Bayesian Definition and 70 Threads

  1. alima

    Comp Sci Which is the probability of JohnCalls given Burglary? Why?

    Questions: P (JohnCalls|Burglary) ? Why? Source of the image: Artificial Intelligence: A Modern Approach - Third Edition, by Stuart Russell and Peter Norvig. My attempt at solving: using Bayes' Theorem = P (A|B) = ( P(B|A) * P(A) ) / P(B) P(JohnCalls|Burglary) = P(J|B) = ( P(B|J) * P(J) /...
  2. Fra

    I Thoughts about this Bayesian Mechanics paper?

    Looking for something else I just stumbled over this paper the declare as introducing a field they call "bayesian mechanics". I thought I would create a new thread for a change and just highlight this paper. It's the first time I've seen this from the authors so I don't have their full...
  3. Artemisa

    Error floors in this Bayesian analysis

    In this article((https://arxiv.org/pdf/2001.04581.pdf)), the authors use a Bayesian analysis based on the positions of astrophysical bodies and their errors in the medians. This statistical analysis uses the markov chain monte carlo chains. The uncertainties in the positions are large, so what...
  4. jedishrfu

    B How Can Bayesian Search Theory Simplify Finding Lost Everyday Items?

    https://bigthink.com/smart-skills/bayesian-search-find-stuff-lost/
  5. T

    I A Bayesian question of choosing a white or black dog

    An excellent article on Bayes and Bayesian statistics was found on Houston Public Radio.https://uh.edu/engines/epi1876.htm The problem is in the first 2 paragraphs of the article.. I will summarize: Your wife and her friend went out and got you a white dog for your birthday, and you wonder...
  6. B

    How are hyperparameters determined in Bayesian optimization?

    Hello, I am better studying the theory that is the basis of Bayesian optimization with a Gaussian Process and the acquisition function EI. I would like to expose what I think I understand and ask you to correct me if I'm wrong. The aim is to find the best ##\theta## parameters for a parametric...
  7. S

    I Bayesian statistics in science

    [Moderator's note: This thread has been split off from a previous thread since its topic is best addressed in a separate discussion. This post has been edited to focus on the topic for separate discussion.] Jaynes has used in the derivation of the rules of probability as the logic of plausible...
  8. B

    Python Laplace approximation in Bayesian inference

    Hello everybody, I am working on a Python project in which I have to make Bayesian inference to estimate 4 or more parameters using MCMC. I also need to evaluate the evidence and I thought to do so through the Laplace approximation in n-dimensions: $$ E = P(x_0)2\pi^{n/2}|C|^{1/2} $$ Where C...
  9. Dale

    Insights Posterior Predictive Distributions in Bayesian Statistics

    [url="https://www.physicsforums.com/insights/posterior-predictive-distributions-in-bayesian-statistics/"]Continue reading...
  10. hdp12

    Bernoulli and Bayesian probabilities

    Summary:: Hello there, I'm a mechanical engineer pursuing my graduate degree and I'm taking a class on machine learning. Coding is a skill of mine, but statistics is not... anyway, I have a homework problem on Bernoulli and Bayesian probabilities. I believe I've done the first few parts...
  11. Dale

    Insights How Bayesian Inference Works in the Context of Science

    Continue reading...
  12. Dale

    Insights Frequentist vs Bayesian Probability: What's the Difference?

    [url="https://www.physicsforums.com/insights/frequentist-probability-vs-bayesian-probability/"]Continue reading...
  13. Dale

    Insights How to Get Started with Bayesian Statistics

    Continue reading...
  14. jim mcnamara

    B An objective Bayesian analysis of life’s early start & late arrival

    Article: https://www.pnas.org/content/early/2020/05/12/1921655117 Phys.org link https://phys.org/news/2020-05-odds-life-intelligence-emerging-planet.html An issue I see is Mars and Venus. Mars may have had some life forms, and may still. Venus never got that far. So, in a sense, we are 1...
  15. D

    On being alive now and Bayesian probabilities....

