Search results for "Bayesian linear regression"

Bayesian Methodology in Statistics

2009

Bayesian methods provide a complete paradigm for statistical inference under uncertainty. These may be derived from an axiomatic system and provide a coherent methodology which makes it possible to incorporate relevant initial information, and which solves many of the difficulties that frequentist methods are known to face. If no prior information is to be assumed, the more frequent situation met in scientific reporting, a formal initial prior function, the reference prior, mathematically derived from the assumed model, is used; this leads to objective Bayesian methods, objective in the precise sense that their results, like frequentist results, only depend on the assumed model and the data…

Data Augmentation Approach in Bayesian Modelling of Presence-only Data

2011

Abstract Ecologists are interested in prediction of potential distribution of species in suitable areas, essential for planning conservation and management strategies. Unfortunately, often the only available information in such studies is the true presence of the species at few locations of the study area and the associated environmental covariates over the entire area, referred as presence-only data. We propose a Bayesian approach to estimate logistic linear regressions adapted to presence-only data through the introduction of a random approximation of the correction factor in the adjusted logistic model that allows us to overcome the need to know a priori the prevalence of the species.

Multivariate exponential smoothing: A Bayesian forecast approach based on simulation

2009

This paper deals with the prediction of time series with correlated errors at each time point using a Bayesian forecast approach based on the multivariate Holt-Winters model. Assuming that each of the univariate time series comes from the univariate Holt-Winters model, all of them sharing a common structure, the multivariate Holt-Winters model can be formulated as a traditional multivariate regression model. This formulation facilitates obtaining the posterior distribution of the model parameters, which is not analytically tractable: simulation is needed. An acceptance sampling procedure is used in order to obtain a sample from this posterior distribution. Using Monte Carlo integration the …

A Bayesian analysis of classical hypothesis testing

1980

The procedure of maximizing the missing information is applied to derive reference posterior probabilities for null hypotheses. The results shed further light on Lindley’s paradox and suggest that a Bayesian interpretation of classical hypothesis testing is possible by providing a one-to-one approximate relationship between significance levels and posterior probabilities.

What Bayesians Expect of Each Other

1991

Abstract Our goal is to study general properties of one Bayesian's subjective beliefs about the behavior of another Bayesian's subjective beliefs. We consider two Bayesians, A and B, who have different subjective distributions for a parameter θ, and study Bayesian A's expectation of Bayesian B's posterior distribution for θ given some data Y. We show that when θ can take only two values, Bayesian A always expects Bayesian B's posterior distribution to lie between the prior distributions of A and B. Conditions are given under which a similar result holds for an arbitrary real-valued parameter θ. For a vector parameter θ we present useful expressions for the mean vector and covariance matrix …

An introduction to Bayesian reference analysis: inference on the ratio of multinomial parameters

1998

This paper offers an introduction to Bayesian reference analysis, often described as the more successful method to produce non-subjective, model-based, posterior distributions. The ideas are illustrated in detail with an interesting problem, the ratio of multinomial parameters, for which no model-based Bayesian analysis has been proposed. Signposts are provided to the huge related literature.

Methods and Tools for Bayesian Variable Selection and Model Averaging in Normal Linear Regression

2018

In this paper, we briefly review the main methodological aspects concerned with the application of the Bayesian approach to model choice and model averaging in the context of variable selection in regression models. This includes prior elicitation, summaries of the posterior distribution and computational strategies. We then examine and compare various publicly available R-packages, summarizing and explaining the differences between packages and giving recommendations for applied users. We find that all packages reviewed (can) lead to very similar results, but there are potentially important differences in flexibility and efficiency of the packages.

Reference Posterior Distributions for Bayesian Inference

1979

Contributed discussion on article by Pratola

2016

The author should be commended for his outstanding contribution to the literature on Bayesian regression tree models. The author introduces three innovative sampling approaches which allow for efficient traversal of the model space. In this response, we add a fourth alternative.

Mathematical Modeling for Neuropathic Pain: Bayesian Linear Regression and Self-Organizing Maps Applied to Carpal Tunnel Syndrome

2020

A better understanding of the connection between risk factors associated with pain and function may assist therapists in optimizing therapeutic programs. This study applied mathematical modeling to analyze the relationship of psychological, psychophysical, and motor variables with pain, function, and symptom severity using Bayesian linear regressions (BLR) and self-organizing maps (SOMs) in carpal tunnel syndrome (CTS). The novelty of this work was a transfer of the symmetry mathematical background to a neuropathic pain condition, whose symptoms can be either unilateral or bilateral. Duration of symptoms, pain intensity, function, symptom severity, depressive levels, pinch tip grip force, a…