# 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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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...
2. ### 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...
3. ### B Bayesian Search Common Sense

https://bigthink.com/smart-skills/bayesian-search-find-stuff-lost/
4. ### 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...
5. ### 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...
6. ### I Bayesian Stats: Resources about Mercer's Theorem for Gaussian Processes

Hi, Question(s): 1. Are there any good resources that explain, at a very simple level, how Mercer's theorem is related to valid covariance functions for gaussian processes? (or would anyone be willing to explain it?) 2. What is the intuition behind this condition for valid covariance...
7. ### 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. ### 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...

10. ### 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...

14. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### Bayesian 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 equations.Consequently, I...
28. ### 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. ### 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. ### 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. ### 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. ### MHB Tricky Bayesian question using posterior predictive distributions

A game is played using a biased coin, with unknown p. Person A and Person B flip this coin until they get a head. The person who tosses a head first wins. If there is a tie, where both people took an equal number of tosses to flip a head, then a fair coin is flipped once to determine the winner...
33. ### 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...
34. ### MHB Bayesian vs Frequentist: How Do Bayesians Approach Data Analysis?

how would you classify the bayesian camp? i am a bit confused between the bayesians and the classical frequentist --Distribution: Only rely only on data or Distribution: Use experience & data --Parameter: “Fixed”, like a constant or Parameter: “Random” like a variable --Interval...
35. ### 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...
36. ### 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...
37. ### 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...
38. ### Bayesian point estimate

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...
39. ### 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...
40. ### 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...
41. ### A simple Bayesian example

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...
42. ### 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
43. ### Bayesian solution to inverse problem (ill-posed)

I posted it in math, But I think maybe it is more physics then math... Hello, I'm trying to understand the algorithm(‘‘juggling search’’) used in the following article : http://www.cns.atr.jp/~kawato/Ppdf/1...00105-main.pdf In short they have a model of IO cells that are connected...
44. ### Bayesian Statistics Homework: Finding the Bayes Solution for Point Estimation

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, 0<x<\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...
45. ### 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...
46. ### 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...
47. ### Bayesian probability question

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...
48. ### Bayesian computation of joint density, marginal posterior

Homework Statement Hi, so I am having trouble understanding the steps to get to certain densities. For example, suppose i have data y1,...,yJ ~ Binomial (nj,θj) We also have that θj ~ Beta (α,β) Now our joint posterior is: p(β,α,θ|y) ~ p(α,β) ∏ (\Gamma(α+β) / \Gamma(α)\Gamma(β))...
49. ### Bayesian statistics learning materials

Does anyone here know any good Bayesian statistics, Bayesian hypothesis testing, Bayesian inference, etc. learning materials (preferably online)?
50. ### 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...