    Hi everyone! I am new here, I have been reading you for many years and I just registered hoping that you can help me out with these disturbing thoughts, as they are taking away too much of my time :( Let's say my lifespan is around 80 years. The lifespan of the universe is of the order of...
  16. Buzz Bloom

    I Questions about error range from Bayesian statistics

    About cosmology: https://www.physicsforums.com/threads/what-is-the-probability-that-the-universe-is-absolutely-flat.971984/#post-6180036 Planck paper: https://arxiv.org/pdf/1502.01589.pdf As in PCP13 we adopt a Bayesian framework for testing theoretical models. In the Planck paper, pages 38-40...
  17. Buzz Bloom

    I Qs re Cosmological Models Using Bayesian Probability Methods

    I am familiar with non-Bayesian methods for calculating best fit values of various parametric models, but I have not had any experience with cosmological models calculations. My understanding is that these models have five parameters: H0, Ωr, Ωm, Ωk, ΩΛ, and the last four satisfy the constraint...
  18. mertcan

    I Bayesian Information Criterion Formula Proof

    Hi everyone, while I was digging arima model I saw that BIC value is given as $k*log(n)-2*log(L)$ where $L$ is the maximized value of likelihood function whereas $k$ is number of parameters. I have found the proof of AIC but no any clue about that. I wonder how it is derived. Could you help me...
  19. R

    I Multiple hypothesis testing for radar tracking in clutter

    Hello All, The goal is to formulate a multiple hypothesis test for a radar tracking problem when false alarms are occurring and to apply a particle filter on this update step, however I first need to come to/understand the multiple hypothesis formulation in this problem. Say we are interested...
  20. phinds

    I Specific question re Bayesian statistics/analysis

    I am reading "Thinking Fast and Slow" (fantastic book by the way) and I ran across a statement that has me flummoxed. The justification for the statement was said to be "Bayesian analysis" so I looked into that and frankly it's just more than I want to get into so I'm wondering if someone can...
  21. ChrisVer

    A Bayesian Priors and relation with ignorance

    Hi everyone. I am reading through these very interesting (in terms of topics) notes: https://arxiv.org/abs/1807.05996 And so far I am at Section 5. The author gives me the impression they don't seem to fear to call what is Bayesian and what is Frequentist, making the distinction in applications...
  22. T

    MHB Question about Bayesian Inference, Posterior Distribution

    I have a posterior probability of $$p_i $$which is based on a Beta prior and some data from a binomial distribution: I have another procedure: $P(E)=\prod_{i \in I} p_i^{k_i}(1-p_i)^{1-k_i}$ which gives me the probability of a specific event of successes and failures for the set of $I$ in a...
  23. R

    Bayesian Probability Distributions

    Hi, I was having some trouble doing some bayesian probability problems and was wondering if I could get any help. I think I was able to get the first two but am confused on the last. If someone could please check my work to make sure I am correct and help me on the last question that would be...
  24. stevendaryl

    B Probabilities associated with temporal uncertainty

    This seems like a simple matter, but apparently it is controversial: Is it meaningful to talk about probabilities for temporal uncertainty? If I find myself in a room without a clock, I might wonder what time it is. I know that I entered the room at 9:00, so it has to be later than that. I know...
  25. T

    MHB Probability calculation with Bayesian Networks

    Given this base data (taken from Graphical Models )$P(C) = 0.5$ $P(\lnot C) = 0.5$ $P(R | C) = 0.8$ $P(R | \lnot C) = 0.2$ $P(\lnot R | C) = 0.2$ $P(\lnot R | \lnot C) = 0.8$ $P(S | C) = 0.1$ $P(S | \lnot C) = 0.5$ $P( \lnot S | \lnot C) = 0.5$ $P( \lnot S | C) = 0.9$ $P(W | \lnot S, \lnot...
  26. L

    I Yet another Bayesian probability question

    But a very simple one. Just to check I'm not getting it wrong. Suppose you have a very large enclosure with 100 animals. 70 of these animals are cats, 30 are dogs. There is enough food for all the animals, but you introduce a new type of food, to see whether either cats or dogs will show a...
  27. W

    How Can MCMC Methods Aid in Bayesian Parameter Estimation for Complex Models?

    Hi folks. I have the following question.I have a model M containing 20 adjustable parameters k = {k_j}. I also have 40-50 measured temporal profiles e = {e_i} at my disposal. I can use M to predict the experimental values after solving complex systems of differential equations.Consequently, I...
  28. W

    MHB Bayesian parameter estimation via MCMC?

    Hi folks. I have the following question. I have a model M containing 20 adjustable parameters k = {k_j}. I also have 40-50 measured temporal profiles e = {e_i} at my disposal. I can use M to predict the experimental values after solving complex systems of differential...
  29. J

    B Regarding bayesian analysis/inference/ predictions

    I am forever hearing heady claims that bayesian (something or other) can help people to make better decisions and overall get closer to the truth of things. However I have yet to discover an article, audio lecture or anything that really explains in a layway how to use or even understand this...
  30. I

    Struggling with Bayesian Truth Serum formula

    Hi there, right now, I am struggling to successfully calculate scores with the Bayesian Truth formula and I hope this is the right place to find someone who can help me along For everyone, who doesn’t know it, I will summarize it briefly : The Bayesian Truth Serum is an scoring method, that...
  31. P

