scholarly journals A Bayesian Markov Model with Pólya-Gamma Sampling for Estimating Individual Behavior Transition Probabilities from Accelerometer Classifications

2020 ◽  
Vol 25 (3) ◽  
pp. 365-382
Author(s):  
Toryn L. J. Schafer ◽  
Christopher K. Wikle ◽  
Jay A. VonBank ◽  
Bart M. Ballard ◽  
Mitch D. Weegman
Keyword(s):  
Markov Model ◽  
Transition Probabilities ◽  
Individual Behavior

scholarly journals States Transitions Inference of Postpartum Depression Based on Multi-State Markov Model

2021 ◽  
Vol 18 (14) ◽  
pp. 7449
Author(s):  
Juan Xiong ◽  
Qiyu Fang ◽  
Jialing Chen ◽  
Yingxin Li ◽  
Huiyi Li ◽  
...  
Keyword(s):  
Postpartum Depression ◽  
Markov Model ◽  
Normal State ◽  
Sojourn Time ◽  
Transition Probabilities ◽  
Transition Probability ◽  
Public Health Problem ◽  
Mental States ◽  
Hazard Ratio ◽  
Multiple Time

Background: Postpartum depression (PPD) has been recognized as a severe public health problem worldwide due to its high incidence and the detrimental consequences not only for the mother but for the infant and the family. However, the pattern of natural transition trajectories of PPD has rarely been explored. Methods: In this research, a quantitative longitudinal study was conducted to explore the PPD progression process, providing information on the transition probability, hazard ratio, and the mean sojourn time in the three postnatal mental states, namely normal state, mild PPD, and severe PPD. The multi-state Markov model was built based on 912 depression status assessments in 304 Chinese primiparous women over multiple time points of six weeks postpartum, three months postpartum, and six months postpartum. Results: Among the 608 PPD status transitions from one visit to the next visit, 6.2% (38/608) showed deterioration of mental status from the level at the previous visit; while 40.0% (243/608) showed improvement at the next visit. A subject in normal state who does transition then has a probability of 49.8% of worsening to mild PPD, and 50.2% to severe PPD. A subject with mild PPD who does transition has a 20.0% chance of worsening to severe PPD. A subject with severe PPD is more likely to improve to mild PPD than developing to the normal state. On average, the sojourn time in the normal state, mild PPD, and severe PPD was 64.12, 6.29, and 9.37 weeks, respectively. Women in normal state had 6.0%, 8.5%, 8.7%, and 8.8% chances of progress to severe PPD within three months, nine months, one year, and three years, respectively. Increased all kinds of supports were associated with decreased risk of deterioration from normal state to severe PPD (hazard ratio, HR: 0.42–0.65); and increased informational supports, evaluation of support, and maternal age were associated with alleviation from severe PPD to normal state (HR: 1.46–2.27). Conclusions: The PPD state transition probabilities caused more attention and awareness about the regular PPD screening for postnatal women and the timely intervention for women with mild or severe PPD. The preventive actions on PPD should be conducted at the early stages, and three yearly; at least one yearly screening is strongly recommended. Emotional support, material support, informational support, and evaluation of support had significant positive associations with the prevention of PPD progression transitions. The derived transition probabilities and sojourn time can serve as an importance reference for health professionals to make proactive plans and target interventions for PPD.

scholarly journals Forecasting the Long-Run Behavior of the Stock Price of Some Selected Companies in the Malaysian Construction Sector: A Markov Chain Approach

2020 ◽  
Vol 5 (2) ◽  
pp. 296-308
Author(s):  
Wajeeh Mustafa Sarsour ◽  
Shamsul Rijal Muhammad Sabri
Keyword(s):  
Markov Model ◽  
Stock Prices ◽  
Stock Price ◽  
Transition Probabilities ◽  
Return Time ◽  
Price Increase ◽  
State Model ◽  
Construction Sector ◽  
Long Run ◽  
Three State Model

The fluctuations in stock prices produce a high risk that makes investors uncertain about their investment decisions. The present paper provides a methodology to forecast the long-term behavior of five randomly selected equities operating in the Malaysian construction sector. The method used in this study involves Markov chains as a stochastic analysis, assuming that the price changes have the proparty of Markov dependency with their transition probabilities. We identified a three-state Markov model (i.e., increase, stable, fall) and a two-state Markov model (i.e., increase and fall). The findings suggested that the chains had limiting distributions. The mean return time was computed for respective equities as well as to determine the average duration to return to a stock price increase. The analysis might aid investors in improving their investment knowledge, and they will be able to make better decisions when an equity portfolio possesses higher transition probabilities, higher limiting distribution, and lowest mean return time in response to a price increase. Finally, our investigations suggest that investors are more likely to invest in the GKent based on the three-state model, while VIZIONE seems to be a better investment choice based on a two-state model.

