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As per available reports about 7 Journals and more than 10 upcoming international Conferences are presently dedicated exclusively to Bayesian statistics and about 197 articles have been published on Bayesian statistics.
Bayesian statistics is a subset of the field of statistics in which the evidence about the true state of the world is expressed in terms of degrees of belief or, more specifically, Bayesian probabilities. Such an interpretation is only one of a number of interpretations of probability and there are other statistical techniques that are not based on "degrees of belief". The general set of statistical techniques can be divided into a number of activities, many of which have special Bayesian versions.
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Scope and Importance:
Bayesian statistics is a system for describing epistemological uncertainty using the mathematical language of probability. In the 'Bayesian paradigm,' degrees of belief in states of nature are specified; these are non-negative, and the total belief in all states of nature is fixed to be one. Bayesian statistical methods start with existing 'prior' beliefs, and update these using data to give 'posterior' beliefs, which may be used as the basis for inferential decisions.
1. Statistical inference
Bayesian inference is an approach to statistical inference, that is distinct from frequentist inference. It is specifically based on the use of Bayesian probabilities to summarize evidence.
2. Statistical modeling
The formulation of statistical models for use in Bayesian statistics has the additional feature, not present with other types of statistical techniques, of requiring the formulation of a set of prior distributions for any unknown parameters. Such prior distributions are as much part of the statistical model as the part that expresses the probability distribution of observations given the model parameters. The specification of a set of prior distributions for a problem may involve hyper parameters and hyperprior distributions.
3. Design of experiments
The usual considerations in the design of experiments are extended in the case of Bayesian design of experiments to include the influence of prior beliefs. Importantly, the application of sequential analysis techniques allow the outcome of earlier experiments to influence the design of the next experiment, based on the updating of beliefs as expressed by the prior and posterior distribution. Part of the problem of the design of experiments is that they should make good use of resources of all types: one example of the Bayesian design of experiments aimed at such efficiency is the multi-armed bandit problem.
4. Statistical graphics
Statistical graphics includes methods for data exploration, for model validation, etc. The use of certain modern computational techniques for Bayesian inference, specifically the various types of Markov chain Monte Carlo techniques, have led to the need for checks, often made in graphical form, on the validity of such computations in expressing the required posterior distributions.
Explicitly Bayesian statistical methods tend to be used in three main situations. The first is where one has no alternative but to include quantitative prior judgments, due to lack of data on some aspect of a model, or because the inadequacies of some evidence have to be acknowledged through making assumptions about the biases involved. These situations can occur when a policy decision must be made on the basis of a combination of imperfect evidence from multiple sources, an example being the encouragement of Bayesian methods by the Food and Drug Administration (FDA) division responsible for medical devices.
The second situation is with moderate-size problems with multiple sources of evidence, where hierarchical models can be constructed on the assumption of shared prior distributions whose parameters can be estimated from the data. Common application areas include meta-analysis, disease mapping, multi-Centre studies, and so on. With weakly-informative prior distributions the conclusions may often be numerically similar to classic techniques, even if the interpretations may be different.
The third area concerns where a huge joint probability model is constructed, relating possibly thousands of observations and parameters, and the only feasible way of making inferences on the unknown quantities is through taking a Bayesian approach: examples include image processing, spam filtering, signal analysis, and gene expression data. Classical model-fitting fails, and MCMC or other approximate methods become essential.
There is also extensive use of Bayesian ideas of parameter uncertainty but without explicit use of Bayes theorem. If a deterministic prediction model has been constructed, but some of the parameter inputs are uncertain, then a joint prior distribution can be placed on those parameters and the resulting uncertainty propagated through the model, often using Monte Carlo methods, to produce a predictive probability distribution. This technique is used widely in risk analysis, health economic modeling and climate projections, and is sometimes known as probabilistic sensitivity analysis.
Another setting where the 'updating' inherent in the Bayesian approach is suitable is in machine-learning; simple examples can be found in modern software for spam filtering, suggesting which books or movies a user might enjoy given his or her past preferences, or ranking schemes for millions of on-line gamers. Formal inference may only be approximately carried out, but the Bayesian perspective allows a flexible and adaptive response to each additional item of information.
Bayesian Statistics conference aims at bringing together researchers and practitioners to discuss recent developments in statistical methods, computational methods, methodologies for data analysis and applications in statistics.
Market Analysis:
Use of biostatistics in biotechnology industry is currently on the rise, with over 27,600 biostatistics professional working in biotech sector in US alone. Industry experts predict, that based on the current rate of integration of technology and data mining in current biotechnology industry, by 2022, an unprecedented rise of 27% in employment of biostatisticians in biotech sector alone can be observed. Furthermore, with continued growth of biotechnology industry, the global biotech revenue is expected to increase from $90 billion in 2011 to $200 billion in 2016. Also, as the field of biostatistics is always under development and improvement, biotech companies are spending a lot of resources and capital in R&D, for example Swiss Biotech Giant, Roche, spent $10, 187 million in 2012 and in subsequent years, maintained a constant increase rate of 10% in its annual R&D funds.
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This page was last updated on April 26, 2024