Combining probabilities with Bayes' Theorem, especially as used for conditional inference.

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80 views

Are there alternatives to the Bayesian update rule?

Are there any other methods to update my belief in a hypothesis aside from the Bayesian update rule?
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1answer
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Prior predictive density given by $f(y) = {f(y\mid \lambda) g(\lambda)}\big/{g(\lambda | y)}$?

(I guess stats.SE is the right place for this) I'm reading Albert's book "Bayesian computation with R". To get theprior predictive density, he extensively uses this formula $$f(y) = \frac{f(y\mid ...
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37 views

Why is Bayes theorem more popular than the normal definition of P(A|B)? [duplicate]

As everyone knows, the conditional probability of A given B is $P(A|B) = \frac{P(A\cap B)}{P(B)}$, and Bayes' theorem is derived from that equation to $P(A|B) = \frac{P(B|A)P(A)}{P(B)}$. I'm pretty ...
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0answers
17 views

A way to make Bayes' rule common sense to me? [closed]

Although I understand Bayes' rule/theorem I always forget its intuition. I solved a lot of exercises to practice it. I remember the equation, but I find it hard to remember the intuition itself. I ...
1
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1answer
45 views

Linear discriminant analysis (Fisher) = Bayes?

I'd like to ask a question, I am reading book right now about mail filtering, both methods: naïve Bayes and Fisher are there very similar in implementation. I am also writing a paper on Bayesian spam ...
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1answer
433 views

Please help me understand this bayes probabilities chart

I am trying to understand a research paper. It contains a chart of prior and posterior probabilities (Bayes Probabilities) of an individual stock. However, I need guidance in interpreting what the ...
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0answers
10 views

How to choose between two models on the basis of the normalised posterior distributions?

Suppose you are given two normalised posterior densities $\pi_1(\theta|y)$ and $\pi_2(\theta|y)$, based on the data $y$, and arising from model 1 and model 2, respectively. You are asked to find ...
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1answer
23 views

Find corresponding linear discriminant function in a two-class, three-dimensional classification

I am new to Patter Recognition and I am kind of stuck at a homework assignment. Any help regarding the issue will be appreciated. Thank you very much. In a two-class, three-dimensional ...
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15 views

bayes estimate possion distribution function

Let {X\, ...,Xn) be random sample from random variable which has Poisson distribution with parameter A. Assume that the prior distribution A for is Gamma(1, 1) and that you have observed sample of ...
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1answer
82 views

Interpreting prior and posterior

I am bit puzzled on how we can interpret the posterior. Assume a coin which is 0.1 probable to be unfair. So our prior probability on the coin being unfair is 0.1, and being fair is 0.9. Also by ...
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0answers
23 views

What are some advanced algorithms in bayesian networks? [closed]

What are some advanced algorithms in bayesian networks? I am familiar with the conventional algorithms of network construction and inference in bayesian networks. What are some algorithms that provide ...
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3answers
47 views

Bayesian Risk and Subjectivity

I am studying the differences in bayesian and frequentist approaches to point estimation. I understand that there are objective and subjective approaches to Bayesian and some people don't like the ...
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1answer
57 views

Help setting up pymc to solve this problem relating to distribution of colors in M&M's

My overall goal is to work through the "Bayesian Methods for Hackers" book. So far I understand how to do simple things with pymc (like determining the parameters for a linear model and for a ...
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0answers
24 views

Bayes Rule with 1 Signal but 2 Unknowns

This is a question I originally posted in the math.stackexchange site, but didn't get much of an answer. Suppose I have an unknown variable $X_i = \alpha_i + \beta_i$ where $\alpha$ is one of 2 ...
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3answers
61 views

Bayes probability confidence

I use Bayes theorem to estimate the impact of a sales person on customer's decision to buy a product. $ P(buy|salesperson) = \frac{P(salesperson|buy) P(buy)}{P(salesperson)} $ Naturally, some ...
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1answer
33 views

“Multiple definitions of node p[1]” Error using WinBUGS [closed]

I have written the following code in WinBUGS and every time I try to compile the data after loading in the data I get the same error which is "Multiple definitions of node ...
7
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1answer
104 views

What would be an example of when L2 is a good loss function for computing a posterior loss?

