Introduction: basic notions about Bayesian inference

Petris, Giovanni De; Petrone, Sonia; Campagnoli, Patrizia

doi:10.1007/b135794_1

Cited by 5 publications

(5 citation statements)

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“…Trends in DLM are commonly represented by second order polynomials (Pole et al, 1994), which describe either growth or decline in the system level. The state vector representing this component 𝐴𝐴 𝐴𝐴1𝑡𝑡 = (𝜇𝜇1,𝑡𝑡, 𝜇𝜇2,𝑡𝑡) 𝑇𝑇 comprises two components: the level and the slope.…”

Section: Model Componentsmentioning

confidence: 99%

“…One can think of a DLM as a linear regression model where the regression coefficients are allowed to vary smoothly over time. These models can capture time series features such as trend, seasonality, and regression associations (Petris et al, 2009). DLMs are a specific case of a broad class of models called state-space models (Petris et al, 2009) wherein an observable/measurable phenomenon (y t ) at a given time t depends on an underlying unobserved (latent) state (θ t ) of a particular system.…”

Section: Bayesian Dlmmentioning

confidence: 99%

“…These models can capture time series features such as trend, seasonality, and regression associations (Petris et al, 2009). DLMs are a specific case of a broad class of models called state-space models (Petris et al, 2009) wherein an observable/measurable phenomenon (y t ) at a given time t depends on an underlying unobserved (latent) state (θ t ) of a particular system. The DLM allows the modeler to update their beliefs about the current value of this unobserved state each time a new observation is made using an associated algorithm named the Kalman filter.…”

Section: Bayesian Dlmmentioning

confidence: 99%

“…Bayesian inference is recursive by nature where model parameters are updated as new observations are added, making it a natural fit for time series analysis (Petris et al, 2009). Bayesian forecasting in DLMs is controlled by a series of equations that are commonly known as the Kalman filter algorithm, which are described below.…”

Section: Bayesian Forecastingmentioning

confidence: 99%

See 3 more Smart Citations

On‐Line Warning System for Pipe Burst Using Bayesian Dynamic Linear Models

Henriques‐Silva

Duchesne

St‐Gelais³

et al. 2023

Water Resources Research

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Pipe breaks are a recurrent problem in water distribution networks and detecting them quickly is crucial to minimize the economic and environmental costs for municipalities. This study presents a burst detection methodology applying Bayesian dynamic linear models (DLMs) on water flow time series combined with an outlier monitoring tool. The model is used to characterize the actual flow and, for each time, a one‐step ahead forecast distribution is obtained recursively before moving onto the next observation. The outlier detection method consists of comparing the main model with an alternative one wherein the mean flow is shifted to a higher value (as bursts tend to increase flow) to evaluate which model best fit the observed data. If the alternative model is favored, a burst alarm is issued. To verify the performance of this approach, the DLM and monitoring tool were applied on 2 yr of flow data from two district meter areas (DMAs) in Halifax (Canada), and a historical break data set is used to assess model accuracy. The model was able to detect up to 75% and 71.2% of the pipe breaks, with a false alarm rate of 5.15% and 12% in the first and second DMA, respectively. Finally, the proposed model allows for straightforward interpretation of model parameters, nonlinear relationship between flow and predictors of interest, naturally describes the uncertainty for future predictions, can easily accommodate missing values and can be tuned to maximize break detection or minimize false alarm rates to adapt to specific objectives of water infrastructure managers.

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Section: Model Componentsmentioning

confidence: 99%

Section: Bayesian Dlmmentioning

confidence: 99%

Section: Bayesian Dlmmentioning

confidence: 99%

Section: Bayesian Forecastingmentioning

confidence: 99%

See 2 more Smart Citations

On‐Line Warning System for Pipe Burst Using Bayesian Dynamic Linear Models

Henriques‐Silva

Duchesne

St‐Gelais³

et al. 2023

Water Resources Research

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“…Linear-Gaussian assumptions in the LDS result in the following state-space equations (Petris et al, 2009;Grewal & Andrews, 2015) h…”

Section: The Linearmentioning

confidence: 99%

Enforcing mean reversion in state space models for prawn pond water quality forecasting

Dabrowski

Rahman

Pagendam

et al. 2020

Computers and Electronics in Agriculture

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The contribution of this study is a novel approach to introduce mean reversion in multi-step-ahead forecasts of state-space models. This approach is demonstrated in a prawn pond water quality forecasting application.The mean reversion constrains forecasts by gradually drawing them to an average of previously observed dynamics. This corrects deviations in forecasts caused by irregularities such as chaotic, non-linear, and stochastic trends. The key features of the approach include (1) it enforces mean reversion, (2) it provides a means to model both short and long-term dynamics, (3) it is able to apply mean reversion to select structural state-space components, and (4) it is simple to implement. Our mean reversion approach is demonstrated on various state-space models and compared with several time-series models on a prawn pond water quality dataset. Results show that mean reversion reduces long-term forecast errors by over 60% to produce the most accurate models in the comparison. more) of pond water temperature typically varies within some bounds. These bounds are maintained as the underlying process seeks thermodynamic equilibrium within a changing environment. Without knowledge of the underlying process, the longer-term dynamics can appear as a slowly varying stochastic trend. Forecasting such processes can be challenging when stochastic trends cause forecasts to deviate. Models should realistically incorporate some form of constraint or bounds. Our hypothesis is that such a constraint can be imposed by modelling the stochastic variations with a fixed attractor distribution that long-term trends are drawn towards. In this form, the long-term behaviour of the process may have some stable, marginal distribution when integrated over time (long periods of time or just the recent past). In this study we propose a novel approach to introduce an attractor distribution in non-stationary state-space models. The attractor distribution models previously observed dynamics. Mean reversion is enforced through introducing pseudoobservations into the Kalman filter during forecasting. These pseudo-observations are samples of the attractor distribution mean. The result is that the filtering operation during forecasting naturally draws the forecasts towards the mean of the previously observed dynamics.The proposed approach can model both short and long-term dynamics and it allows for the selection of which state space components should be mean reverting. Furthermore, the approach is easily implemented using the standard Kalman filter and it has broad appeal as it addresses problems that are found in many domains other than aquaculture. . Sequential data assimilation with a nonlinear quasi-geostrophic model using monte carlo methods to forecast error statistics.

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Stochastic Trends

2011

Statistical Methods for Trend Detection and Analysis in the Environmental Sciences

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Introduction: basic notions about Bayesian inference

Cited by 5 publications

References 0 publications

On‐Line Warning System for Pipe Burst Using Bayesian Dynamic Linear Models

On‐Line Warning System for Pipe Burst Using Bayesian Dynamic Linear Models

Enforcing mean reversion in state space models for prawn pond water quality forecasting

Stochastic Trends

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