Ensemble-based method for the inverse Frobenius–Perron operator problem: Data-driven global analysis from spatiotemporal “Movie” data

Some Thoughts About Data Type, Distribution, and Statistical Significance

Markovian models involving transition probabilities have been used in a wide variety of fields including psychology, ethnic studies, advertising, international trade, agricultural and labor economics.(1) Many types of models are available and this paper deals with the estimation of transition probabilities in the case of limited information where data on market shares, not physical movements between states, are observable. Heavy use is made of the simple two‐share case to exemplify theory.

There has been growing interest in the estimation of transition probabilities among stages (Hestbeck et al. , 1991; Brownie et al. , 1993; Schwarz et al. , 1993) in tag-return and capture-recapture models. This has been driven by the increasing interest in meta-population models in ecology and the need for parameter estimates to use in these models. These transition probabilities are composed of survival and movement rates, which can only be estimated separately when an additional assumption is made (Brownie et al. , 1993). Brownie et al. (1993) assumed that movement occurs at the end of the interval between time i and i + 1. We generalize this work to allow different movement patterns in the interval for multiple tag-recovery and capture-recapture experiments. The time of movement is a random variable with a known distribution. The model formulations can be viewed as matrix extensions to the model formulations of single open population capturerecapture and tag-recovery experiments (Jolly, 1965; Seber, 1965; Brownie et al. , 1985). We also present the results of a small simulation study for the tag-return model when movement time follows a beta distribution, and later another simulation study for the capture-recapture model when movement time follows a uniform distribution. The simulation studies use a modified program SURVIV (White, 1983). The Relative Standard Errors (RSEs) of estimates according to high and low movement rates are presented. We show there are strong correlations between movement and survival estimates in the case that the movement rate is high. We also show that estimators of movement rates to different areas and estimators of survival rates in different areas have substantial correlations.

Extraction and prediction of coherent patterns in incompressible flows through space–time Koopman analysis

PRM113 - ESTIMATION OF TRANSITION PROBABILITIES BETWEEN ESOPHAGEAL CANCER AND ITS PRECANCEROUS LESIONS BASED ON A MARKOV MODEL

This tutorial presents practical guidance on transforming various typesof information published in journals, or available online from government and other sources, into transition probabilities for use in state-transition models, including cost-effectiveness models. Much, but not all, of the guidance has been previously published in peer-reviewed journals. Our purpose is to collect it in one location to serve as a stand-alone resource for decision modelers who draw most or all of their information from the published literature. Our focus is on the technical aspects of manipulating data to derive transition probabilities. We explain how to derive model transition probabilities from the following types of statistics: relative risks, odds, odds ratios, and rates. We then review the well-known approach for converting probabilities to match the model’s cycle length when there are two health-state transitions and how to handle the case of three or more health-state transitions, for which the two-state approach is not appropriate. Other topics discussed include transition probabilities for population subgroups, issues to keep in mind when using data from different sources in the derivation process, and sensitivity analyses, including the use of sensitivity analysis to allocate analyst effort in refining transition probabilities and ways to handle sources of uncertainty that are not routinely formalized in models. The paper concludes with recommendations to help modelers make the best use of the published literature.

Markovian Credit Risk Transition Probabilities under Non-Negativity Constraints for the US Portfolio 1984-2004

When data from several independent Markov chains are aggregated over each time point, least square estimation of transition probabilities faces the problem of multi-collinearity. We propose here an estimation procedure which involves use of ridge regression for the ordinary least square estimators. Performance of this estimator is then compared with that of the ordinary least squares.

We analyze losses resulting from uncertain transition probabilities in Markov decision processes with bounded nonnegative rewards. We assume that policies are precomputed using exact dynamic programming with the estimated transition probabilities, but the system evolves according to different, true transition probabilities. Given a bound on the total variation error of estimated transition probability distributions, we derive upper bounds on the loss of expected total reward. The approach analyzes the growth of errors incurred by stepping backwards in time while precomputing value functions, which requires bounding a multilinear program. Loss bounds are given for the finite horizon undiscounted, finite horizon discounted, and infinite horizon discounted cases, and a tight example is shown.

