The relationship between the power prior and hierarchical models

Abstract Background Like many developing countries, Thailand has experienced a rapid rise in obesity, accompanied by a rapid change in occupational structure. It is plausible that these two trends are related, with movement into sedentary occupations leading to increases in obesity. National health examination survey data contains information on obesity and socioeconomic conditions that can help untangle the relationship, but analysis is challenging because of small sample sizes. Methods This paper explores the relationship between occupation and obesity using data on 10,127 respondents aged 20–59 from the 2009 National Health Examination Survey. Obesity is measured using waist circumference. Modelling is carried out using an approach known as Multiple Regression with Post-Stratification (MRP). We use Bayesian hierarchical models to construct prevalence estimates disaggregated by age, sex, education, urban-rural residence, region, and occupation, and use census population weights to aggregate up. The Bayesian hierarchical model is designed to protect against overfitting and false discovery, which is particularly important in an exploratory study such as this one. Results There is no clear relationship between the overall sedentary nature of occupations and obesity. Instead, obesity appears to vary occupation by occupation. For instance, women in professional occupations, and men who are agricultural or fishery workers, have relatively low rates of obesity. Conclusion Bayesian hierarchical models plus post-stratification offers new possibilities for using surveys to learn about complex health issues.

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Teacher’s Corner: Moving Between Hierarchical Modeling Notations

Journal of Educational and Behavioral Statistics ◽

10.3102/10769986022001119 ◽

1997 ◽

Vol 22 (1) ◽

pp. 119-123

Author(s):

John Ferron

Keyword(s):

Hierarchical Models ◽

Mixed Model ◽

Hierarchical Modeling ◽

The Relationship

Students studying hierarchical models are often confronted with multiple notational representations. The purpose of this note is to illustrate the relationship between HLM notation and mixed model notation. This is accomplished by explicitly mapping the parameters across notations for a concrete example involving the hierarchical modeling of change.

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Expropriation of Church Property in Nineteenth-Century Mexico and Colombia: A Comparison

The Americas A Quarterly Review of Latin American History ◽

10.2307/980320 ◽

1969 ◽

Vol 25 (4) ◽

pp. 387-401 ◽

Cited By ~ 1

Author(s):

Robert J. Knowlton

Keyword(s):

Nineteenth Century ◽

Latin America ◽

Private Property ◽

Church And State ◽

Power Prior ◽

Independent States ◽

National Power ◽

The Relationship ◽

Newly Independent States ◽

The Church

Among the major sources of conflict between liberals and conservatives in nineteenth-century Latin America was the controversy over the relationship between Church and State and the position of the Church in the newly independent states. Not infrequently the issues occasioned violence and bloodshed and long periods of instability while the conservative defenders of a privileged Church disputed with reforming liberals attempting to enforce their ideas. Such was the case in Colombia and Mexico when liberalism reached its apogee in the middle of the nineteenth century. In both countries there had been many years of conflict between conservatives who were generally pro-clerical and espoused centralist ideas about government and liberals who were anti-clerical and favored federalism. The liberals also believed in legal equality, the sanctity of private property, individualism, laissez faire, and the necessity of limiting the Church to a purely spiritual role in society. Although liberals in both countries had achieved national power prior to the 1850’s, the Mexican Constitution of 1857 and the Colombian Rionegro Constitution of 1863 symbolized the liberals’ victory and enshrined their principles; for years those constitutions provided the rallying point for liberals against the opposition.

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Oposición legislativa y patronazgo político. Gasto en empleo público de los estados en México, 2001-2012

región y sociedad ◽

10.22198/rys.2018.71.a773 ◽

2017 ◽

Vol 30 (71) ◽

Cited By ~ 1

Author(s):

Alejandra Armesto ◽

Juan C. Olmeda

Keyword(s):

Hierarchical Models ◽

Public Spending ◽

State Legislatures ◽

Executive Branch ◽

State Governments ◽

Public Employment ◽

Mexican State ◽

Political Patronage ◽

Per Capita ◽

The Relationship

En el artículo se argumenta que el patronazgo político depende de la fuerza de negociación de la oposición en el Congreso. Esta hipótesis se pone a prueba a través del análisis del gasto público en salarios de los gobiernos estatales en México. Se combina información estadística sobre el salario del sector público por habitante para el periodo 2001-2012, con datos de la encuesta a expertos en política estatal en México, que considera la fortaleza e influencia de la oposición en las legislaturas estatales. El análisis especifica modelos jerárquicos lineales, y muestra que el nivel de patronazgo será mayor cuanto más limitado esté el Poder Ejecutivo por la oposición legislativa. Estos hallazgos contribuyen con una hipótesis original a los estudios acerca del patronazgo y de la relación entre la oposición en el Congreso y el Ejecutivo.Legislative opposition and political patronage. Mexican states’ public employment spending, 2001-2012This article argues that political patronage depends on the opposition’s bargaining strength in Congress. This hypothesis is tested by analyzing Mexican state governments’ public spending on salaries. Statistical information on public sector’s salary per capita for the period 2001-2012 is combined with data from the survey of state policy experts in Mexico, and which takes into consideration the opposition’s strength and influence on state legislatures. The analysis specifies linear hierarchical models and shows that the patronage level will be higher the more limited the executive branch by the legislative opposition. These findings contribute a hypothesis to studies concerning patronage and the relationship between the opposition in Congress and the Executive.