    Bayesian Network Homework: Equations & Solutions

    Homework Statement Homework EquationsThe Attempt at a Solution For part A I solved for P(B|JC) = P(B,JC)/P(JC) For part B I am thinking P(B|!JC, MC) = P(B, !JC, MC) / P(!JC, MC) For part C I am thinking P(JC|MC) = P(JC, MC)/P(MC) Am I on track with these equations? Especially for part c...
  32. Q

    Knee deep in Bayesian statistics and

    Hello all, To just begin, I am having a lot of trouble keeping my brain in the Bayesian view and not letting it revert back to a Frequentist way of thinking. Not to mention having troubles with unbinned MLE estimation. If I say something wrong, please let me know. My questions are...
  33. S

    How to fit given function to blurred data points?

    Are there any elaborated theory or method how to fit parameters of a function family to data given by probability distributions of data points instead of given coordinates of points precisely without error? I think this is a very general problem, I hope it is already solved. Important: I...
  34. I

    Bayesian stats: how to update probability?

    I am trying to use Bayesian methods (Bayes rule) to predict further datapoints (at point n,n+1,n+2 etc..)... I begin by generating a normal pdf using previous 75 datapoints (prior: n-75 to n-1) with mean value, μ: 1.25 and standard deviation, δ: 3.67. Note: previous datapoints range from...
  35. P

    Looking for people in bayesian modeling

    I am starting a project on signal detection theory (cognitive focus), and working with a winbugs expansion in matlab. I am looking for good references, papers, books, anything that fully cover the theory of bayesian modeling and statistical inference (mostly with graphical modeling, since that...
  36. R

    How Does Bayesian Estimation Determine Point Estimates with Prior Distributions?

    Homework Statement Let Y_n be the nth order statistic of a random sample of size n from a distribution with pdf f(x|\theta)=1/\theta from 0 to \theta, zero elsewhere. Take the loss function to be L(\theta, \delta(y))=[\theta-\delta(y_n)]^2. Let \theta be an observed value of the random variable...
  37. carllacan

    Difference between prediction and update on Bayesian Filters

    Hi. I have a couple ofsimple question about Bayesian Filters, just to check that I'm correctly grasping everything. I've been thinking on the difference between the prediction and update steps. I understand the "Physical" difference: in the first one we calculate the probability of the world...
  38. carllacan

    What is the true value given successive sub-unity sensor readings?

    We have a sensor that measures a certain value that lies in the range (0, 3). The sensor is not perfect, and sometimes it fails. When this happens it ouputs a value under 1, regadless of the actual value. The failure probability is 0,01. Suposing the sensor outputs a value under 1, what is the...
  39. T

    How Can Bayesian Analysis Estimate Player A's Winning Probability in a Match?

    Hi, I am trying to learn something about Bayesian Analysis by doing an example. I have a series of 10 matches played between A and B, where each match is the first to 3 points. With an example data set that looks like this: ABBAA BAAA AABBA BBB BABB AAA AABA BAAA AABBB AAA I...
  40. S

    Quantum Bayesian Interpretation of QM

    Any comments (pro-con) on this Quantum Bayesian interpretation of QM by Fuchs & Schack ?: http://arxiv.org/pdf/1301.3274.pdf
  41. J

    Bayesian Stats - Finding a Posterior Distribution

    Homework Statement Let x be the number of successes in n independent Bernoulli trials, each one having unknown probability θ of success. Assume θ has prior distribution θ ~ Unif(0,1). An extra trial, z, is performed, independent of the first n given θ, but with probability θ/2 of success. Show...
  42. T

    Bayesian Statistics - obtaining parameters for model from real data

    Hello, I've got some data on an epidemic in various locations - the total number of agents and number killed by the infection after 1 year. -This gives gives me a distribution of percentages of the populations that have been killed by the infection. (but all the percentage values are relatively...
  43. B

    Can Bayesian Informed Priors Improve Electric Car Parking Time Predictions?

    Hello, I am building a model that simulates the travel patterns of electric cars using a series of iterative conditional distributions. I have a dataset to build the pdfs. In one part of the model I generate a parking time from a conditional distribution. I create a parking time...
  44. C

    Bayesian statistics learning materials

    Does anyone here know any good Bayesian statistics, Bayesian hypothesis testing, Bayesian inference, etc. learning materials (preferably online)?
  45. I

    Bayesian network simplification.

    Let's say we have a bayesian network G. Consider a subset A of this network consisting of a set of nodes and all the edges between them. Assume, for the sake of simplicity, that all nodes in A are binary (either true or false) and strongly anticorrelated i.e. if anyone of the nodes in A are...
  46. 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...
  47. 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
  48. 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...
  49. 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...
  50. 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...
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