The approach and interpretation of probability associated with Bayes theorem; usually used as opposed to the frequentist approach. It can be seen as an extension of logic that enables reasoning with propositions whose truth or falsity is uncertain. A Bayesian probabilist starts with some prior ...

learn more… | top users | synonyms

3
votes
2answers
83 views

A house is guarded by two alarms

I am trying to wrap my head around the following problem A house is guarded by two alarms. If Alarm 1 fires, p(theft) = 80% If Alarm 2 fires, p(theft) = 70% If both alarms fire at the same time, ...
2
votes
1answer
39 views

Bayes - dual estimation of parameter value and parameter growth

I am trying to find an bayesian approach to the following problem: Image a bucket with 100 white balls and an unknown number of red balls During each year, one can take a sample with replacement of ...
2
votes
1answer
24 views

Bayesian statistics, bivariate prior distribution

I've got a simple question buy I'm not sure how to solve it. It's a bit long. Suppose you've got $n$ iid random variables $X_1$, $\dots$, $X_n$ from the normal distribution with unknown mean $M$ and ...
1
vote
1answer
24 views

Bayes with conditional independence

I have a problem that I can't work out I've two conditional independent A,B such as $P(A,B|C) = P(A|C)P(B|C)$ Now I've to find posterior formula for: $P(C | A,B)$, now what I got was pretty ...
-1
votes
1answer
27 views

Improper Prior Distribution

What is the clear mathematics definition about improper prior distributions? Can you give me some book or article links about it?
0
votes
2answers
151 views

Improper Uniform Prior Distribution

In Bayesian method, choosing the prior distribution is an important step when using the Bayesian method. When choosing prior, we consider the prior knowledge to choose which prior distribution is the ...
0
votes
1answer
21 views

What is this distribution formulated with w, m and sum sign?

I have a binary classification problem, part of which is defined as follows : p(x|y=1) $\sim w (m_1 , \sum_1$) and p(x|y=0) $\sim w (m_0 , \sum_0$) Where $\sum_1$ is a covariance matrix : $$ ...
0
votes
0answers
72 views

Bayesian sequential updates of normally distributed variables

Suppose that you can observe data that are independently and identically distributed as $N(\mu, 1)$. Your prior distribution for $\mu$ is $N(m, v)$. After observing $n_1$ data with sample mean ...
0
votes
0answers
25 views

Bayesian estimate for unfair die

Suppose you have a six-sided die that you suspect is not fair and toss it N times. What would be a Bayesian approach to estimating the probability of the six outcomes given that you suspect the die ...
0
votes
1answer
71 views

Why a beta distribution with the parameters $\alpha=0$ and $\beta=0$ as a prior is bad

what happened if I define a beta distribution with $\alpha=0$ and $\beta=0$ as a prior? in other words if $p(\theta) \varpropto \frac{1}{\theta(1-\theta)}$. Thanks
0
votes
0answers
91 views

Marginal and conditional probability table without joint probability table

I've a Bayesian network, with discrete node values: for every node I've the conditional probability table $p(A|B)$, where $A$ is the node itself and $B$ is the set of the parents nodes. Now I would ...
2
votes
2answers
51 views

Bayesian learning for input “If A, then B.”

Can anyone point me to literature on Bayesian learning when the new information has the form “If A, then B”? I’m familiar with the rule that after one learns X, posterior probability P(Y) equals prior ...
0
votes
0answers
11 views

$X_1,\ldots,X_8$ come from a Pareto with $\beta=1$. $\alpha$ has a prior Gamma($A$,$B$). Find posterior distribution

Can anyone confirm that it would be a Gamma($A+8,B$). I got; $$\left[\alpha^8 x^{-8(\alpha+1)}\right] \left[\alpha^{A-1}e^{-\alpha \beta}\right]$$ Which is proportional to, ...
1
vote
0answers
35 views

multiplication of 2 PDFs

If I multiply the two PDFs, does the variance of the result PDF becomes narrower than the two PDFs always? In other words, if I multiply likelihood and prior to get the posterior, is the variance of ...
0
votes
0answers
18 views

Effect of proximal projection using a divergence measure, on the maximizer of the function

Suppose we have a probability distribution $p(\mathbf{x})$ and we know : $$ \mathbf{x}^* = \arg\max_{\mathbf{x}} p(\mathbf{x}) $$ Suppose we do a projection of this distribution onto another family ...
3
votes
2answers
158 views

Is politically incorrect conclusion more likely to be true by Bayesian Logic? [closed]

We got many beliefs. Some are hidden and some are repeated. False beliefs are repeated more because people like it. True beliefs are hidden if people do not like it. So for the same amount of ...
0
votes
0answers
38 views

How do I prove and expand Bayesian Networks?

