Generalized parallel tempering on Bayesian inverse problems

In the current work we present two generalizations of the Parallel Tempering algorithm in the context of discrete-time Markov chain Monte Carlo methods for Bayesian inverse problems. These generalizations use state-dependent swapping rates, inspired by the so-called continuous time Infinite Swapping algorithm presented in Plattner et al. (J Chem Phys 135(13):134111, 2011). We analyze the reversibility and ergodicity properties of our generalized PT algorithms. Numerical results on sampling from different target distributions, show that the proposed methods significantly improve sampling efficiency over more traditional sampling algorithms such as Random Walk Metropolis, preconditioned Crank–Nicolson, and (standard) Parallel Tempering.

Longitudinal Projection of Herd Prevalence of Influenza A(H1N1)pdm09 Virus Infection in the Norwegian Pig Population by Discrete-Time Markov Chain Modelling

In order to quantify projections of disease burden and to prioritise disease control strategies in the animal population, good mathematical modelling of infectious disease dynamics is required. This article investigates the suitability of discrete-time Markov chain (DTMC) as one such model for forecasting disease burden in the Norwegian pig population after the incursion of influenza A(H1N1)pdm09 virus (H1N1pdm09) in Norwegian pigs in 2009. By the year-end, Norway’s active surveillance further detected 20 positive herds from 54 random pig herds, giving an estimated initial population prevalence of 37% (95% CI 25–52). Since then, Norway’s yearly surveillance of pig herd prevalence has given this study 11 years of data from 2009 to 2020 to work with. Longitudinally, the pig herd prevalence for H1N1pdm09 rose sharply to >40% in three years and then fluctuated narrowly between 48% and 49% for 6 years before declining. This initial longitudinal pattern in herd prevalence from 2009 to 2016 inspired this study to test the steady-state discrete-time Markov chain model in forecasting disease prevalence. With the pig herd as the unit of analysis, the parameters for DTMC came from the initial two years of surveillance data after the outbreak, namely vector prevalence, first herd incidence and recovery rates. The latter two probabilities formed the fixed probability transition matrix for use in a discrete-time Markov chain (DTMC) that is quite similar to another compartmental model, the susceptible–infected–susceptible (SIS) model. These DTMC of predicted prevalence (DTMCP) showed good congruence (Pearson correlation = 0.88) with the subsequently observed herd prevalence for seven years from 2010 to 2016. While the DTMCP converged to the stationary (endemic) state of 48% in 2012, after three time steps, the observed prevalence declined instead from 48% after 2016 to 25% in 2018 before rising to 29% in 2020. A sudden plunge in H1N1pdm09 prevalence amongst Norwegians during the 2016/2017 human flu season may have had a knock-on effect in reducing the force of infection in pig herds in Norway. This paper endeavours to present the discrete-time Markov chain (DTMC) as a feasible but limited tool in forecasting the sequence of a predicted infectious disease’s prevalence after it’s incursion as an exotic disease.

Open Markov Type Population Models: From Discrete to Continuous Time

We address the problem of finding a natural continuous time Markov type process—in open populations—that best captures the information provided by an open Markov chain in discrete time which is usually the sole possible observation from data. Given the open discrete time Markov chain, we single out two main approaches: In the first one, we consider a calibration procedure of a continuous time Markov process using a transition matrix of a discrete time Markov chain and we show that, when the discrete time transition matrix is embeddable in a continuous time one, the calibration problem has optimal solutions. In the second approach, we consider semi-Markov processes—and open Markov schemes—and we propose a direct extension from the discrete time theory to the continuous time one by using a known structure representation result for semi-Markov processes that decomposes the process as a sum of terms given by the products of the random variables of a discrete time Markov chain by time functions built from an adequate increasing sequence of stopping times.

Effects of control measures and their impacts on COVID-19 transmission dynamics

Governments around the world have grappled with the COVID-19 pandemic for more than a year. Control measures such as social distancing, use of face masks in public places, business and school closures, city or transportation lockdowns, mass gathering bans, population education and engagement, contact tracing, and improved mass testing protocols are being used to contain the pandemic. Currently, there are no studies to date that rank the effectiveness of these measures, resulting in government responses that may be uncoordinated and inefficient. In this study, we developed a Discrete Time Markov Chain model that captures the above control measures and ranks them. We found that the importance of the measures changes over time and depends on the stage of transmission dynamics, as well as the ecological environment. For example, contact tracing is a powerful measure to effectively control the pandemic, however, our results show that while it is indeed helpful during the early stages of the pandemic, it is much less important after a vaccination program takes effect. Besides, our model improved the standard SEIR compartmental model by taking into account the dynamic temporal transmission and recovery probabilities along with considering a portion of the population that will not comply with government-mandated control measures. If implemented, our novel and unique model may assist many countries in pandemic control decisions.

Financial Risk Information Spreading on Metapopulation Networks

The financial risk information diffuses through various kinds of social networks, such as Twitter and Facebook. Individuals transmit the financial risk information which can migrate among different platforms or forums. In this paper, we propose a financial risk information spreading model on metapopulation networks. The subpopulation represents a platform or forum, and individuals migrate among them to transmit the information. We use a discrete-time Markov chain approach to describe the spreading dynamics’ evolution and deduce the outbreak threshold point. We perform numerical simulation on artificial networks and discover that the financial risk information can be promoted once increasing the information transmission probability and active subpopulation fraction. The weight variance and migration probability cannot significantly affect the financial risk spreading size. The discrete-time Markov chain approach can reasonably predict the above phenomena.

Evaluation of the efficiency of forward error correction of transport protocol data blocks

A model of a transport connection controlled by a transport protocol with the technology of forward error correction in the selective failure mode in the form of a discrete-time Markov chain is proposed. The model takes into account the influence of the protocol parameters, the level of errors in the communication channels, the round-trip delay and the technological parameters of forward error correction on the throughput of the transport connection. The analysis of the dependence of the advantages of the transport protocol with forward error correction over the classical transport protocol is carried out.

Cost of care for persons with dementia: using a discrete-time Markov chain approach with administrative and clinical data from the dementia service Centres in Austria

Background There is growing evidence that the cost for dementia care will increase rapidly in the coming years. Therefore, the objective of this paper was to determine the economic impact of treating clients with dementia in outpatient Dementia Service Centres (DSCs) and simulate the cost progression with real clinical and cost data. Methods To estimate the cost for dementia care, real administrative and clinical data from 1341 clients of the DSCs were used to approximate the total cost of non-pharmaceutical treatment and simulate the cost progression with a discrete-time Markov chain (DTMC) model. The economic simulation model takes severity and progression of dementia into account to display the cost development over a period of up to ten years. Results Based on the administrative data, the total cost for treating these 1341 clients of the DSCs came to 67,294,910 EUR in the first year. From these costs, 74% occurred as indirect costs. Within a five-year period, these costs will increase by 7.1-fold (16.2-fold over 10 years). Further, the DTMC shows that the greatest share of the cost increase derives from the sharp increase of people with severe dementia and that the cost of severe dementia prevails the cost in later periods. Conclusion The DTMC model has shown that the cost increase of dementia care is mostly driven by the indirect cost and the increase of severity of dementia within any given year. The DTMC reveals also that the cost for mild dementia will decrease steadily over the time period of the simulation, whereas the cost for severe dementia increases sharply after running the simulation for 3 years.