L2 loss, together with L0 and L1 loss, are three a very common "default" loss functions used when summarising a posterior by the minimum posterior expected loss. One reason for this is perhaps that ...
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1answer
64 views

Posterior predictive test quantities

I've been trying to figure out problem 6.2 from Gelman's book, second edition, page 192 on Bayesian data analysis. Can anyone help? a) Set up predictive test quantities to check the following ...
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1answer
48 views

How to simplify $P (X|Y, Z)$ when $X$ is independent of $Y$ but not $Z$? [duplicate]

How do I simplify $P (X|Y, Z)$ if I know that $X$ is independent of $Y$ but not $Z$.
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48 views

Bayes Net: how to calculate joint distribution?

I originally posted this question to Computer Science Stack Exchange, but then I was told that CrossValidated site existed. I've been reading many questions, but none of them seem to answer my doubts. ...
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0answers
20 views

Am I fine in implementing Naive Bayes Classifier?

I have implemented one Sentiment Analysis using Naive Bayes Classifier. To do this I have taken the following steps. First I checked the problem, the nature of data (continuous or discrete) and ...
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7answers
198 views

Why is $p(A) \times p(B|A) = p(B) \times p(A|B)$?

Is there an easy way or simple example to get why it must be that $$ p(A) \times p(B|A) = p(B) \times p(A|B) $$? I get that $p(A) \times p(B|A)$ can be seen as probability of $B$ occurring, weighted ...
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1answer
43 views

Why is it called “mode” in MAP estimation?

When estimating parameters with MAP, why is it written that we are estimating the "mode"? I thought it would be the mean of the posterior distribution?
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1answer
45 views

Conditional probability density function

Let $\theta$ be the parameter of the probability density function $f(x)$. If it is mentioned that $f(x|\theta)$ be the conditional probability density function, then what does $f(x|\theta)$ mean? ...
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47 views

How to compute the probability of $P(a|b,e)$ given $P(a|b), P(a|e)$ and $A$ independent of $B$?

The following is given: $$ \begin{align} P(b) &= P(e) = 0.1\\ P(a|e) &= 0.2\\ P(a|b) &= 0.95\\ P(a|\neg b, \neg e) &= 0\\ B &{\perp\!\!\!\perp} E \end{align} $$ Is there any way ...
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15 views

Describing a distribution of probabilities/percentages

Is there a better way to describe this probability? \begin{equation} Pr(Y_{sij}|R_n) = \frac{Y_{sij|R_n} \sum_{ij}Y_{sij}}{\sum_{ij|R_n} Y_{ij}\sum_{sij}Y_{sij}} \end{equation} The $R_n$ describes ...
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2answers
34 views

Conditions under which “explaining away” does vs. does not occur

My understanding of "explaining away" is as follows. If there is an effect, C, that can result from two independent causes, A and B, then observing only C makes A more likely than observing both C and ...
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35 views

Marginal distribution MLE or MCMC

I'm a bit confused about how to maximise the following likelihood: $\mathcal{L}(k, \lambda, p) \sim \mathrm{Binomial}(n, k, p)\mathrm{Poisson}(\lambda, n)$ i.e. my probability is relatd to a number ...
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83 views

Resources for the “ah ha” moment when learning Bayes' theorem

I've been studying statistics for a little while and I keep coming back to Bayes' theorem trying to relearn it and have that "ah ha" moment with it. I keep coming back to it because I understand just ...
3
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1answer
95 views

Would a one-tailed t-test technically be considered Bayesian?

I'm just curious whether the expectation implied from a one-tailed test would somehow be considered a prior, and whether this is enough for it to be in the purview of Bayesian statistics.
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1answer
48 views

Deriving the Bayes Filter Correction Equation

The correction rule for Bayes filters is: $$p\left(x_{k}|D_{k}\right)=\dfrac{p\left(y_{k}|x_{k}\right)\cdot p\left(x_{k}|D_{k-1}\right)}{p\left(y_{k}|D_{k-1}\right)} $$ For: State at time $k$ is ...
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38 views

How to combine probabilities, weighting by strength of evidence?

Let's say that I'm trying to classify an item as a member of either class c1, class c2, class c3, etc. out of a large number of classes. In my training set, feature A appears only once; it happens to ...
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1answer
23 views

Terminology Numerator Baye's Rule?

I am considering this formulation of Baye's Rule $\mathrm{Pr}(\theta | D) = \frac {\mathrm{Pr}(\theta)\mathrm{Pr}(D|\theta)}{\int \mathrm{Pr}(D|\theta)\mathrm{Pr}(\theta)\mathrm{d}\theta}$ Is there ...
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3answers
563 views

What math/stats knowledge does learning Bayesian probability require?

