scholarly journals A causal partition of trait correlations: using graphical models to derive statistical models from theoretical language

Ecosphere ◽  
2018 ◽  
Vol 9 (9) ◽  
pp. e02422
Author(s):  
James Patrick Cronin ◽  
Donald R. Schoolmaster
Keyword(s):  
Graphical Models ◽  
Statistical Models ◽  
Theoretical Language ◽  
Trait Correlations

scholarly journals Mixtures and products in two graphical models

2018 ◽  
Vol 9 (1) ◽  
pp. 1-20 ◽  
Author(s):  
Anna Seigal ◽  
Guido Montufar
Keyword(s):  
Maximum Likelihood ◽  
Closed Form ◽  
Graphical Models ◽  
Statistical Models ◽  
The Other ◽  
Maximum Likelihood Estimates ◽  
Boltzmann Machine ◽  
Algebraic Description ◽  
Binary Random Variables ◽  
Probability Simplex

We compare two statistical models of three binary random variables. One is a mixture model and the other is a product of mixtures model called a restricted Boltzmann machine. Although the two models we study look different from their parametrizations, we show that they represent the same set of distributions on the interior of the probability simplex, and are equal up to closure. We give a semi-algebraic description of the model in terms of six binomial inequalities and obtain closed form expressions for the maximum likelihood estimates. We briefly discuss extensions to larger models.

Learning Probabilistic Graphical Models

2012 ◽  
pp. 223-236
Author(s):  
Juan I. Alonso-Barba ◽  
Jens D. Nielsen ◽  
Luis de la Ossa ◽  
Jose M. Puerta
Keyword(s):  
Graphical Models ◽  
Statistical Models ◽  
Relevant Literature ◽  
Joint Probability ◽  
Probabilistic Graphical Models ◽  
Compact Representation ◽  
Joint Probability Distribution ◽  
Inference Algorithms ◽  
Probabilistic Queries ◽  
Local Parameters

Probabilistic Graphical Models (PGM) are a class of statistical models that use a graph structure over a set of variables to encode independence relations between those variables. By augmenting the graph by local parameters, a PGM allows for a compact representation of a joint probability distribution over the variables of the graph, which allows for efficient inference algorithms. PGMs are often used for modeling physical and biological systems, and such models are then in turn used to both answer probabilistic queries concerning the variables and to represent certain causal and/or statistical relations in the domain. In this chapter, the authors give an overview of common techniques used for automatic construction of such models from a dataset of observations (usually referred to as learning), and they also review some important applications. The chapter guides the reader to the relevant literature for further study.

Book Reviews

2010 ◽  
Vol 48 (4) ◽  
pp. 1033-1035
Keyword(s):  
Causal Inference ◽  
Graphical Models ◽  
Statistical Models ◽  
Propensity Scores ◽  
Identification Problem ◽  
Qualitative Reasoning ◽  
Swine Flu ◽  
Categorical Variables ◽  
Ecological Inference ◽  
Inference Problem

Karim Chalak of Boston College reviews “Statistical Models and Causal Inference: A Dialogue with the Social Sciences” by David A. Freedman,. The EconLit Abstract of the reviewed work begins “Twenty papers explore the foundations of statistical models and their limitations for causal inference, drawing examples from political science, public policy, law, and epidemiology. Papers discuss issues in the foundations of statistics--probability and statistical models; statistical assumptions as empirical commitments; statistical models and shoe leather; methods for the U.S. Census 2000 and statistical adjustments; “solutions” to the ecological inference problem; a rejoinder to Gary King; black ravens, white shoes, and case selection--inference with categorical variables; the chance that an earthquake will occur; salt and blood pressure--conventional wisdom reconsidered; the swine flu vaccine and Guillain-Barre syndrome--a case study in relative risk and specific causation; whether survival analysis is an epidemiological hazard; regression adjustments in experiments with several treatments; whether randomization justifies logistic regression; the grand leap; specifying graphical models for causation and the identification problem; weighting regressions by propensity scores; the so-called “Huber sandwich estimator” and “robust standard errors”; endogeneity in probit response models; whether diagnostics can have much power against general alternatives; and types of scientific inquiry--the role of qualitative reasoning. The late Freedman was Professor of Statistics at the University of California, Berkeley. Index.”

scholarly journals On the interpretation of inflated correlation path weights in concentration graphs

2021 ◽  
Author(s):  
Alberto Roverato
Keyword(s):  
Graphical Models ◽  
Statistical Models ◽  
Centrality Measures ◽  
Full Description ◽  
Theoretical Interest ◽  
Association Measure ◽  
Association Structure ◽  
Concentration Graphs ◽  
Order Structures ◽  
Insight Into

AbstractStatistical models associated with graphs, called graphical models, have become a popular tool for representing network structures in many modern applications. Relevant features of the model are represented by vertices, edges and other higher order structures. A fundamental structural component of the network is represented by paths, which are a sequence of distinct vertices joined by a sequence of edges. The collection of all the paths joining two vertices provides a full description of the association structure between the corresponding variables. In this context, it has been shown that certain pairwise association measures can be decomposed into a sum of weights associated with each of the paths connecting the two variables. We consider a pairwise measure called an inflated correlation coefficient and investigate the properties of the corresponding path weights. We show that every inflated correlation weight can be factorized into terms, each of which is associated either to a vertex or to an edge of the path. This factorization allows one to gain insight into the role played by a path in the network by highlighting the contribution to the weight of each of the elementary units forming the path. This is of theoretical interest because, by establishing a similarity between the weights and the association measure they decompose, it provides a justification for the use of these weights. Furthermore we show how this factorization can be exploited in the computation of centrality measures and describe their use with an application to the analysis of a dietary pattern.

Statistical Models: Theory and Practice

2005 ◽  
Author(s):  
David Freedman
Keyword(s):  
Statistical Models ◽  
Theory And Practice

The Prediction of Adolescents At-Risk for Attempting Suicide Using Tree-Based Statistical Models

2011 ◽  
Author(s):  
Eric E. Pierson ◽  
Holmes W. Finch
Keyword(s):  
At Risk ◽  
Statistical Models

Generation of Reduced Statistical Models for NLP and MINLP Optimization

1997 ◽  
Vol 21 (1-2) ◽  
pp. S505-S510 ◽  
Author(s):  
S Noronha
Keyword(s):  
Statistical Models
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