily computed for a variety of systems as we demonstrate. Under this observability definition we establish filter stability results for a v …

Filter stability is a classical problem in the study of partially observed Markov processes (POMP), also known as hidden Markov models (HMM). For a POMP, an incorrectly initialized non-linear filter is said to be (asymptotically) stable if the filter eventually corrects itself as more measurements are collected. Filter stability results in the literature that provide rates of convergence typically rely on very restrictive mixing conditions on the transition kernel and measurement kernel pair, and do not consider their effects independently. In this paper, we introduce an alternative approach using the Dobrushin coefficients associated with both the transition kernel as well as the measurement channel. Such a joint study, which seems to have been unexplored, leads to a concise analysis that can be applied to more general system models under relaxed conditions: in particular, we show that if $(1 - \delta (T))(2-\delta (Q)) < 1$, where $\delta (T)$ and $\delta (Q)$ are the Dobrushin coeff …

Partially observed Markov process (POMP) models are powerful tools for time series modeling and analysis. Inherited the flexible framework of R package pomp, the is2 package extends some useful Monte Carlo statistical methodologies to improve on convergence rates. A variety of efficient statistical methods for POMP models have been developed including fixed lag smoothing, second-order iterated smoothing, momentum iterated filtering, average iterated filtering, accelerate iterated filtering and particle iterated filtering. In this paper, we show the utility of these methodologies based on two toy problems. We also demonstrate the potential of some methods in a more complex model, employing a nonlinear epidemiological model with a discrete population, seasonality, and extra-demographic stochasticity. We discuss the extension beyond POMP models and the development of additional methods within the framework provided by is2.

In this paper we focus on the problem of learning an optimal policy for Active Visual Search (AVS) of objects in known indoor environments with an online setup. Our POMP method uses as input the current pose of an agent (e.g. a robot) and a RGB-D frame. The task is to plan the next move that brings the agent closer to the target object. We model this problem as a Partially Observable Markov Decision Process solved by a Monte-Carlo planning approach. This allows us to make decisions on the next moves by iterating over the known scenario at hand, exploring the environment and searching for the object at the same time. Differently from the current state of the art in Reinforcement Learning, POMP does not require extensive and expensive (in time and computation) labelled data so being very agile in solving AVS in small and medium real scenarios. We only require the information of the floormap of the environment, an information usually available or that can be easily extracted from an a pri …