Learning parametric policies and transition probability models of markov decision processes from data

One of the main challenges in the study of time-varying networks is the interplay of memory effects with structural heterogeneity. In particular, different nodes and dyads can have very different statistical properties in terms of both link formation and link persistence, leading to a superposition of typical timescales, suboptimal parametrizations, and substantial estimation biases. Here we develop an unbiased maximum-entropy framework to study empirical network trajectories by controlling for the observed structural heterogeneity and local link persistence simultaneously. An exact mapping to a heterogeneous version of the one-dimensional Ising model leads to an analytic solution that rigorously disentangles the hidden variables that jointly determine both static and temporal properties. Additionally, model selection via likelihood maximization identifies the most parsimonious structural level (either global, node specific, or dyadic) accounting for memory effects. As we illustrate on real-world social networks, this method enables an improved estimation of dyadic transition probabilities, relaxation times, and structural breaks between dynamical regimes. In the resulting picture, the graph follows a generalized configuration model with given degrees and given time-persisting degrees, undergoing transitions between empirically identifiable stationary regimes. Published by the American Physical Society 2024

This paper investigates the transmission of educational attainment from parents to offspring as a mediator of intergenerational class mobility in Europe. The study covers the last two decades with data drawn from a cross-national large-scale sample survey, namely the European Social Survey (ESS), for the years 2002–2018. Interest has focused on the question of the persistence of inequality of educational opportunities by examining the attainment of nominal levels of education and the association between the educational attainment of the parent with the highest level of education and their descendants. The study also covers new trends in social mobility that consider education as a “positional good”, and a novel method of incorporating educational expansion into the transition probabilities is proposed, providing answers to whether the rising accessibility of educational qualifications attenuates the association between social origin and educational attainment. Therefore, the concept of positionality is taken into account in the estimation of intergenerational transition probabilities, and to complement the analysis, mobility measures are provided for both methods, nominal and positional. The proposed positional method is validated through a correlation analysis between the upward mobility scores (nominal and positional) with the Education Expansion Index (EEI) for the respective years. The upward mobility scores estimated via the positional method are more highly correlated with the EEI for all years, indicating a better alignment with the broader trends in educational participation and achievement.

A proposed new generation of evidence-based microsimulation models to inform global control of cervical cancer

This study aims to quantify transition probabilities between frailty states (not-frail, pre-frail, frail) and from different frailty states to the occurrence of a cardiovascular disease (CVD) event; and to examine how age, sex and sociodemographic factors influence these transitions. 18,077 initially healthy individuals (91% Caucasians, 56% females) aged ≥65 years enrolled in the ASPREE study who had no prior CVD event and ADL (Activity of Daily Living) disability at recruitment were followed for a median of 7.4 years. Frailty was annually assessed using a 64-item Frailty Index. Continuous-time multi-state Markov modelling was used. The estimated transition probabilities from frail to CVD increased over time (11% at five years, and 18% at ten years) and consistently exceeded the corresponding five- and ten-year transition probabilities from pre-frail to CVD (8% and 14% respectively). Compared to males, females had a 26% higher relative risk of progressing to a pre-frail/frail state; however, they had about 50% lower relative risk of transitioning from pre-frail/frail to CVD. Older age, socioeconomic and geographic disparities were associated with up to 38% higher relative risk of worsening frailty and progression to CVD. Similar findings were observed when using the Fried phenotype. The probability of transiting from pre-frail/frail to CVD increased over time, even among initially healthy older people. Targeted prevention strategies may be helpful to delay frailty progression and reduce CVD risk in older age, particularly socioeconomically disadvantaged individuals or those residing outside major cities, and different approaches may be required in females and males.

Understanding the role of larger-scale processes in modulating the assembly, structure, and dynamics of communities is critical for forecasting the effects of climate-change and managing ecosystems. Developing this comprehensive perspective is difficult though, because species interactions are complex, interdependent, and dynamic through space and time. Typically, experiments focus on tractable subsets of interactions that will be most critical to investigate and explain shifts in communities, but qualitatively base these choices on experience, natural history, and theory. One quantitative approach to identify the putative forces regulating communities, without reducing system complexity, is estimating transition probabilities among species occupying space (i.e., multispecies Markov chain models). Although not mechanistic, these models estimate the relative frequency and importance of ecological pathways in community assembly and dynamics, and can serve as a framework to identify how pathways change across large scales and which are most important to investigate further. Here, we demonstrate this method in the Gulf of Maine (GOM) intertidal zone, where research has largely focused on the local-scale processes that influence communities, while the mechanisms responsible for more regional shifts in communities are less clear. Transition probabilities of faunal elements were quantified bimonthly for ~2.5yr in local intertidal communities at three replicate sites in the southern, mid-coast, and northern GOM. Transitions related to mortality, colonization, and replacement by mussels, barnacles, red algae, and encrusting corallines differed regionally, suggesting specific pathways related to consumer pressure and recruitment vary across the GOM with shifting intertidal community structure. Combined with species abundance data and insights from previous research, we develop and evaluate the pathways by which communities likely change in the GOM. Species interactions in local communities can be complex, and this complexity should be incorporated into hypothesis building, experiments, theory, interpretations, and forecasts in ecology. Such a comprehensive approach will be critical to understand how regional shifts in local interactions can drive large-scale community change.