Using a Bayesian change-point statistical model with autoregressive terms to study the monthly number of dispensed asthma medications by public health services

In this paper, it is proposed a Bayesian analysis of a time series in the presence of a random change-point and autoregressive terms. The development of this model was motivated by a data set related to the monthly number of asthma medications dispensed by the public health services of Ribeirão Preto, Southeast Brazil, from 1999 to 2011. A pronounced increase trend has been observed from 1999 to a specific change-point, with a posterior decrease until the end of the series. In order to obtain estimates for the parameters of interest, a Bayesian Markov Chain Monte Carlo (MCMC) simulation procedure using the Gibbs sampler algorithm was developed. The Bayesian model with autoregressive terms of order 1 fits well to the data, allowing to estimate the change-point at July 2007, and probably reflecting the results of the new health policies and previously adopted programs directed toward patients with asthma. The results imply that the present model is useful to analyse the monthly number of dispensed asthma medications and it can be used to describe a broad range of epidemiological time series data where a change-point is present.Peer Reviewe

Using a Bayesian change-point statistical model with autoregressive terms to study the monthly number of dispensed asthma medications by public health services

In this paper, it is proposed a Bayesian analysis of a time series in the presence of a random change-point and autoregressive terms. The development of this model was motivated by a data set related to the monthly number of asthma medications dispensed by the public health services of Ribeirão Preto, Southeast Brazil, from 1999 to 2011. A pronounced increase trend has been observed from 1999 to a specific change-point, with a posterior decrease until the end of the series. In order to obtain estimates for the parameters of interest, a Bayesian Markov Chain Monte Carlo (MCMC) simulation procedure using the Gibbs sampler algorithm was developed. The Bayesian model with autoregressive terms of order 1 fits well to the data, allowing to estimate the change-point at July 2007, and probably reflecting the results of the new health policies and previously adopted programs directed toward patients with asthma. The results imply that the present model is useful to analyse the monthly number of dispensed asthma medications and it can be used to describe a broad range of epidemiological time series data where a change-point is present

Using a Bayesian change-point statistical model with autoregressive terms to study the monthly number of dispensed asthma medications by public health services

In this paper, it is proposed a Bayesian analysis of a time series in the presence of a random change-point and autoregressive terms. The development of this model was motivated by a data set related to the monthly number of asthma medications dispensed by the public health services of Ribeirao Preto, Southeast Brazil, from 1999 to 2011. A pronounced increase trend has been observed from 1999 to a specific change-point, with a posterior decrease until the end of the series. In order to obtain estimates for the parameters of interest, a Bayesian Markov Chain Monte Carlo (MCMC) simulation procedure using the Gibbs sampler algorithm was developed. The Bayesian model with autoregressive terms of order 1 fits well to the data, allowing to estimate the change-point at July 2007, and probably reflecting the results of the new health policies and previously adopted programs directed toward patients with asthma. The results imply that the present model is useful to analyse the monthly number of dispensed asthma medications and it can be used to describe a broad range of epidemiological time series data where a change-point is present

Dynamic Bayesian smooth transition autoregressive models applied to hourly electricity load in southern Brazil

Dynamic Bayesian Smooth Transition Autoregressive (DBSTAR) models are proposed for nonlinear autoregressive time series processes as alternative to both the classical Smooth Transition Autoregressive (STAR) models of Chan and Tong (1986) and the Bayesian Simulation STAR (BSTAR) models of Lopes and Salazar (2005). Unlike those, DBSTAR models are sequential polynomial dynamic analytical models suitable for inherently non-stationary time series with non-linear characteristics such as asymmetric cycles. As they are analytical, they also avoid potential computational problems associated with BSTAR models and allow fast sequential estimation of parameters. Two types of DBSTAR models are defined here based on the method adopted to approximate the transition function of their autoregressive components, namely the Taylor and the B-splines DBSTAR models. A harmonic version of those models, that accounted for the cyclical component explicitly in a flexible yet parsimonious way, were applied to the well-known series of annual Canadian lynx trappings and showed improved fitting when compared to both the classical STAR and the BSTAR models. Another application to a long series of hourly electricity loading in southern Brazil, covering the period of the South-African Football World Cup in June 2010, illustrates the short-term forecasting accuracy of fast computing harmonic DBSTAR models that account for various characteristics such as periodic behaviour (both within-the-day and within-the-week) and average temperature

A Bayesian Framework for Estimating Seismic Wave Arrival Time

Because earthquakes have a large impact on human society, statistical methods for better studying earthquakes are required. One characteristic of earthquakes is the arrival time of seismic waves at a seismic signal sensor. Once we can estimate the earthquake arrival time accurately, the earthquake location can be triangulated, and assistance can be sent to that area correctly. This study presents a Bayesian framework to predict the arrival time of seismic waves with associated uncertainty. We use a change point framework to model the different conditions before and after the seismic wave arrives. To evaluate the performance of the model, we conducted a simulation study where we could evaluate the predictive performance of the model framework. The results show that our method has acceptable performance of arrival time prediction with accounting for the uncertainty

Modeling migraine severity with autoregressive ordered probit models

This paper considers the problem of modeling migraine severity assessments and their dependence on weather and time characteristics. Since ordinal severity measurements arise from a single patient dependencies among the measurements have to be accounted for. For this the autore- gressive ordinal probit (AOP) model of Müller and Czado (2004) is utilized and fitted by a grouped move multigrid Monte Carlo (GM-MGMC) Gibbs sampler. Initially, covariates are selected using proportional odds models ignoring this dependency. Model fit and model comparison are discussed. The analysis shows that humidity, windchill, sunshine length and pressure differences have an effect in addition to a high dependence on previous measurements. A comparison with proportional odds specifications shows that the AOP models are preferred

Are apparent findings of nonlinearity due to structural instability in economic time series?

Many modelling issues and policy debates in macroeconomics depend on whether macroeconomic times series are best characterized as linear or nonlinear. If departures from linearity exist, it is important to know whether these are endogenously generated (as in, e.g., a threshold autoregressive model) or whether they merely reflect changing structure over time. We advocate a Bayesian approach and show how such an approach can be implemented in practice. An empirical exercise involving several macroeconomic time series shows that apparent findings of threshold type nonlinearities could be due to structural instability

What do Bayesian methods offer population forecasters?

The Bayesian approach has a number of attractive properties for probabilistic forecasting. In this paper, we apply Bayesian time series models to obtain future population estimates with uncertainty for England and Wales. To account for heterogeneity found in the historical data, we add parameters to represent the stochastic volatility in the error terms. Uncertainty in model choice is incorporated through Bayesian model averaging techniques. The resulting predictive distributions from Bayesian forecasting models have two main advantages over those obtained using traditional stochastic models. Firstly, data and uncertainties in the parameters and model choice are explicitly included using probability distributions. As a result, more realistic probabilistic population forecasts can be obtained. Second, Bayesian models formally allow the incorporation of expert opinion, including uncertainty, into the forecast. Our results are discussed in relation to classical time series methods and existing cohort component projections. This paper demonstrates the flexibility of the Bayesian approach to simple population forecasting and provides insights into further developments of more complicated population models that include, for example, components of demographic change