What is Bayesian: Definition and 78 Discussions

Thomas Bayes (/beɪz/; c. 1701 – 1761) was an English statistician, philosopher, and Presbyterian minister.
Bayesian (/ˈbeɪʒiən/) refers either to a range of concepts and approaches that relate to statistical methods based on Bayes' theorem, or a follower of these methods.
A number of things have been named after Thomas Bayes, including:

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  1. B

    Bayesian probability question about Dirichlet prior distributions

    Hi there, I have a question about Bayesian probability. I have a list of the starting times of journeys. I binned the data into 15 minute bins so I have 96 bins in total (4*24=96). So for example a journey start time of 08:05 am would be in bin number 29. As an example here is the data for...
  2. M

    Bayesian method vs.maximum likelihood

    Hi, Wondering if there is any priorities one method has versus the other one and are there any specific cases where to use one vs.other? regards
  3. H

    Bayesian model for hierarchical evaluation

    Hi I have a problem in which I have to search a huge library in order to find documents similar to that of a given query document. The library is organised into clusters and each cluster contains documents of a particular class. Given a query document, first we retrieve the most...
  4. W

    Difference between Bayesian & Modern Probability

    Hi all, What is the difference between Bayesian Probability http://en.wikipedia.org/wiki/Bayesian_probability and the normal probability that we study at University, isn't Bayesian Probability simply the conditional probability that we study in Probability & Measure or in any other text...
  5. U

    Wave Function Collapse and Bayesian Probabilty

    I'm curious as to whether or not there is a connection to be drawn between the phenomenon of wave function collapse and the idea of Bayesian inference. I began thinking about this within the context of one of the variants of the Monty Hall problem. If you have one kid, what's the probability...
  6. M

    Will someone please explain Bayesian statistics?

    I don't know much algebra (I kind of skipped it and went to geometry), but I do sort of understand statistics. I can certainly perform a z-test or a t-test and know when they should or shouldn't be used.
  7. S

    Applying Bayesian Inference to Test Hypothesis on 100 Samples of Random Numbers

    how is bayesian inference actually applied? Say I have (100samples) a series of random numbers between 1 to 10. How do I test for the hypothesis that "there is a bias for the numbers 5,7" ?
  8. K

    MHB Bayesian Inference: Probability of Digital Audio Device Working

    An absent minded professor goes for a walk carrying a digital audio device using 2 batteries. He has 2 fresh replacement batteries stashed away in one of four pockets. Sure enough, both batteries lose their charge and he removes them. Not wanting to throw the deplete batteries into the woods...
  9. M

    Bayesian Conditionalization

    Hello, I'm stuck at the following problem on Baysesian conditionalization: Prove that conditionalizing once on (A or B) is equal to conditionalizing first on A and then on B. As a hint, I was asked to define H(x) = P(X given A). Any help would be appreciated.
  10. B

    A little help understanding this bayesian problem (very basic)

    Homework Statement so I'm trying to teach myself bayes, and i got a book, and I'm going through trying to do the exercises, and lo and behold, i get stuck on the first one. i thought i was getting it, but the answer given at the back of the book is different than mine. Homework...
  11. I

    Bayesian inference of Poisson likelihood and exponential prior.

    Hey I have some problems understanding my statistics homework. I am given a data set giving the number of calls arriving to different switchboards in three hours as well as the total phone call duration in minutes for each switch board. Something like i y_i t_i -------------- 1...
  12. P

    Bayesian Networks: P(a,b,c,d) Calculation

    suppose i have 2 bayesian networks... a->b and c->d ie b depends on a and d depends on b now P(a,b,c,d)=P(a)*P(b|a)*P(c|a,b)*P(d|a,b,c) =P(a)*P(b|a)*P(c)*P(d|c) Am i right...? please reply..i need it as quickly as possible...
  13. S

    How to incorporate evidence into parameters of a Bayesian network?

    Greetings, Maybe I'm getting a little bit confused, but I'm looking for resources which explain how to update parameters of a Bayesian network as a result of observations. There are various inference methods, but unless I'm missing something here, these methods produce a posterior...
  14. E

    Bayesian Estimation: Posterior Mean Estimator

    Homework Statement X_1 , \dots ,X_n \sim U[0, \theta] iid. \theta \sim U[0,1] derive the Bayesian posterior mean estimator Homework Equations f(\theta |\vec{X}) = \frac{f( \vec{X}|\theta)f(\theta )}{f( \vec{X})} The Attempt at a Solution My line of thinking... First, the marginal...
  15. Z

    Bayesian Network for Continuous Random Variable?

