Search results for "Prediction interval"
showing 10 items of 12 documents
Modeling Chickenpox Dynamics with a Discrete Time Bayesian Stochastic Compartmental Model
2018
[EN] We present a Bayesian stochastic susceptible-exposed-infectious-recovered model in discrete time to understand chickenpox transmission in the Valencian Community, Spain. During the last decades, different strategies have been introduced in the routine immunization program in order to reduce the impact of this disease, which remains a public health's great concern. Under this scenario, a model capable of explaining closely the dynamics of chickenpox under the different vaccination strategies is of utter importance to assess their effectiveness. The proposed model takes into account both heterogeneous mixing of individuals in the population and the inherent stochasticity in the transmiss…
Finding Prediction Limits for a Future Number of Failures in the Prescribed Time Interval under Parametric Uncertainty
2012
Computing prediction intervals is an important part of the forecasting process intended to indicate the likely uncertainty in point forecasts. Prediction intervals for future order statistics are widely used for reliability problems and other related problems. In this paper, we present an accurate procedure, called ‘within-sample prediction of order statistics', to obtain prediction limits for the number of failures that will be observed in a future inspection of a sample of units, based only on the results of the first in-service inspection of the same sample. The failure-time of such units is modeled with a two-parameter Weibull distribution indexed by scale and shape parameters β and δ, …
Improved Frequentist Prediction Intervals for Autoregressive Models by Simulation
2015
It is well known that the so called plug-in prediction intervals for autoregressive processes, with Gaussian disturbances, are too narrow, i.e. the coverage probabilities fall below the nominal ones. However, simulation experiments show that the formulas borrowed from the ordinary linear regression theory yield one-step prediction intervals, which have coverage probabilities very close to what is claimed. From a Bayesian point of view the resulting intervals are posterior predictive intervals when uniform priors are assumed for both autoregressive coefficients and logarithm of the disturbance variance. This finding opens the path how to treat multi-step prediction intervals which are obtain…
Mapping risk factors for depression across the lifespan: An umbrella review of evidence from meta-analyses and Mendelian randomization studies
2018
The development of depression may involve a complex interplay of environmental and genetic risk factors. PubMed and PsycInfo databases were searched from inception through August 3, 2017, to identify meta-analyses and Mendelian randomization (MR) studies of environmental risk factors associated with depression. For each eligible meta-analysis, we estimated the summary effect size and its 95% confidence interval (CI) by random-effects modeling, the 95% prediction interval, heterogeneity with I 2 , and evidence of small-study effects and excess significance bias. Seventy meta-analytic reviews met the eligibility criteria and provided 134 meta-analyses for associations from 1283 primary studie…
Bayesian forecasting with the Holt–Winters model
2010
Exponential smoothing methods are widely used as forecasting techniques in inventory systems and business planning, where reliable prediction intervals are also required for a large number of series. This paper describes a Bayesian forecasting approach based on the Holt–Winters model, which allows obtaining accurate prediction intervals. We show how to build them incorporating the uncertainty due to the smoothing unknowns using a linear heteroscedastic model. That linear formulation simplifies obtaining the posterior distribution on the unknowns; a random sample from such posterior, which is not analytical, is provided using an acceptance sampling procedure and a Monte Carlo approach gives …
A nonlinear mixed model approach to predict energy expenditure from heart rate.
2021
Abstract Objective. Heart rate (HR) monitoring provides a convenient and inexpensive way to predict energy expenditure (EE) during physical activity. However, there is a lot of variation among individuals in the EE-HR relationship, which should be taken into account in predictions. The objective is to develop a model that allows the prediction of EE based on HR as accurately as possible and allows an improvement of the prediction using calibration measurements from the target individual. Approach. We propose a nonlinear (logistic) mixed model for EE and HR measurements and an approach to calibrate the model for a new person who does not belong to the dataset used to estimate the model. The …
A Forecasting Support System Based on Exponential Smoothing
2010
This chapter presents a forecasting support system based on the exponential smoothing scheme to forecast time-series data. Exponential smoothing methods are simple to apply, which facilitates computation and considerably reduces data storage requirements. Consequently, they are widely used as forecasting techniques in inventory systems and business planning. After selecting the most adequate model to replicate patterns of the time series under study, the system provides accurate forecasts which can play decisive roles in organizational planning, budgeting and performance monitoring.
Weighted-Average Least Squares (WALS): Confidence and Prediction Intervals
2022
We extend the results of De Luca et al. (2021) to inference for linear regression models based on weighted-average least squares (WALS), a frequentist model averaging approach with a Bayesian flavor. We concentrate on inference about a single focus parameter, interpreted as the causal effect of a policy or intervention, in the presence of a potentially large number of auxiliary parameters representing the nuisance component of the model. In our Monte Carlo simulations we compare the performance of WALS with that of several competing estimators, including the unrestricted least-squares estimator (with all auxiliary regressors) and the restricted least-squares estimator (with no auxiliary reg…
Holt–Winters Forecasting: An Alternative Formulation Applied to UK Air Passenger Data
2007
Abstract This paper provides a formulation for the additive Holt–Winters forecasting procedure that simplifies both obtaining maximum likelihood estimates of all unknowns, smoothing parameters and initial conditions, and the computation of point forecasts and reliable predictive intervals. The stochastic component of the model is introduced by means of additive, uncorrelated, homoscedastic and Normal errors, and then the joint distribution of the data vector, a multivariate Normal distribution, is obtained. In the case where a data transformation was used to improve the fit of the model, cumulative forecasts are obtained here using a Monte-Carlo approximation. This paper describes the metho…
A Bayesian SIRS model for the analysis of respiratory syncytial virus in the region of Valencia, Spain
2014
We present a Bayesian stochastic susceptible-infected-recovered-susceptible (SIRS) model in discrete time to understand respiratory syncytial virus dynamics in the region of Valencia, Spain. A SIRS model based on ordinary differential equations has also been proposed to describe RSV dynamics in the region of Valencia. However, this continuous-time deterministic model is not suitable when the initial number of infected individuals is small. Stochastic epidemic models based on a probability of disease transmission provide a more natural description of the spread of infectious diseases. In addition, by allowing the transmission rate to vary stochastically over time, the proposed model provides…