A semi-markov model for clinical trials

1965 ◽  
Vol 2 (02) ◽  
pp. 269-285 ◽  
Author(s):  
George H. Weiss ◽  
Marvin Zelen
Keyword(s):  
Clinical Trials ◽  
Probability Distribution ◽  
Acute Leukemia ◽  
Markov Model ◽  
Markov Models ◽  
Transition Probabilities ◽  
State Transitions ◽  
Semi Markov Processes ◽  
Absorbing States ◽  
Epidemic Diseases

This paper applies the theory of semi-Markov processes to the construction of a stochastic model for interpreting data obtained from clinical trials. The model characterizes the patient as being in one of a finite number of states at any given time with an arbitrary probability distribution to describe the length of stay in a state. Transitions between states are assumed to be chosen according to a stationary finite Markov chain.Other attempts have been made to develop stochastic models of clinical trials. However, these have all been essentially Markovian with constant transition probabilities which implies that the distribution of time spent during a visit to a state is exponential (or geometric for discrete Markov chains). Markov models need also to assume that the transitions in the state of a patient depend only on absolute time whereas the semi-Markov model assumes that transitions depend on time relative to a patient. Thus the models are applicable to degenerative diseases (cancer, acute leukemia), while Markov models with time dependent transition probabilities are applicable to colds and epidemic diseases. In this paper the Laplace transforms are obtained for (i) probability of being in a state at timet, (ii) probability distribution to reach absorption state and (iii) the probability distribution of the first passage times to go from initial states to transient or absorbing states, transient to transient, and transient to absorbing. The model is applied to a clinical study of acute leukemia in which patients have been treated with methotrexate and 6-mercaptopurine. The agreement between the data and the model is very good.

The Markov Model of Labor Force Activity 2012-17: Extended Tables of Central Tendency, Shape, Percentile Points, and Bootstrap Standard Errors

2019 ◽  
Vol 28 (1-2) ◽  
pp. 15-108 ◽  
Author(s):  
Gary R. Skoog ◽  
James E. Ciecka ◽  
Kurt V. Krueger
Keyword(s):  
Markov Model ◽  
Labor Force ◽  
Transition Probabilities ◽  
Standard Errors ◽  
Central Tendency ◽  
Statistical Measures ◽  
Gender And Education ◽  
Labor Force Activity ◽  
Force Data

Abstract This paper updates the Skoog-Ciecka-Krueger (2011) study which used 2005-09 U.S. population labor force data to estimate worklife expectancies. This update presents estimates using 2012-17 labor force data for persons ages 18 and over by sex and education. These updated estimates are presented as before as a set of worklife tables, including extended probability calculations and other statistical measures useful to forensic economists. Transition probabilities, by age, gender, and education, are contained in the electronic supplementary materials.

scholarly journals Testing the Semi Markov Model Using Monte Carlo Simulation Method for Predicting the Network Traffic

2020 ◽  
pp. 713-720
Author(s):  
Shirin Kordnoori ◽  
Hamidreza Mostafaei ◽  
Shaghayegh Kordnoori ◽  
Mohammadmohsen Ostadrahimi
Keyword(s):  
Monte Carlo ◽  
Markov Model ◽  
Markov Processes ◽  
Network Traffic ◽  
Markov Models ◽  
Transition Probabilities ◽  
Simulation Method ◽  
Monte Carlo Algorithm ◽  
Statistical Characteristics ◽  
Semi Markov Processes

Semi-Markov processes can be considered as a generalization of both Markov and renewal processes. One of the principal characteristics of these processes is that in opposition to Markov models, they represent systems whose evolution is dependent not only on their last visited state but on the elapsed time since this state. Semi-Markov processes are replacing the exponential distribution of time intervals with an optional distribution. In this paper, we give a statistical approach to test the semi-Markov hypothesis. Moreover, we describe a Monte Carlo algorithm able to simulate the trajectories of the semi-Markov chain. This simulation method is used to test the semi-Markov model by comparing and analyzing the results with empirical data. We introduce the database of Network traffic which is employed for applying the Monte Carlo algorithm. The statistical characteristics of real and synthetic data from the models are compared. The comparison between the semi-Markov and the Markov models is done by computing the Autocorrelation functions and the probability density functions of the Network traffic real and simulated data as well. All the comparisons admit that the Markovian hypothesis is rejected in favor of the more general semi Markov one. Finally, the interval transition probabilities which show the future predictions of the Network traffic are given.