    There are no Bayesian Networks for continuous random variables, as far as I know. And the Netica Bayesian Network software discretize continuous random variables to build bayesian models. Are there any reasons for this? Has anyone proposed continuous random variable bayesian networks?
  16. L

    Bayesian Inference: Finding Distribution of W Before Experiment

    Homework Statement An urn has 6 balls: black and white. Initially, the number of white balls W is distributed uniformly in {0,1,...,6}. Two balls are taken from the urn: one white and one black. Find the distribution of W before the experiment. The Attempt at a Solution So, initially...
  17. Z

    Bayesian Inference: Prob of Dry Pavement Outside House

    (Moderator's note: thread moved from "Set Theory, Logic, Probability, Statistics") Hi guys, Say outside of my house, there are 20% chance of rain, and 40% chance the sprinker is on. When it is rain the pavement outside of house must be wet. And if the sprinkler is on, it also wet my...
  18. A

    Bayesian Probability - two criminals, blood, and various things

    Homework Statement I am trying to work out what I believe to be a fairly simple 'odds ratio' problem using Bayesian probability for my physics class. Here is the statement of the problem: "Two criminals have left traces of their own blood at the scene of a crime. A suspect, Oliver, is tested...
  19. N

    Bayesian probability: The lighthouse problem

    Homework Statement Hi all. Please take a look at this problem: http://web.gps.caltech.edu/classes/ge193/practicals/practical3/Lighthouse.pdf I am stuck at question 2 and 3. For question 1 I get the following: d_k = \beta \tan(\theta_k)+\alpha. For question 2 and 3, I know I...
  20. C

    Bayesian Inference: Understanding the Relationship between Events and Causality

    I've been reading some about Bayesian statistics, and am a little confused. I never really covered Bayesian stuff as an undergrad, and am now a physicist, so I haven't had to learn it. I have been trying to think of things in terms of more interesting examples than the trivial coin flipping...
  21. Z

    Derivation of bayesian inference in Hidden Markov model

    hi, everyone, I have a problem when I learn the Bayesian tracking in an Hidden Markov model. Firstly ,the Hidden Markov model is represented here: http://en.wikipedia.org/wiki/Recursive_Bayesian_estimation secondly, the problem I encounted is in the follow formula ONE...
  22. M

    Bayesian or not Bayesian,this is my problem

    I have a set of 10000 elements to buy; I want to do some quality assurance activity in order to avoid to buy invalid elements. I have an automatic test that provides the probability of correctness of an element; moreover I know that the test gives a 20% of false positive and a 30 % of false...
  23. V

    Can You Self-Learn Bayesian Statistics and R Programming?

    There isn't a course at my university for Bayesian stats, but I was wondering if it would be possible to teach myself. Does anyone know of any good intro texts or online resources for leaning Bayesian Statistics? Also I want to learn to use R some over the break. Does anyone know of any good...
  24. S

    Understanding Bayesian Inference & Gaussian Distribution

    I am reading a topic on Bayesian Inference.I read books from different authors but they are all the same. I cannot see how the terms are derived. Could anyone briefly explain what is going on and what is it that we are trying to find using this Bayesian. Bayesian is a combination of belief...
  25. I

    How Do You Calculate Disease Probability with Bayesian Statistics?

    I know the Bayesian formula is given by the ff: P(Ei|A) = P(A | Ei) * P (Ei) / summation of P (A | En) * P (En) over n however how do you solve this type of problem: The probability of a person having a disease is 5%, The probability of testing negative in a checkup given that you...
  26. Fredrik

    Two similar Bayesian problems. Did I get them right?

    I would appreciate if someone could help me solve and understand these two problems. The first version of this post contained my attempts to solve them, but I have deleted those parts because I saw that I had messed up badly. I really suck at this type of problems, but perhaps someone can show...
  27. D

    Bayesian probability of this problem

    This problem I took from an IQ test I found: Consider two breeding strategies of the fictional Furble. Dominator Furbles can fight for a breeding territory, and if they win, will be able to rear 10 offspring. An alternative is to share territory with another Furble which will allow each to...
  28. S

    Bayesian Stat Mech reverses Entropy?

    Cosma Shalizi has a brief paper in the arxiv: http://www.arxiv.org/PS_cache/cond-mat/pdf/0410/0410063.pdf containing a proof that if you use Bayesian degree of belief oriented probability in forming statistical mechanics a la Jaynes, entropy comes out non-increasing; the arrow of time...
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