Attempting to understand Exercise 20 (pdf page 44) in the paper: (Warning: large paper; small exercise) Bayesian Reasoning and Machine Learning The party animal problem corresponds to the ...
2
votes
0answers
43 views

Does this question work with Bayes formula?

Looking at slide 11, Example 1.10 from: http://www-users.aston.ac.uk/~cornford/probmod/ProbMod310810_Ch1.pdf Luke has been told he’s lucky and has won a prize in the lottery. There are 5 prizes ...
0
votes
1answer
16 views

Probability of one node given all the others in a bayes network

For a bayes network which has $n$ nodes, $X_1, X_2, ... , X_n$. Is there any efficient way to calculate $P(X_i|X_1,X_2,...,X_{i-1},X_{i+1},...X_n)$, without constructing the full joint distribution?
1
vote
1answer
41 views

conjugate prior

A class of sampling distribution is a conjugate family of a prior distribution, if the posterior distribution belongs to the same family for all priors and all samples. Why is this phrase incorrect?
1
vote
0answers
96 views

Estimating conditional probability as a function of time

My question relates to estimating from a time series a time dependent conditional probability without having a prior parametric model of anything. Suppose I have two variables: r and I, and each can ...
2
votes
1answer
92 views

Bayes factor and Posterior odds

Consider the following posterior odds \begin{equation*} \frac{P(H|D_1,D_2)}{P(\overline{H}|D_1,D_2)}=\frac{P(D_2|H,D_1)\times P(D_1|H)P(H)}{P(D_2|\overline{H},D_1)\times ...
0
votes
0answers
18 views

Computing Object Classification with bayesian statistics

Say I want to know if there is a zebra $\theta$, in an image $x$. According to Bayes statistics applies to image recognition, I should be computing: ...
0
votes
0answers
26 views

Bayesian ranking system acting up

My Bayesian ranking system seems to be acting quirky.. and I'm wondering about my implementation. This is basically my formula: ...
0
votes
1answer
59 views

determining maximum a posteriori (MAP) hypothesis

I have this problem: You are given a coin that may or may not be biased. Specifically, you have three hypotheses about the coin: ...
0
votes
0answers
28 views

Jeffery's prior - help

I'm studying Bayesian inference and looking at prior choices. Currently I have looked at Laplace's uniform prior choice and now I am trying to understand Jeffrey's prior. I am having trouble ...
-2
votes
1answer
33 views

Can likelihood be changed when the prior changes?

I have a data which follows gamma distribution and want to know the uncertainty of the parameters of this data. •Data∼Gamma(α,β) •Parameters α∼Gamma(kα,θα) β∼Gamma(kβ,θβ) I used Winbugs (code ...
0
votes
0answers
97 views

Bayes' Theorem Question, with a twist

I have a very old past high school exam question I am trying to solve (for interest only). It's a straightforward application of Bayes' Theorem, with the last part of the question containing a slight ...
1
vote
0answers
24 views

Growing of a score function

The argument that I'm dealing is very specific, I hope to make you understand the problem without going into detail. I have this score function: \begin{align} score = MargL^q + MargL^{\theta} ...
1
vote
1answer
44 views

When using Bayes Rule, what are the rules for flipping the conditions and the event of interest?

Here is Bayes Rule: $$P(A\mid B) = \frac{P(B\mid A) P(A)}{P(B)}$$ This paper (http://www.cogsci.northwestern.edu/Bayes/Sivia_1996.pdf) uses Bayes rule on page 21 in the context of model selection ...
6
votes
1answer
119 views

What is the most general formalism for machine learning?

Most of the literature I can find in the field of machine learning is extremely practical, listing many techniques you can use like neural networks, SVMs, random forests, and so on. There are lots of ...
0
votes
0answers
26 views

Bayesian Network understanding

I am confused by the definition of Bayesian Network. It's well know that graph $G$ of Bayesian Network can be viewed in two very different ways: As a data structure that provides the skeleton for ...
1
vote
1answer
61 views

Bayesian Probability Question - Parameter Estimation

I would like help on the following question and I will show my work. Here is the question in my notes and I will follow up with my work: Q: Suppose a forest is segmented into strips, referred to as ...
0
votes
0answers
27 views

Is a prior distribution always a random probability measure?