I study undergraduate "pure" math and philosophy. I know that a number of philosophers use Bayesian probability to augment their epistemic logic. My school teaches Bayesian probability as a brief part ...
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3answers
274 views

Why Normalizing Factor is Required in Bayes Theorem?

Bayes theorem goes $$ P(\textrm{model}|\textrm{data}) = \frac{P(\textrm{model}) \times P(\textrm{data}|\textrm{model})}{P(\textrm{data})} $$ This is all fine. But, I've read somewhere: ...
2
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1answer
45 views

Updating belief

Lets say I think that event 'E' has a probability 'p' of happening. Then I go around and ask a number of friends if they think event 'E' will happen, they can either answer Yes or No. Now I know that ...
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29 views

Normal learning - multiple signals

I'm having trouble with the exercise below. I know that $E(η_t|z_t)= E(η_t) + [Cov(η_t,z_t)/Var(z_t)](z_t - E(z_t)) $ but still can't show 'b'. I imagine I'm missing something very simple... Can ...
3
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1answer
74 views

Guessing the length of a fish

I would like to solve the following excercise. Any help is appreciated. 90% of the fish in our pond are males, the rest are females. The length of the males are: $X+5$ inches, where $X\sim ...
2
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1answer
84 views

Problem expressing full conditionals

I have this problem, $Y_{i}$~Gamma($\alpha$,$\beta$) 1...N $\alpha$~Exp($\lambda$) $\beta$~Exp($\lambda$) $\lambda$=0.001,Find the full conditionals. I have done the following: ...
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12 views

Naive Bayes classifier to identify “mouse-like” human tumor from mouse gene signature

I am a PhD student in biochemistry, and my lab has a mouse model for breast cancer. We have a gene signature that I would like to use to identify "mouse-like" human tumors for further analysis. I have ...
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0answers
24 views

Complement naive bayes

I would like some help in understanding how does Complement Naive Bayes work. I have googled the paper Complement Naive Bayes I understand that naive bayes works by computing the probability of a ...
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0answers
95 views

Implementation of Bayes posterior predictive check

I have a question concerning the implementation of a bayes posterior predictive check. Let us assume i have this model (implementation is in R and jags): ...
4
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1answer
80 views

What is meant by this formulation of Bayes' Rule?

From the Wikipedia article on Bayesian inference, we get the following formulation of Bayes' Rule: $$p(\theta \mid \mathbf{X},\alpha) = \frac{p(\mathbf{X} \mid \theta) p(\theta \mid ...
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22 views

Meta analysis, joint posterior distribution of study effect

Meta analysis (with common study variation $\sigma$) often assumes that: $$ X_{i,j} | \theta_i \overset{ind}{\sim} N(\theta_i,\sigma)\\ \theta_i \overset{i.i.d.}{\sim} N(\mu,\tau) $$ where ...
2
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1answer
53 views

Probability of being each demographic

Relatively simple problem, but can't see how to solve it. Rephrasing in terms of everyday events. Assume there is a fair in town for three days. Each day the total visitors are known, and so are ...
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1answer
48 views

Bayes' rule and multiple conditioning

This is going to be a stupid question, but I know I am missing something, so here it goes: My textbook (Probabilistic Robotics, p.17) trivially states that Bayes' rule gives: $ p(x |y,z) = \frac{p(y ...
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28 views

Am I thinking correctly about this Bayes Problem

I am playing with the following problem. Recently a company has had some resignations. About x out of Total people resigned in one year. Some of the resignations were due to natural movement, ...
2
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1answer
53 views

Bayesian inference

Assume two demographics $[F,M]$ and each person has a choice of attending only one of four different lectures $[A,B,C,D]$ all occurring at the same time so they can only attend one. The following ...
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57 views

Conjugate prior equivalent prior sample size with respect to the mean

In Cowles's book ([Applied Bayesian Statistics - With R and OpenBUGS Examples–(http://www.springer.com/statistics/statistical+theory+and+methods/book/978-1-4614-5695-7)), page 108, there is a ...
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1answer
45 views

winbugs multiple definition of node [duplicate]

I wrote this code in WinBUGS but I cant run it! It says 'multiple definitions of node tau' ...