Bayesian Inference of Trend and Difference-Stationarity

1994 ◽  
Vol 10 (3-4) ◽  
pp. 596-608 ◽  
Author(s):  
Robert E. McCulloch ◽  
Ruey S. Tsay
Keyword(s):  
Time Series ◽  
Bayesian Inference ◽  
Model Selection ◽  
Odds Ratio ◽  
Model Discrimination ◽  
Posterior Probabilities ◽  
Competing Models ◽  
Computational Difficulty ◽  
Changes Over Time ◽  
Over Time

This paper proposes a general Bayesian framework for distinguishing between trend- and difference-stationarity. Usually, in model selection, we assume that all of the data were generated by one of the models under consideration. In studying time series, however, we may be concerned that the process is changing over time, so that the preferred model changes over time as well. To handle this possibility, we compute the posterior probabilities of the competing models for each observation. This way we can see if different segments of the series behave differently with respect to the competing models. The proposed method is a generalization of the usual odds ratio for model discrimination in Bayesian inference. In application, we employ the Gibbs sampler to overcome the computational difficulty. The procedure is illustrated by a real example.

On Bayesian model selection for INGARCH models viatrans-dimensional Markov chain Monte Carlo methods

2021 ◽  
pp. 1471082X2110347
Author(s):  
Panagiota Tsamtsakiri ◽  
Dimitris Karlis
Keyword(s):  
Time Series ◽  
Model Selection ◽  
Bayesian Model ◽  
Linear Models ◽  
Simulation Experiment ◽  
Mean Values ◽  
The Past ◽  
Competing Models ◽  
Selection For ◽  
Log Linear

There is an increasing interest in models for discrete valued time series. Among them, the integer autoregressive conditional heteroscedastic (INGARCH) is a model that has found several applications. In the present article, we study the problem of model selection for this family of models. Namely we consider that an observation conditional on the past follows a Poisson distribution where its mean depends on its past mean values and on past observations. We consider both linear and log-linear models. Our purpose is to select the most appropriate order of such models, using a trans-dimensional Bayesian approach that allows jumps between competing models. A small simulation experiment supports the usage of the method. We apply the methodology to real datasets to illustrate the potential of the approach.

scholarly journals Bayesian Inference and Testing Any Hypothesis You Can Specify

2018 ◽  
Vol 1 (2) ◽  
pp. 281-295 ◽  
Author(s):  
Alexander Etz ◽  
Julia M. Haaf ◽  
Jeffrey N. Rouder ◽  
Joachim Vandekerckhove
Keyword(s):  
Bayesian Inference ◽  
Model Selection ◽  
Hypothesis Testing ◽  
Likelihood Ratio ◽  
Special Form ◽  
Null Hypothesis ◽  
Bayes Factor ◽  
Alternative Hypotheses ◽  
Competing Models

Hypothesis testing is a special form of model selection. Once a pair of competing models is fully defined, their definition immediately leads to a measure of how strongly each model supports the data. The ratio of their support is often called the likelihood ratio or the Bayes factor. Critical in the model-selection endeavor is the specification of the models. In the case of hypothesis testing, it is of the greatest importance that the researcher specify exactly what is meant by a “null” hypothesis as well as the alternative to which it is contrasted, and that these are suitable instantiations of theoretical positions. Here, we provide an overview of different instantiations of null and alternative hypotheses that can be useful in practice, but in all cases the inferential procedure is based on the same underlying method of likelihood comparison. An associated app can be found at https://osf.io/mvp53/ . This article is the work of the authors and is reformatted from the original, which was published under a CC-By Attribution 4.0 International license and is available at https://psyarxiv.com/wmf3r/ .

scholarly journals Investigating changes over time of annual rainfall in Zimbabwe

2010 ◽  
Vol 14 (12) ◽  
pp. 2671-2679 ◽  
Author(s):  
D. Mazvimavi
Keyword(s):  
Time Series ◽  
Regression Analysis ◽  
Quantile Regression ◽  
Rainy Season ◽  
Annual Rainfall ◽  
Rainfall Time Series ◽  
Average Rainfall ◽  
Quantile Regression Analysis ◽  
Changes Over Time ◽  
Over Time

Abstract. There is increasing concern in southern Africa about the possible decline of rainfall as a result of global warming. Some studies concluded that average rainfall in Zimbabwe had declined by 10% or 100 mm during the last 100 years. This paper investigates the validity of the assumption that rainfall is declining in Zimbabwe. Time series of annual rainfall, and total rainfall for (a) the early part of the rainy season, October-November-December (OND), and (b) the mid to end of the rainy season, January-February-March (JFM) are analysed for the presence of trends using the Mann-Kendall test, and for the decline or increase during years with either high or low rainfall using quantile regression analysis. The Pettitt test has also been utilized to examine the possible existence of change or break-points in the rainfall time series. The analysis has been done for 40 rainfall stations with records starting during the 1892–1940 period and ending in 2000, and representative of all the rainfall regions. The Mann-Kendal test did not identify a significant trend at all the 40 stations, and therefore there is no proof that the average rainfall at each of these stations has changed. Quantile regression analysis revealed a decline in annual rainfall less than the tenth percentile at only one station, and increasing of rainfall greater than the ninetieth percentile at another station. All the other stations had no changes over time in both the low and high rainfall at the annual interval. Climate change effects are therefore not yet statistically significant within time series of total seasonal and annual rainfall in Zimbabwe. The general perception about declining rainfall is likely due to the presence of multidecadal variability characterized by bunching of years with above (e.g. 1951–1958, 1973–1980) and below (e.g. 1959–1972, 1982–1994 ) average rainfall.

