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Bayesian and Non-Bayesian Methods of Inference
Annals of Internal Medicine, 1983Excerpt Statistics is an indispensable tool in clinical research. Disagreements over the use of various approaches such as those reflected in the letters-to-the-editor section of this issue (1,2) s...
Robert D. Small, Stanley S. Schor
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Journal of the American Statistical Association, 1989
Abstract A method is proposed for approximating the marginal posterior density of a continuous function of several unknown parameters, thus permitting inferences about any parameter of interest for nonlinear models when the sample size is finite. Possibly tedious numerical integrations are replaced by conditional maximizations, which are shown to be ...
Thomas J. Leonard +2 more
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Abstract A method is proposed for approximating the marginal posterior density of a continuous function of several unknown parameters, thus permitting inferences about any parameter of interest for nonlinear models when the sample size is finite. Possibly tedious numerical integrations are replaced by conditional maximizations, which are shown to be ...
Thomas J. Leonard +2 more
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2011
The Bayesian view of probability leads to statistical inferences expressed as probability distributions for uncertain parameters, computed by updating initial beliefs or uncertainty according to new data, using Bayes’ theorem. These inferences can be computed analytically in some simple settings, but computationally demanding numerical integrations are
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The Bayesian view of probability leads to statistical inferences expressed as probability distributions for uncertain parameters, computed by updating initial beliefs or uncertainty according to new data, using Bayes’ theorem. These inferences can be computed analytically in some simple settings, but computationally demanding numerical integrations are
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bayesian inference and computation
2011This chapter provides a overview of Bayesian inference, mostly emphasising that it is a universal method for summarising uncertainty and making estimates and predictions using probability statements conditional on observed data and an assumed model (Gelman 2008). The Bayesian perspective is thus applicable to all aspects of statistical inference, while
Rousseau, Judith +2 more
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Approximately Bayesian Inference
Journal of the American Statistical Association, 1994Abstract Consider statistical inference about a scalar parameter and suppose that information about that parameter is to be summarized by a system of interval estimates. It is well known that methods of interval estimation that do not correspond to Bayesian inference with respect to some prior distribution have some logical difficulties.
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2007
The subject of this chapter is sequential Bayesian inference in which we consider the Bayesian estimation of a dynamic system which is changing in time. Let θ k denote the state of the system, i. e. a vector which contains all relevant information required to describe the system, at some (discrete) time k. Then the goal of sequential Bayesian inference
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The subject of this chapter is sequential Bayesian inference in which we consider the Bayesian estimation of a dynamic system which is changing in time. Let θ k denote the state of the system, i. e. a vector which contains all relevant information required to describe the system, at some (discrete) time k. Then the goal of sequential Bayesian inference
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Application of Bayesian approaches in drug development: starting a virtuous cycle
Nature Reviews Drug Discovery, 2023Lisa M Lavange, Stephen J Ruberg
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Bayesian reaction optimization as a tool for chemical synthesis
Nature, 2021Jason M Stevens, Jun Li, Ryan P Adams
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