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Volume 6, Issue 2 2010 Article 17 The International Journal of Biostatistics CAUSAL INFERENCE Bayesian Inference for Partially Identified Models Paul Gustafson, University of British Columbia Recommended Citation: Gustafson, Paul (2010) "Bayesian Inference for Partially Identified Models," The International Journal of Biostatistics: Vol. 6: Iss. 2, Article 17. DOI: 10.2202/1557-4679.1206 Bayesian Inference for Partially Identified Models Paul Gustafson Abstract Identification can be a major issue in causal modeling contexts, and in contexts where observational

J. Intell. Syst. 20 (2011), 209–225 DOI 10.1515/JISYS.2011.012 © de Gruyter 2011 Generalized Bayesian Inference Nets Model and Diagnosis of Cardiovascular Diseases Booma Devi Sekar, Mingchui Dong and Jiayi Dou Abstract. A generalized Bayesian inference nets model (GBINM) is proposed to aid re- searchers to construct Bayesian inference nets for various applications. The benefit of such a model is well demonstrated by applying GBINM in constructing a hierarchical Bayesian fuzzy inference nets (HBFIN) to diagnose five important types of cardiovascular diseases (CVD

uncertainty introduced by the sparse fatigue life data and the fatigue model can help to improve the fatigue life assessment by identifying the best fatigue life model. Accordingly, this paper proposed a fatigue life estimation method by considering the parameters uncertainty and model uncertainty simultaneously. Bayesian methods are used in this paper to facilitate the fatigue life estimation of gas turbine blades. A coherent framework is built up to handle the parameter uncertainty and model uncertainty using Bayesian inference. In detail, a group of probability

1 Introduction Stochastic kinetic models, most naturally represented by Markov jump processes (MJPs), can be used to model a wide range of real-world phenomena including the evolution of biological systems such as intra-cellular processes (Golightly and Wilkinson, 2005; Wilkinson, 2009), predator-prey interaction (Boys et al., 2008; Ferm et al., 2008; Golightly and Wilkinson, 2011) and epidemics (Bailey, 1975; O’Neill and Roberts, 1999; Boys and Giles, 2007). The focus of this paper is to perform exact and fully Bayesian inference for the parameters governing the

Chapter 3 A Crash Course in Bayesian Inference In a Bayesian setting the calculus of probability is used to characterize and update an individual’s state of knowledge or degree of beliefs with respect to quantities such as model pa- rameters or future observations. The prior distribution p(θ) discussed in the previous section is meant to describe the initial state of knowledge about the model parameter vec- tor θ—before observing the sample Y , e.g., data on output growth, inflation, and nominal interest rates. The Bayesian approach prescribes consistency among

.P., Ronquist F., Nielsen R. & Bollback J.P. 2001. Bayesian inference of phylogeny and its impact on evolutionary biology. Science 294: 2310–2314. http://dx.doi.org/10.1126/science.1065889 [25] Jow H., Hudelot C., Rattray M. & Higgs P.G. 2002. Bayesian phylogenetics using an RNA substitution model applied to early mammalian evolution. Mol. Biol. Evol. 19: 1591–1601. [26] Lum J.K., Nikaido M., Shimamura M., Shimodaira H., Shedlock A.M., Okada N. & Hasegawa M. 2000. Consistency of SINE insertion topology and flanking sequence tree: quantifying relationships among

the case of varying mutation and sequencing-error rates. Wutke et al. (2016) used a Metropolis-Hastings algorithm to carry out Bayesian inference of selection at selected sites responsible for variation in color phenotypes in horses by integrating over nuisance parameters and sampling over allele frequency paths. A common feature of the methods reviewed above is the need to approximate the transition density of the WF diffusion in order to carry out inference, and the methods differ from one another in how this is done. Recently, Jenkins and Spanó (2015

Abstract

One of the basic subsystems of the collective water supply system is the water distribution subsystem which has a direct impact on the reliability and safety of water supply to consumers. Failures of water pipes may cause water losses (leaks), interruptions in the water supply to consumers and can be the cause of secondary water pollution in the water supply network. It was proposed to use Bayesian inference to locate failures on the water supply network and to determine a posteriori probability of water network failure. It was found that the conditional probability of distribution water supply network failure is definitely higher than the conditional probability of home connections failure. The research results should be used by the water supply company during the development of an operational strategy for the renovation and modernization of the water supply network.

noted as “an N .” Table 2 2 × J 2\times J contingency table constructed from the observed number m x j {m_{xj}} . Treatment Outcome Total Y = 0 Y=0 Y = j Y=j Y = J − 1 Y=J-1 X = 1 X=1 m 10 {m_{10}} … m 1 j … m 1( J –1) ∑ j m 1 j {\sum _{j}}{m_{1j}} X = 0 X=0 m 00 {m_{00}} … m 0 j … m 0( J –1) ∑ j m 0 j {\sum _{j}}{m_{0j}} 3 Bayesian inference of causal effects In Section 3.1 , we present the region of N , in which the likelihood function is nonzero. In Section 3.2 , we present a Bayesian approach to make inferences about ( 3 ), using the region given in Section

Abstract

The determination of acoustic material parameters using ultrasonic transmission measurements can mathematically be described as an inverse problem. The question concerning the influence of uncertainties on the problem's solution can be answered using a statistical approach. Therefore, the sources of uncertainty have to be identified statistically. A method for linearising the model function using the Guide to the expression of uncertainty in measurement is introduced for inverse problems. The statistical inversion of the model is executed by means of two different approaches, that are compared and interpreted exemplarily.