scholarly journals Bayesian inference and testing any hypothesis you can specify

2018 ◽  
Author(s):  
Alexander Etz ◽  
Julia M. Haaf ◽  
Jeffrey N. Rouder ◽  
Joachim Vandekerckhove
Keyword(s):  
Bayesian Inference ◽  
Model Selection ◽  
Hypothesis Testing ◽  
Likelihood Ratio ◽  
Special Form ◽  
Null Hypothesis ◽  
Bayes Factor ◽  
Alternative Hypotheses ◽  
Competing Models

Hypothesis testing is a special form of model selection. Once a pair of competing models is fully defined, their definition immediately leads to a measure of how strongly each model supports the data. The ratio of their support is often called the likelihood ratio or the Bayes factor. Critical in the model selection endeavor is the specification of the models. In the case of hypothesis testing, it is of the greatest importance that we specify exactly what is meant by a "null" hypothesis as well as the alternative to which it is contrasted, and that these are suitable instantiations of theoretical positions. Here, we provide an overview of different instantiations of null and alternative hypotheses that can be useful in practice, while the underlying method of likelihood comparison is universal and identical in all cases. An associated app can be found via https://osf.io/mvp53/.

scholarly journals Evolution of Agricultural Production in Portugal during 1850–2018: A Geographical and Historical Perspective

Land ◽  
2021 ◽  
Vol 10 (8) ◽  
pp. 776
Author(s):  
Cláudia M. Viana ◽  
Dulce Freire ◽  
Patrícia Abrantes ◽  
Jorge Rocha
Keyword(s):  
Time Series ◽  
Food Security ◽  
Agricultural Production ◽  
Security Evaluation ◽  
Global Food Security ◽  
Historical Perspectives ◽  
Production Values ◽  
Current Production ◽  
Changes Over Time ◽  
Over Time

Agricultural statistical data enable the detection and interpretation of the development of agriculture and the food supply situation over time, which is essential for food security evaluation in any country. Based on the historical agricultural statistics, this study produces a long spatial time-series with annual production values of three cereals relevant to global food security—wheat, maize, and rice, aiming to provide geographical and historical perspectives. Therefore, we reconstructed past and current production patterns and trends at the district level over 169 years, which supported a space–time cross-reading of the general characteristics of the regional agricultural production value distributions and relative densities in Portugal. Particularly, the production trends of wheat, maize, and rice showed three different situations: growth (maize), stability (rice), and decline (wheat). For decades, maize and wheat production alternated, depending on agricultural years and political aspects, such as the Wheat Campaign (1929–1938). The changes over time presented a pattern that, in the case of these three cereals, enabled a clear division of the country into major regions according to cereal production. Overall, maize and rice, both grown on irrigated croplands, presented a similar pattern in some regions of Portugal, mainly the central region. In this study, a preliminary analysis was presented and related to successive public policies; however, notably, there are more lessons to be learned from this long spatial time-series.

Comparison of two devices for measuring exercise transcutaneous oxygen pressures in patients with claudication

VASA ◽  
2015 ◽  
Vol 44 (5) ◽  
pp. 355-362 ◽  
Author(s):  
Marie Urban ◽  
Alban Fouasson-Chailloux ◽  
Isabelle Signolet ◽  
Christophe Colas Ribas ◽  
Mathieu Feuilloy ◽  
...  
Keyword(s):  
Oxygen Pressure ◽  
Optical Sensors ◽  
Chemical Sensors ◽  
Transcutaneous Oxygen ◽  
Starting Values ◽  
Two Systems ◽  
Transcutaneous Oxygen Pressure ◽  
New Sensors ◽  
Changes Over Time ◽  
Over Time

Abstract. Summary: Background: We aimed at estimating the agreement between the Medicap® (photo-optical) and Radiometer® (electro-chemical) sensors during exercise transcutaneous oxygen pressure (tcpO2) tests. Our hypothesis was that although absolute starting values (tcpO2rest: mean over 2 minutes) might be different, tcpO2-changes over time and the minimal value of the decrease from rest of oxygen pressure (DROPmin) results at exercise shall be concordant between the two systems. Patients and methods: Forty seven patients with arterial claudication (65 + / - 7 years) performed a treadmill test with 5 probes each of the electro-chemical and photo-optical devices simultaneously, one of each system on the chest, on each buttock and on each calf. Results: Seventeen Medicap® probes disconnected during the tests. tcpO2rest and DROPmin values were higher with Medicap® than with Radiometer®, by 13.7 + / - 17.1 mm Hg and 3.4 + / - 11.7 mm Hg, respectively. Despite the differences in absolute starting values, changes over time were similar between the two systems. The concordance between the two systems was approximately 70 % for classification of test results from DROPmin. Conclusions: Photo-optical sensors are promising alternatives to electro-chemical sensors for exercise oximetry, provided that miniaturisation and weight reduction of the new sensors are possible.

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