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 ...

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22 views

Bayesian linear regression cost function

I am studying classification using linear regression . Now, I want to map it in Bayesian regression. Let talk about binary classification using linear regression again. Assume that I have a set ...
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31 views

Change of Variables for two level Guassian model

I have a multivariate Gaussian distribution from which two variables, u and v, are drawn. The next variables, U and V, are U = 1/(u^2+5) + N(0,sig_U) and V = v^3 + N(0,sig_V). U and V are known, ...
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28 views

continuous bayes formula [closed]

A standard derivation with $\mu = 1.3$ and $r = 0.15$ defines the 1D-Position $p_1$ of an moving object at time $t_1$. At $t_2$ the new position is measured three times: $X_1 = 2.1$, $X_2 = 2.3$ and ...
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1answer
26 views

Need help with P(D) in a Bayesian model

So I've been reading about Bayesian models so I tried I'd have a toy example I could play with. Consider the following: You are at a bus stop and you observe the bus arriving at various times $t_1, ...
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28 views

Countable Baye's theorem?

Disclaimer: If this is a foolish question, I'm sorry.. this is the first time I've looked at probability theory in very many years, and have begun to re-read everything from scratch... Question: If ...
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19 views

Given the data set is the Bayesian estimation the best solution for solving the expected value?

I am very new to this. I have several measurements that from which I need to estimate a truth value. Each of them comes with an estimated error. I know that the observation error are biased (I don't ...
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0answers
7 views

What is a gibbs predictor

I was reading an article and I don't know what a gibbs predictor is. What is it guys? Any suggestions where I should look guys. I would really appreciate some help
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14 views

Simultaneous multiple perturbations in Markov chain Monte Carlo

I'm coding a McMC algorithm for geophysical applications. Using the Metropolis-Hastings scheme to accept/reject the proposed models is smth that i thought i completely understood, but i don't. To be ...
2
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0answers
18 views

Fredholm Integral in Bayesian Appliation

Let $X = x_1, x_2, \ldots, x_n$ be a sequence of Bernoulli random variables with $k$ successes. Suppose that, given $X$, the posterior predictive probability of $x_{n+1} = x$ is known to be $g(x)$ ...
2
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1answer
52 views

Jaynes' taxicab problem

I am currently reading Jaynes' Probability Theory, The Logic of Science and am still trying to absorb everything. On page 190, he poses the following intriguing question, paraphrased here. Suppose ...
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48 views

Game Theory - Bayes Rule, Sequential Game

I am trying to solve the following model, but I get a few weird results. Sorry if it is too long... Nature moves first and with probability $p$ assigns player's 1 type to be High ($1-p$ for Low) ...
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19 views

What is the problem with this model parameter estimation algorithm?

In a statistical model with parameters $\theta$ and unobserved laten variables $Z$, the model likelihood is $$L(\theta;X)=Pr(X|\theta)=\sum_ZPr(X,Z|\theta)$$ The standard way to estimate $\theta$ ...
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6 views

Gaussian Mixture Model as Graphical Model

Could anyone show me a simple gaussian mixture model as graphical model (bayesian network) and explain to me the joint distributions? This is a question of an exam I am learning for. I basically know ...
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8 views

Bayes Classifier for items with correlation

I am familiar with Bayes classifiers and regression in general, but I am not a mathematician and so I was hoping someone here could answer this. I have a set of objects, for this purpose lets say ...
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0answers
17 views

What machine learning tool is best suited for taking time series and descriptive and making a binomial classification. [migrated]

I have an interesting task of utilizing log data from computer servers in a server farm and predicting if a particular server is likely to fail in the next 24 hours. My data set will be comprised of ...
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2answers
39 views

Betting: Gambler's Fallacy vs. Law of Large Numbers

I know this has been asked before, but I think not in this exact way, so here goes: Suppose you're going to bet on the flip of a coin. Your bet is always "HEADS", but the amount of your bet may vary, ...
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22 views

learning phenomena in bayesian technique

I have identified using bayesian method for my auto tagging application. I am dealing with user facebook post. Post belongs to ...
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0answers
32 views

How would I analyze the accuracy of a model that predicts World Cup matches?

Say, someone made a bunch of predictions for each game between Team A and Team B, such that there's a predicted probability for each of the three possible outcomes adding up to $1.0$ : Team A winning, ...
3
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4answers
63 views

Bayes, two tests in a row

I came up with a standard Bayesian example as to point out my confusion. There is an epidemic. A person has a probability $\frac{1}{100}$ to have the disease. The authorities decide to test the ...
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1answer
36 views

Confusion in Posterior Probability Calculation

I know posterior probability as, $P(\theta|x)= [(P(x|\theta)*(P(\theta))/(P(x))]$, as given in http://en.wikipedia.org/wiki/Posterior_probability I am slightly confused with the term ...
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1answer
39 views

So I have the following question, dont have much info on class notes and not sure how to tackle it, any suggestions, any help?

A seller has a single item for sale (which she values at zero). There are two potential buyers. The seller decides to use the following auction format to sell the object: each bidder submits a sealed ...
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1answer
29 views

Bayes - bias of a coin

struggling with a basic question on the bias of a coin. Assume that i believe, as prior, that a coin is 40% probable to be fair and 60% probable to be unfair, with the estimated prior bias following a ...
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1answer
49 views

Variational Methods, why KL divergence is the difference between true distribution and approximating distribution.

Likelihood = $L(\textbf{w}) = P(V\mid \textbf{w})$. $$\ln P(V\mid \textbf{w}) = \ln \sum_H P(H,V\mid \textbf{w})$$ $$= \ln \sum_H Q(H\mid V)\frac{P(H,V\mid \textbf{w})}{Q(H\mid V)}$$ $$\geq ...
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0answers
26 views

determinant and trace of a huge positive definite matrix

I have a problem to compute the determinant and the trace of inverse matrix: $det(\Gamma^{-1}+I_n⊗\Phi^T\Phi)$ and $tr[(\Gamma^{-1}+I_n⊗\Phi^T\Phi)^{-1}]$ where $\Gamma$ is a huge positive definite ...
3
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2answers
80 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
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1answer
34 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
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1answer
19 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 ...
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1answer
19 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 ...
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1answer
18 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?
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1answer
18 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
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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 : $$ ...
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50 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 ...
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22 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
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1answer
34 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
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0answers
46 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 ...
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2answers
49 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 ...
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7 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, ...
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32 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 ...
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0answers
13 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 ...
2
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2answers
130 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 ...
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0answers
25 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
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0answers
41 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 ...
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1answer
13 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
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1answer
32 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?
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37 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
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1answer
78 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 ...
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17 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: ...
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21 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: ...
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1answer
44 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: ...
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20 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 ...