Search results for "Bayesian Inference"
showing 10 items of 120 documents
Correcting for non-ignorable missingness in smoking trends
2015
Data missing not at random (MNAR) is a major challenge in survey sampling. We propose an approach based on registry data to deal with non-ignorable missingness in health examination surveys. The approach relies on follow-up data available from administrative registers several years after the survey. For illustration we use data on smoking prevalence in Finnish National FINRISK study conducted in 1972-1997. The data consist of measured survey information including missingness indicators, register-based background information and register-based time-to-disease survival data. The parameters of missingness mechanism are estimable with these data although the original survey data are MNAR. The u…
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.
Bayesian hierarchical Poisson models with a hidden Markov structure for the detection of influenza epidemic outbreaks
2015
Considerable effort has been devoted to the development of statistical algorithms for the automated monitoring of influenza surveillance data. In this article, we introduce a framework of models for the early detection of the onset of an influenza epidemic which is applicable to different kinds of surveillance data. In particular, the process of the observed cases is modelled via a Bayesian Hierarchical Poisson model in which the intensity parameter is a function of the incidence rate. The key point is to consider this incidence rate as a normal distribution in which both parameters (mean and variance) are modelled differently, depending on whether the system is in an epidemic or non-epide…
Bayesian Markov switching models for the early detection of influenza epidemics
2008
The early detection of outbreaks of diseases is one of the most challenging objectives of epidemiological surveillance systems. In this paper, a Markov switching model is introduced to determine the epidemic and non-epidemic periods from influenza surveillance data: the process of differenced incidence rates is modelled either with a first-order autoregressive process or with a Gaussian white-noise process depending on whether the system is in an epidemic or in a non-epidemic phase. The transition between phases of the disease is modelled as a Markovian process. Bayesian inference is carried out on the former model to detect influenza epidemics at the very moment of their onset. Moreover, t…
Bayesian survival analysis with BUGS
2020
Survival analysis is one of the most important fields of statistics in medicine and biological sciences. In addition, the computational advances in the last decades have favored the use of Bayesian methods in this context, providing a flexible and powerful alternative to the traditional frequentist approach. The objective of this article is to summarize some of the most popular Bayesian survival models, such as accelerated failure time, proportional hazards, mixture cure, competing risks, multi-state, frailty, and joint models of longitudinal and survival data. Moreover, an implementation of each presented model is provided using a BUGS syntax that can be run with JAGS from the R programmin…
Explaining German outward FDI in the EU: a reassessment using Bayesian model averaging and GLM estimators
2021
The last decades have seen an increasing interest in FDI and the process of production fragmentation. This has been particularly important for Germany as the core of the European Union (EU) production hub. This paper attempts to provide a deeper under standing of the drivers of German outward FDI in the EU for the period 1996–2012 by tackling the two main challenges faced in the modelization of FDI, namely the variable selection problem and the choice of the estimation method. For that purpose, we first extend previous BMA analysis developed by Camarero et al. (Econ Model 83:326–345, 2019) by including country-pair-fixed effects to select the appropriate set of variables. Second, we compare…
Bayesian assessment of times to diagnosis in breast cancer screening
2008
Breast cancer is one of the diseases with the most profound impact on health in developed countries and mammography is the most popular method for detecting breast cancer at a very early stage. This paper focuses on the waiting period from a positive mammogram until a confirmatory diagnosis is carried out in hospital. Generalized linear mixed models are used to perform the statistical analysis, always within the Bayesian reasoning. Markov chain Monte Carlo algorithms are applied for estimation by simulating the posterior distribution of the parameters and hyperparameters of the model through the free software WinBUGS.
Bayesian analysis of a disability model for lung cancer survival
2016
Bayesian reasoning, survival analysis and multi-state models are used to assess survival times for Stage IV non-small-cell lung cancer patients and the evolution of the disease over time. Bayesian estimation is done using minimum informative priors for the Weibull regression survival model, leading to an automatic inferential procedure. Markov chain Monte Carlo methods have been used for approximating posterior distributions and the Bayesian information criterion has been considered for covariate selection. In particular, the posterior distribution of the transition probabilities, resulting from the multi-state model, constitutes a very interesting tool which could be useful to help oncolog…