Let $(\mathcal{X}, \mathcal{B})$ be a measurable space and let its probability measure be $P$. In Bayesian statistics, we may wish to define a prior $\mu$ on the space of all such probability ...
1
vote
0answers
15 views

Determining the liklihood in Baye's rule for parameter estimation

I have used Bayesian statistics in classes but what I am trying to do now is different than anything I have done in class. Previously, I was given information and certain numbers adn I could ...
0
votes
0answers
59 views

Monty Hall Problem Extended Using Bayes's Theory

I know there is a question on the website concerning the extension of the monty hall problem. The question is provided with very good answers given by the participants on the website which I would ...
1
vote
1answer
44 views

completing the square for matrices

I'd like to calculate the posterior distribution given the prior distribution $w\sim N(0,\Sigma_p)$ and the likelihood $y|X,w\sim N(X^\top w,\sigma_n^2I).$ Ignoring everything that does not contain ...
1
vote
0answers
53 views

Monty Hall Problem Solve Using Detailed Algebra

I have been searching the monty hall problem for two days now and I generally understand it but I am having a very hard time solving the monty hall problem using Bayes's theory. I do not know what ...
-1
votes
2answers
51 views

Help with Bayes's theory

I know how to use this form of the Bayes's theory : $P(A | B) = P(A ∩ B)/ P(B)$ But how do I use?: $P (A | B,C) = P (B | A,C) P(A | C)/ P(B | C)$ What does the comma mean? I know its a simple ...
0
votes
1answer
80 views

Finding a posterior distribution of an exponential distribution parameter theta

Suppose that $X_1, ... , X_n$ each have an exponential distribution with parameter $\theta$, and suppose that the prior for $\theta$ is an exponential distribution with parameter $\lambda$. Find the ...
2
votes
0answers
25 views

Is this problem suited for Bayesian inference?

Suppose that the quality of a widget is distributed according to a score, given by a normal distribution with mean 1 and variance σ^2. A fraction, π of all widgets are defective. The cost of having an ...
1
vote
3answers
79 views

Probability of independent events $P(ab)=P(a)*P(b)$

I know there are two ways to say event $a$ and $b$ are independent: $P(a)*P(b)=P(ab)$ $P(a\mid b)=P(a)$ and I can derive one from the other with the Bayes Formula $P(a|b)=P(ab)/P(b)$. My question ...
1
vote
0answers
46 views

Generalized Bayes Estimator

Consider a decision problem in which the model parameter, $\theta$, is any integer, the distribution for the integer observation, y, given $\theta$ is $P(y|\theta) = 1/3$ if $y \in [\theta - 1, \theta ...
1
vote
0answers
31 views

Why is the marginalized inverse-Wishart distribution not equal to the inverse-gamma distribution?

Given that the inverse-gamma distribution is the one-dimensional version of the inverse-Wishart distribution, why will (philosophically speaking) an inverse-Wishart distribution that originally has ...
0
votes
1answer
46 views

Give the Bayesian Posterior Mode

Suppose that $X_1, X_2, \ldots, X_n$ are IID Bernoulli random variables with success probability equal to an unknown parameter $\theta \in [0,1]$. Let $A$ and $B$ be nonnegative constants. If we ...
1
vote
1answer
33 views

Conditional probability with bayes rule??

http://cseweb.ucsd.edu/~dasgupta/103/2b.pdf part 2.1.2 implies $P(X|Y \cap Z) = \frac{P(X|Y)}{P(Y|Z)}$ Seems to imply that this is true but if you take bayes, the left hand side is: $P(X|Y \cap Z) = ...
3
votes
2answers
86 views

Conjugate priors make calculations easier but at what cost to the model?

As I understand, when we have a parametric pdf and need to estimate the parameter based on some observed fact, we tend to choose a conjugate prior of the pdf for the parameter. Because conjugate prior ...
0
votes
0answers
28 views

How many numbers for the full joint?

Suppose you have 3 binary nodes A, B, C. A and B are independent given C. How many numbers do we need for the full joint? How many numbers do we need for the Baysesian Net? I know the answers to ...
0
votes
0answers
18 views

What happens if the recursive bayes is performed without updating the data?

With a relatively good prior, and recursive Bayes' is performed with new data every iteration, the posterior converges to the real value, under ideal circumstances. But what happens if recursive ...
0
votes
0answers
37 views

Bayes updating (Beta Distribution)

I have been trying to use Bayes' theorem to update a Beta distribution B(alpha, beta). For each iteration of randomly drawn values from some Beta distribution, I multiply my 2D joint likelihood ...