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Environmental Monitoring and Assessment – Normal Response Models
Published in Song S. Qian, Mark R. DuFour, Ibrahim Alameddine, Bayesian Applications in Environmental and Ecological Studies with R and Stan, 2023
Song S. Qian, Mark R. DuFour, Ibrahim Alameddine
Moving forward with the Neuse River Estuary water quality assessment example, we illustrated the concept of updating: the transition of the prior distribution to the posterior distribution upon the observation of data. In our example, we started with a prior derived from water quality model outputs. The model-predicted total nitrogen (TN) concentrations did not agree with the observed values. Nevertheless, the Bayesian approach allows us to gradually update the predicted TN concentration distributions. Once we have several years of observations, our predicted (posterior distribution of) TN concentrations are very close to the observed TN concentration distribution as presented by a histogram (Figures 3.1 and 3.2). This process of updating is the key characteristic of the Bayesian approach. It is a process of learning from experience (observing data): we first summarize the experience (assuming a probability distribution which led to the likelihood function) and then generalize the experience for predicting future experience via the Bayes' theorem. As remarked by Jeffreys [1961], the process of generalization is the most important part because “events that are merely described and have no apparent relation to others may as well be forgotten, and in fact usually are.” The updating procedure as a general methodology is a distinct scientific method that is universal in all scientific endeavors. It represents a common feature of science, just as Karl Pearson elegantly expressed that “the unity of all science consists alone in its method, not in its material” [Pearson, 1900].
Drug evaluation in children
Published in Evelyne Jacqz-Aigrain, Imti Choonara, Paediatric Clinical Pharmacology, 2021
Evelyne Jacqz-Aigrain, Imti Choonara
Two philosophies of statistical analysis co-exist: Frequentist and Bayesian [13]. In the frequentist approach, results are expressed in terms of significance levels, point estimates and confidence intervals. The Bayesian approach is subjective and is best envisaged in terms of the changing opinions of one investigator. It can give probabilities that the clinical effect lies in a particular range and also the size of the most likely effect. This is in stark contrast to the often misinterpreted P-value produced by the usual frequentist approach. The frequentist P-value is the probability of the observations occurring when the null hypothesis is true. The Bayesian approach, by contrast, provides probabilities of the treatment effect that apply directly to the next patient who is similar to those treated in any completed or ongoing trial. Whereas conventional (frequentist) confidence limits are unlikely to exclude a null hypothesis, even when the treatment differs substantially, Bayesian methods utilise all available data to calculate probabilities that may be extrapolated directly to clinical practice.
Study Design-I
Published in Atanu Bhattacharjee, Bayesian Approaches in Oncology Using R and OpenBUGS, 2020
The Bayesian technique is prominent methodology in data science. Data science is inevitable in clinical research. So Bayesian merged tremendously in the clinical trials well. Study design, sample size calculation, and statistical analysis have emerged with the Bayesian technique. The approach to analyzing data in Bayesian is different from the classical approach. Recent computation advancement helped to incorporate Bayesian in clinical trials. It also helped to upgrade data analysis practice. Oncology research is involved with time-to-event outcomes (i.e., death). Data analysis with survival analysis is not straight forward. In the presence of missing or incomplete information, it becomes more complicated. Bayesian helps to overcome different challenges. Recently, Bayesian approach is considered in several clinical trial study design. The adoption of probability is different in the Bayesian technique. The evidence-based probability plays a role in Bayesian. It helps to upgrade the proportion of uncertainty in data analysis logic. The prior information is required to incorporate. The literature review is required to upgrade the prior information. Aim of this chapter is to a show about different study design with Bayesian for oncology clinical trials.
Exploring pre-crash gate violations behaviors of drivers at highway-rail grade crossings using a mixed multinomial logit model
Published in International Journal of Injury Control and Safety Promotion, 2022
Boniphace Kutela, Emmanuel Kidando, Angela E. Kitali, Sia Mwende, Neema Langa, Norris Novat
The nature and structure of the response and explanatory variables enabled the selection of the appropriate model. A mixed multinomial logit (MMNL) model fitted using a Bayesian approach was adopted to associate pre-crash behaviors with different factors. The Bayesian approach, unlike other estimation approaches, including maximum likelihood estimation and maximum simulated likelihood estimation, provides the posterior distribution of all model parameters. Besides, the MMNL model was considered because it accounted for the unordered nature of the response variable categories, unobserved heterogeneity in the data and also the MMNL model formulation does not have the independence of irrelevant alternatives (IIA) property of the standard MNL model (Washington et al., 2003). This study used the intra-class correlation coefficient (ICC) to quantify the impact of unobserved heterogeneity in crash data. The rest of the manuscript is organized as follows. The following sections describe literature related to HRGCs safety studies aimed at evaluating the factors for train-vehicle related injury-crashes and the respective methodological gap. Followed by the data description, analytical approach used, corresponding results and conclude with a discussion of the findings and future research considerations.
Inference of progressively type-II censored competing risks data from Chen distribution with an application
Published in Journal of Applied Statistics, 2020
Essam A. Ahmed, Ziyad Ali Alhussain, Mukhtar M. Salah, Hanan Haj Ahmed, M. S. Eliwa
In statistical inference, the Bayesian technique has some advantages compared with the ML technique. Bayesian inference can be expected to be useful because in many cases, including engineering applications, there is some expert knowledge about the underlying failure mechanism that can be translated into previous information in failure distribution parameters. When the prior information exists, the Bayesian approach provides a posterior distribution that combines prior information and test results. A pragmatic approach to choosing a prior distribution is to select a member of a specific family of distributions such that the posterior distribution belongs to the same family. This is called a conjugate prior distribution. If the prior is conjugate, the posterior after observing the first observation is of the same type and serves as the new prior distribution for the next observation. The new posterior distribution, now incorporating also the second observation, is again within the conjugate class, and so on.
Zero-inflated Bell regression models for count data
Published in Journal of Applied Statistics, 2020
Artur J. Lemonte, Germán Moreno-Arenas, Fredy Castellares
In this paper, we also propose a new zero-inflated regression model on the basis of the ZIBell distribution. So, having accounted for zero-inflation, if the data continue to suggest additional overdispersion, one may consider the ZIBell model instead of the ZIP model. Similar to the ZIP regression model setup, the parameters μ and π are related to covariates (explanatory variables). Furthermore, some quantities (e.g., score function, Fisher information matrix, etc.) related to the ZIBell regression are simple and compact, which makes the frequentist approach very easy to implement. Obviously the Bayesian approach has its merits and could also be applied in our ZIBell regression model and, in addition, these methodologies could be compared and contrasted. However, the comparison of these two methodologies is beyond the scope of this paper and hence can be considered in a future work.