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A Note on the Hierarchical Model and Power Prior Distribution in Bayesian Quantile Regression

Journal of Economics and Administrative Sciences ◽

10.33095/jeas.v20i76.690 ◽

2014 ◽

Vol 20 (76) ◽

pp. 1

Author(s):

طاهر ريسان دخيل

Keyword(s):

Quantile Regression ◽

Hierarchical Model ◽

Prior Distribution ◽

Hierarchical Models ◽

Real Data ◽

Power Parameter ◽

Bayesian Quantile Regression ◽

Power Prior

In this paper, we investigate the connection between the hierarchical models and the power prior distribution in quantile regression (QReg). Under specific quantile, we develop an expression for the power parameter ( ) to calibrate the power prior distribution for quantile regression to a corresponding hierarchical model. In addition, we estimate the relation between the and the quantile level via hierarchical model. Our proposed methodology is illustrated with real data example.

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Neural hierarchical models of ecological populations

10.1101/759944 ◽

2019 ◽

Author(s):

Maxwell B. Joseph

Keyword(s):

Neural Networks ◽

Hierarchical Models ◽

Large Data ◽

Ecological Processes ◽

Natural Systems ◽

Bird Populations ◽

Continental Scale ◽

North American Bird ◽

The Relationship

AbstractNeural networks are increasingly being used in science to infer hidden dynamics of natural systems from noisy observations, a task typically handled by hierarchical models in ecology. This paper describes a class of hierarchical models parameterized by neural networks: neural hierarchical models. The derivation of such models analogizes the relationship between regression and neural networks. A case study is developed for a neural dynamic occupancy model of North American bird populations, trained on millions of detection/non-detection time series for hundreds of species, providing insights into colonization and extinction at a continental scale. Flexible models are increasingly needed that scale to large data and represent ecological processes. Neural hierarchical models satisfy this need, providing a bridge between deep learning and ecological modeling that combines the function representation power of neural networks with the inferential capacity of hierarchical models.

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Interstellar gas in the central region of the Galaxy

Symposium - International Astronomical Union ◽

10.1017/s0074180900101032 ◽

1967 ◽

Vol 31 ◽

pp. 239-251 ◽

Cited By ~ 3

Author(s):

F. J. Kerr

Keyword(s):

Central Region ◽

Galactic Plane ◽

Neutral Hydrogen ◽

Continuum Emission ◽

Galactic Centre ◽

Interstellar Gas ◽

Hydrogen Recombination ◽

The Galaxy ◽

Centre Region ◽

The Relationship

A review is given of information on the galactic-centre region obtained from recent observations of the 21-cm line from neutral hydrogen, the 18-cm group of OH lines, a hydrogen recombination line at 6 cm wavelength, and the continuum emission from ionized hydrogen.Both inward and outward motions are important in this region, in addition to rotation. Several types of observation indicate the presence of material in features inclined to the galactic plane. The relationship between the H and OH concentrations is not yet clear, but a rough picture of the central region can be proposed.

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The relationship of the scleractinian corals to the rugose corals

Paleobiology ◽

10.1017/s0094837300025707 ◽

1980 ◽

Vol 6 (02) ◽

pp. 146-160 ◽

Cited By ~ 29

Author(s):

William A. Oliver

Keyword(s):

Critical Points ◽

Scleractinian Corals ◽

Convincing Evidence ◽

Early Triassic ◽

Rugose Corals ◽

History Of ◽

The Subject ◽

Relationship Of ◽

The Relationship ◽

Biologic Factors

The Mesozoic-Cenozoic coral Order Scleractinia has been suggested to have originated or evolved (1) by direct descent from the Paleozoic Order Rugosa or (2) by the development of a skeleton in members of one of the anemone groups that probably have existed throughout Phanerozoic time. In spite of much work on the subject, advocates of the direct descent hypothesis have failed to find convincing evidence of this relationship. Critical points are:(1) Rugosan septal insertion is serial; Scleractinian insertion is cyclic; no intermediate stages have been demonstrated. Apparent intermediates are Scleractinia having bilateral cyclic insertion or teratological Rugosa.(2) There is convincing evidence that the skeletons of many Rugosa were calcitic and none are known to be or to have been aragonitic. In contrast, the skeletons of all living Scleractinia are aragonitic and there is evidence that fossil Scleractinia were aragonitic also. The mineralogic difference is almost certainly due to intrinsic biologic factors.(3) No early Triassic corals of either group are known. This fact is not compelling (by itself) but is important in connection with points 1 and 2, because, given direct descent, both changes took place during this only stage in the history of the two groups in which there are no known corals.

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Choosing a Markov blanket

Behavioral and Brain Sciences ◽

10.1017/s0140525x19002632 ◽

2020 ◽

Vol 43 ◽

Author(s):

Thomas Parr

Keyword(s):

Markov Blanket ◽

Target Article ◽

The Relationship

Abstract This commentary focuses upon the relationship between two themes in the target article: the ways in which a Markov blanket may be defined and the role of precision and salience in mediating the interactions between what is internal and external to a system. These each rest upon the different perspectives we might take while “choosing” a Markov blanket.

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