Artificial Intelligence - What Is Bayesian Inference?


Bayesian inference is a method of calculating the likelihood of a proposition's validity based on a previous estimate of its likelihood plus any new and relevant facts.

In the twentieth century, Bayes' Theorem, from which Bayesian statistics are derived, was a prominent mathematical technique employed in expert systems.

The Bayesian theorem has been used to issues such as robot locomotion, weather forecasting, juri metry (the application of quantitative approaches to legislation), phylogenetics (the evolutionary links among animals), and pattern recognition in the twenty-first century.

It's also used in email spam filters and can be used to solve the famous Monty Hall issue.

The mathematical theorem was derived by Reverend Thomas Bayes (1702–1761) of England and published posthumously in the Philosophical Transactions of the Royal Society of London in 1763 as "An Essay Towards Solving a Problem in the Doctrine of Chances." Bayes' Theorem of Inverse Probabilities is another name for it.

A classic article titled "Reasoning Foundations of Medical Diagnosis," written by George Washington University electrical engineer Robert Ledley and Rochester School of Medicine radiologist Lee Lusted and published by Science in 1959, was the first notable discussion of Bayes' Theorem as applied to the field of medical artificial intelligence.

Medical information in the mid-twentieth century was frequently given as symptoms connected with an illness, rather than diseases associated with a symptom, as Lusted subsequently recalled.

They came up with the notion of expressing medical knowledge as the likelihood of a disease given the patient's symptoms using Bayesian reasoning.

Bayesian statistics are conditional, allowing one to determine the likelihood that a specific disease is present based on a specific symptom, but only with prior knowledge of how frequently the disease and symptom are correlated, as well as how frequently the symptom is present in the absence of the disease.

It's pretty similar to what Alan Turing called the evidence-based element in support of the hypothesis.

The symptom-disease complex, which involves several symptoms in a patient, may also be resolved using Bayes' Theorem.

In computer-aided diagnosis, Bayesian statistics analyzes the likelihood of each illness manifesting in a population with the chance of each symptom manifesting given each disease to determine the probability of all possible diseases given each patient's symptom-disease complex.

All induction, according to Bayes' Theorem, is statistical.

In 1960, the theory was used to generate the posterior probability of certain illnesses for the first time.

In that year, University of Utah cardiologist Homer Warner, Jr.

used Bayesian statistics to detect well-defined congenital heart problems at Salt Lake's Latter-Day Saints Hospital, thanks to his access to a Burroughs 205 digital computer.

The theory was used by Warner and his team to calculate the chances that an undiscovered patient having identifiable symptoms, signs, or laboratory data would fall into previously recognized illness categories.

As additional information became available, the computer software could be employed again and again, creating or rating diagnoses via serial observation.

The Burroughs computer outperformed any professional cardiologist in applying Bayesian conditional-probability algorithms to a symptom-disease matrix of thirty-five cardiac diseases, according to Warner.

John Overall, Clyde Williams, and Lawrence Fitzgerald for thyroid problems; Charles Nugent for Cushing's illness; Gwilym Lodwick for primary bone tumors; Martin Lipkin for hematological diseases; and Tim de Dombal for acute abdominal discomfort were among the early supporters of Bayesian estimation.

In the previous half-century, the Bayesian model has been expanded and changed several times to account for or compensate for sequential diagnosis and conditional independence, as well as to weight other elements.

Poor prediction of rare diseases, insufficient discrimination between diseases with similar symptom complexes, inability to quantify qualitative evidence, troubling conditional dependence between evidence and hypotheses, and the enormous amount of manual labor required to maintain the requisite joint probability distribution tables are all criticisms leveled at Bayesian computer-aided diagnosis.

Outside of the populations for which they were intended, Bayesian diagnostic helpers have been chastised for their shortcomings.

When rule-based decision support algorithms became more prominent in the mid-1970s, the application of Bayesian statistics in differential diagnosis reached a low.

In the 1980s, Bayesian approaches resurfaced and are now extensively employed in the area of machine learning.

From the concept of Bayesian inference, artificial intelligence researchers have developed robust techniques for supervised learning, hidden Markov models, and mixed approaches for unsupervised learning.

Bayesian inference has been controversially utilized in artificial intelligence algorithms that aim to calculate the conditional chance of a crime being committed, to screen welfare recipients for drug use, and to identify prospective mass shooters and terrorists in the real world.

The method has come under fire once again, especially when screening includes infrequent or severe incidents, where the AI system might act arbitrarily and flag too many people as being at danger of partaking in the unwanted behavior.

In the United Kingdom, Bayesian inference has also been used into the courtroom.

The defense team in Regina v.

Adams (1996) offered jurors the Bayesian approach to aid them in forming an unbiased mechanism for combining introduced evidence, which included a DNA profile and varying match probability calculations, as well as constructing a personal threshold for convicting the accused "beyond a reasonable doubt." Before Ledley, Lusted, and Warner revived Bayes' theorem in the 1950s, it had previously been "rediscovered" multiple times.

Pierre-Simon Laplace, the Marquis de Condorcet, and George Boole were among the historical figures who saw merit in the Bayesian approach to probability.

The Monty Hall dilemma, named after the presenter of the famous game show Let's Make a Deal, involves a contestant selecting whether to continue with the door they've chosen or swap to another unopened door when Monty Hall (who knows where the reward is) opens one to reveal a goat.

Switching doors, contrary to popular belief, doubles your odds of winning under conditional probability.

~ Jai Krishna Ponnappan

You may also want to read more about Artificial Intelligence here.

See also: 

Computational Neuroscience; Computer-Assisted Diagnosis.

Further Reading

Ashley, Kevin D., and Stefanie BrĂ¼ninghaus. 2006. “Computer Models for Legal Prediction.” Jurimetrics 46, no. 3 (Spring): 309–52.

Barnett, G. Octo. 1968. “Computers in Patient Care.” New England Journal of Medicine
279 (December): 1321–27.

Bayes, Thomas. 1763. “An Essay Towards Solving a Problem in the Doctrine of Chances.” 
Philosophical Transactions 53 (December): 370–418.

Donnelly, Peter. 2005. “Appealing Statistics.” Significance 2, no. 1 (February): 46–48.
Fox, John, D. Barber, and K. D. Bardhan. 1980. “Alternatives to Bayes: A Quantitative 
Comparison with Rule-Based Diagnosis.” Methods of Information in Medicine 19, 
no. 4 (October): 210–15.

Ledley, Robert S., and Lee B. Lusted. 1959. “Reasoning Foundations of Medical Diagnosis.” Science 130, no. 3366 (July): 9–21.

Lusted, Lee B. 1991. “A Clearing ‘Haze’: A View from My Window.” Medical Decision 
Making 11, no. 2 (April–June): 76–87.

Warner, Homer R., Jr., A. F. Toronto, and L. G. Veasey. 1964. “Experience with Bayes’ 
Theorem for Computer Diagnosis of Congenital Heart Disease.” Annals of the 
New York Academy of Sciences 115: 558–67.

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