Clinical Development in the Light of Bayesian Statistics
Emmanuel Lesaffre, Gianluca Baio, Bruno Boulanger in Bayesian Methods in Pharmaceutical Research, 2020
Spiegelhalter et al. (2004) define Bayesian thinking, in the context of health technology assessment, as “The explicit quantitative use of external evidence in the design, monitoring, analysis, interpretation and reporting of a health-care evaluation”. In his thought provoking paper on learning versus confirming in drug development, Sheiner (1997) described the Bayesian view as being particularly suited to the learning phases of drug development. He notes: “The Bayesian view is well suited to this task because it provides a theoretical basis for learning from experience; that is, for updating prior beliefs in the light of new evidence”. The work goes on to emphasize the term Bayesian is adopted to describe a point of view or a thought process, where prior knowledge (i.e. validated scientific theory) is to be incorporated into the analysis of current data. A clear distinction is made between this thought process and formal Bayesian inference (i.e. a statistical method involving the use of a prior probability distribution when analyzing data), with the former being considered the key concept behind Bayes and the latter more the technical details.
Network Meta-Analysis
Ding-Geng (Din) Chen, Karl E. Peace in Applied Meta-Analysis with R and Stata, 2021
Bayesian inference involves a process of fitting a probability model to a set of observed data and summarizes the results for the unobserved parameters or unobserved data given the observed data (Gelman 2014). The essential characteristic of Bayesian methods is that the use of probability for quantifying uncertainty in inferences based on statistical data analysis and the process of Bayesian data analysis can be divided into three steps as following: (1) setting up a joint probability model for all observable data and unobservable parameters in a problem; (2) calculating and interpreting the appropriate posterior distribution, which is known as the conditional probability distribution of the unobserved parameters of interest, given the observed data; (3) evaluating the model fitting and the implications of the resulting posterior distribution (Gelman 2014).
Environmental Monitoring and Assessment – Normal Response Models
Song S. Qian, Mark R. DuFour, Ibrahim Alameddine in Bayesian Applications in Environmental and Ecological Studies with R and Stan, 2023
In the last chapter, we used the Neuse River Estuary water quality assessment as an example to illustrate the basic process of the Bayesian inference. Technically, the Bayesian inference process differs from the classical or frequentist's approach only in the use of a prior distribution. When a flat prior (i.e., ) is used, the difference between the two approaches lies in the interpretation of the likelihood function. The frequentist's approach uses the likelihood function to obtain a point estimate, while the Bayesian approach normalizes the likelihood function to derive the posterior distribution. The frequentist's point estimate is the mode of the likelihood profile, while the Bayesian point estimate is often the mean or the median of the posterior distribution. If the likelihood function profile is symmetric, the two approaches will lead to the same point estimate.
Bayesian inference for quantum state tomography
Published in Journal of Applied Statistics, 2018
D. S. Gonçalves, C. L. N. Azevedo, C. Lavor, M. A. Gomes-Ruggiero
In conclusion, both Bayesian and bootstrap (resampling) methods circumvent the problems related to the problematic data. Nevertheless, notice that the bootstrap estimates (both punctual and interval ones) are ‘contaminated’, since in some of the bootstrap samples, the MLE estimate corresponds to unacceptable values. In other words, the bootstrap distributions of the estimators present unacceptable values, whereas the respective Bayesian posterior distributions do not. Also, Bayesian inference allows one to incorporate prior information and easily considers other likelihoods, providing a general overview in terms of inference (estimation, model selection, and hypothesis test) through the posterior distribution. In addition, some credible intervals of interest, for example for the purity of a density matrix,
A maximum likelihood estimator for left-truncated lifetimes based on probabilistic prior information about time of occurrence
Published in Journal of Applied Statistics, 2018
Rubén Manso, Rafael Calama, Marta Pardos, Mathieu Fortin
As mentioned before, i until it enters the experiment. Let us denote this birth event as E. In forestry, there are many examples of models that predict this event E as a function of time (E. As a consequence, these density and mass functions are instead interpreted as E. Because no date is more likely than another (i.e. all dates are equally likely to ‘occur’ regardless of any E event), the prior 12). 10) and (11). Note that our approach is fully frequentist, that is, no Bayesian inference is carried out. We only use Bayes' rule as a means to assess the terms 10) and (11).
Bayesian rank-based hypothesis testing for the rank sum test, the signed rank test, and Spearman's ρ
Published in Journal of Applied Statistics, 2020
J. van Doorn, A. Ly, M. Marsman, E.-J. Wagenmakers
The debate on alternatives to null hypothesis significance tests based on p-values [63] has led to a renewed interest in the Bayesian alternative known as the Bayes factor. Advantages of such Bayesian tests include the ability to provide evidence in favor of both the null and the alternative hypotheses [12], the ability to straightforwardly synthesize evidence to assess replicability [36], and the ability to monitor the evidence as the data accumulate [51]; see [13,62] for further details on the advantages of Bayesian inference. These advantages are met by the recently proposed Bayes factors for the classical two- and one-sample t-tests [52], as well as for the Bayes factor for Pearson's correlation [37]. These tests have become increasingly popular in the applied sciences. The goal of this paper is to extend these parametric Bayes factors to their rank-based counterparts.
Related Knowledge Centers
- Decision Theory
- Marginal Distribution
- Statistical Inference
- Sequential Analysis
- Radical Probabilism
- Sampling Distribution
- Posterior Predictive Distribution
- Frequentist Inference
- Bernstein–Von Mises Theorem
- Central Tendency