scholarly journals Atmospheric blocking types: Frequencies and transitions

2020 ◽  
Author(s):  
Carola Detring ◽  
Annette Müller ◽  
Lisa Schielicke ◽  
Peter Névir ◽  
Henning W. Rust
Keyword(s):  
Markov Model ◽  
Northern Hemisphere ◽  
Transition Probabilities ◽  
Transition Probability ◽  
Time Step ◽  
Pressure System ◽  
Monthly Basis ◽  
Atlantic Sector ◽  
Weather Patterns ◽  
Significant Difference

Abstract. Stationary, long-lasting blocked weather patterns can lead to extreme conditions such as very high temperatures or heavy rainfall. They are defined by a persistent high pressure system in combination with one or two low pressure systems. The mechanisms for the onset of such weather patterns are still not fully understood. Using a novel method based on the kinematic vorticity number we distinguish between two blocking types, namely High-over-Low and Omega block, in previously-identified blocking periods. Our main goal of this work is to study the temporal evolution of the occurrence probability and the onset, offset, and transition probabilities of blocking on the northern hemisphere. We analyze NCEP-DOE Reanalysis 2 data over the30 year period from 1990 to 2019 in two regions: Euro-Atlantic sector (40° W–30° E) and half northern hemisphere (90° W–90° E). First, we use logistic regression to investigate the temporal development of blocking probabilities depending on years, seasons and months. We find no significant difference in blocking numbers over the 30 year period. But we find large differences in the occurrence probabilities on a monthly basis with strongest increases over the 30 year period in February and March that are compensated by a decrease in December and autumn. Second, we use a Markov model to calculate the transition probabilities for two models: One is composed of two states blocking and no blocking, and another Markov model (three states) that additionally distinguishes between the specific blocking types High-over-Low and Omega blocking as well as of the state no blocking. The description with Markov theory reduces the probability to change from one weather regime to another or to stay within the same regime to a dependency only on the previous time step. Over the 30 year period, we found the largest changes in transition probabilities in the summer season, where the transition probability to Omega blocks increase strongly, while the unblocked state becomes less probable. Hence, Omega blocks become more frequent and stable in summer at the expense of the other states. As a main result, we show that Omega blocking is more likely to occur and more persistent than the High-over-Low blocking pattern.

scholarly journals A Decision Analytical Model Investigating Cost-Effectiveness of Erlotinib

2020 ◽  
Author(s):  
Mohammed Alam
Keyword(s):  
Cost Effectiveness ◽  
Markov Model ◽  
Analytical Model ◽  
State Transition ◽  
Transition Probabilities ◽  
Qaly Gain ◽  
Health State ◽  
Time Varying ◽  
Decision Analytical Model ◽  
The Cost

Background: A decision analytical model investigating cost-effectiveness of Erlotinib was submitted to the UK NICE (National Institute for Health and Care Excellence), which was not based on actual health-state transition probabilities, leading to structural uncertainty in the model. The study adopted a Markov state-transition model for investigating the cost-effectiveness of Erlotinib versus Best Supportive Care (BSC) as a maintenance therapy for patients with non-small cell lung cancer (NSCLC). Methods: Unlike manufacturer submission (MS), the Markov model was governed by transition probabilities, and allowed a negative post-progression survival (PPS) estimate to appear in later cycle. Using published summary survival data, the study employs three fixed- and time-varying approaches to estimate state transition probabilities that are used in a restructured model. Results: Post-progression probabilities and probabilities of death for Erlotinib were different than fixed-transition approaches. The best fitting curves are achieved for both PPS and probability of death across the time for which data were available, but the curves start diverging towards the end of this period. The Markov model which extrapolates the curves forward in time suggests that this difference between a time-varying and fixed-transition becomes even greater. Our models produce an ICER of £54k -£66k per QALY gain, which is comparable to an ICER presented in the MS (£55k/QALY gain). Conclusions: Results from restructured Markov models show robust cost-effectiveness results for Erlotinib vs BSC. Although these are comparable to manufacturer submissions, in terms of magnitude, they vary, and which are crucial for interventions falling near a threshold value. The study will further explore the cost-effectiveness of therapies for NSCLC in Qatar.

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