Bayesian probability

Finally, I decided to research on Bayesian adaptive clinical trials. Unlike conventional clinical trials have substantial uncertainty in intervention arms (e.g. uncertainty in optimal dose/duration), adaptive clinical trials allow us to modify key trial parameters as we are acquiring more information during the experiments, thus reducing the uncertainty and speeding up the evaluation of interventions. Also, adaptive clinical trials allow for dropping arms that do not work well during the experiments based on the interim analysis. Researchers can reallocate people to other arms, thus making it more efficient. In the past decades, statisticians start to use Bayesian in adaptive trials. People may not be familiar with Bayesian, but they actually use Bayesian everyday. If you do have following experience, you have encountered Bayesian. One day, you go to Yelp to see the rating of a restaurant near your house. You found it is 4.9 out of 5, so you think it must be a good restaurant and decide to try. After you try, you find they have the worst food you have ever had, so you pull it to your blacklist and change your belief. As I described in this example, instead of solely based on data to make decisions, the Bayesian approach requires an initial individual belief about the parameter we try to estimate and combine the evidence from the data to reach a Bayesian posterior…

discussion about Bayesian methods in Spatial Statistics. Bayesian methods are approaches to statistical inferences which have been around for several decades and are also used in Geographic Information Systems. The application of these methods in practical problems has increased significantly within the last few years due to recent advances in tools for computation and simulation [1]. At the heart of any Bayesian data analysis method are the likelihood function, which expresses information about…

There are several methods available to reconstruct networks from this widely available data format. My emphasis on the method of Bayesian networks (BN) has relied on their non-pairwise mechanism of inference that introduces effects of “third variables” as a way to control confounding. The vast use and development of BN provides multiple tools to model diverse complexity issues, such as their approaches to causality. Two types of interdependent network models are proposed: factor based and agent…

discovery of networks and the techniques of using Bayesian networks. Furthermore, they discussed the utilisation of this methodology for causal modelling. This source is important at the initial stage of the project as it contributes to the decision-making process at the modelling technique selection stage. However, it is not as important as the other two sources after it was decided not to be used as the modelling method for the system model of this project. Bayesian networks are diagrams for…

fact’ is part of their problem. While many of the predictions are accurate, not all predictions are going to be right. Predictions on the stock market and the economy, as well as predictions on the weather have left a bad rep for some economist. To their defense, economist are working with situation that are constantly changing. For example, if a disease breaks out, vaccinations and other medications can be given to slow down the spread of the outbreak therefore changing a previous conclusions…

Probability concepts like faith, as it exists in the dim intuition, through school education, the surface of that understanding, intuition often conflicts that again with a different point of view, must be thinking more in-depth study to be able to understand. Hot Monty Hall problem, and that is one example. There is not a simple probability, long confused with so many people and academics, the more deeply ponder the problems found. Since 1990, 1991 flared up in hot to 2000, there are more…

as numeracy. Age. Older individuals don’t understand risk information as well, both overestimate and underestimate probabilities (Fuller, Dudley, & Blacktop, 2001), worse risk comprehension than younger individuals (Fausset & Rogers, 2012). Much of the literature supports the idea that decision making effectiveness…

Implementation of Bayesian Method for basic pattern Classification Abstract: This document describes an example of basic pattern classification using the Bayesian method. Based on given two dimensional (2-D) training data for two classes, we created a classifier using discriminant function (which is the logarithmic version of Bayes formula) and used it to classify provided test data. We estimated the necessary statistical parameters, such as mean covariance and prior probabilities, from…

uncertainty. When an “outcome is the result of adding the outcomes of many separate performances, all in certain respects uniform”; in other words, when the frequency-ratio is known, then the experiment is named divisible, while a non-divisible or non-seriable experiment is one which “can be neither itself broken down into a number of uniform additive parts nor treated as part of a divisible experiment” (p. 8). In a non-divisible experiment the frequency-ratio standpoint has no actual sense. One…

As we model this Markov process, we observe the state-dependent output, yet initially we are not able to note any of the states. Each state has a unique probability distribution over each possible output. Thus, information about the sequence of states through which the model makes its way can be obtained from the sequence of outputs generated, while the rest of the model remains hidden. The algorithm tracks a stochastic process through its states by using a recursive method that is optimal in…