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

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Best approach for calculating confidence score (p-value) - for Bayes models

This is a generic question on the best approach for giving a p-value to a "most likely" solution given by a graphical Bayes model. I am building a graphical model in Stan, for finding the most likely ...
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5 views

Comparing results from reference coding and orthogonal coding in a linear model?

The problem: I'm trying to fit a zero-inflated negative binomial model to count data (catches of larval fish). I have three factors, and an offset variable, which is the volume of water filtered by ...
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1answer
30 views

How to do calculate both causal and diagnostic inferences simultaneosly in bayesian networks?

Consider a simple Bayesian network as given below. Question: How to find $P(S|C,W)$? It is fairly straight forward to compute the causal inference $ P(W|S) = P(W|S,R)\cdot P(R) + ...
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1answer
29 views

Questions regarding the Bayes Classifier in *Introduction to Statistical Learning*

I am having trouble grokking some very elementary material regarding Bayesian Classification in Introduction to Statistical Learning at the end of pg. 37 to the very top of pg. 39 (i.e., the section ...
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42 views

How to compute probability

I have a dataset consisting of 4000 observation from each 324 continuous features are extracted. Each observation has been labeled a class. Since each feature from that dataset is continuous, have I ...
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1answer
23 views

Calculate Gini coefficient - Python

given a distribution of $\sigma^2$ ($y \sim LogN(\mu, \sigma^2$) I want to calculate the posterior distribution of the Gini coefficient which is given by: $G = 2\Phi(\frac{\sigma}{\sqrt{2}})-1$ ...
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50 views

Kneser Ney smoothing, why the maths allows division by 0?

I'm studying Natural Language Processing and the various smoothing approaches. I'm finding a little hard to understand how to handle unknown words with the Kneser-Ney smoothing. In particular I'm ...
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13 views

Confusion about the concept of Bayesian Networks

I read a lot about Bayesian networks, including focused literature. However, what I have not yet understood properly is this: What is the use case of Bayesian networks that contain of more than 2 ...
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29 views

Calculating likelihood in R

I want to "by hand" calculate a Bayes factor in a simple case. I'm sure I'm off somewhere in my calculation of likelihood of data under H1. I think I don't "scale" my likelihood under H1 correctly. ...
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How to store a large graph? [closed]

When I try to develop a spelling collector, I realize if I can include the word background (etc:before and after word) into the bayes calculation, may be could increase this spelling collector ...
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1answer
17 views

Bayes decision rule and thresholding

The best possible classification is for a set of samples drawn from any probability distribution is given by the Bayes decision rule. For any distribution, the rule is given by $f(x) = 1 ~if ...
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1answer
40 views

Bayesian inference when observed variable contains uncertainty

I have a very simple graphical model to describe the relationship between two categorical variables $c \in \{0,1\}$ and $l \in \{A,B,C\}$: $$c \rightarrow l$$ I know all the conditional ...
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1answer
31 views

Bayes theorem with unknown model

I have a book on applied statistics that uses a result I don't understand. The example in the book begins with Bayes' theorem applied to hypothesis $H$ and data $D$: $$P(H|D) = \frac{P(D|H) ...
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1answer
115 views

Can I make a decision using a Bayes factor?

Bayes factors denote how well a certain model is supported. Say that I am running a controlled experiment and I have two models: the null model and the alternative model. If I have a high Bayes ...
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1answer
23 views

Simple Marginalization Explanation Please

I am having difficulty understanding this marginalization. Let's say you have this relationship $p(a,b,c) = p(a)p(c|a)p(b|c)$ From that you are trying to get $p(a,b)$ $p(a,b) = p(a) \sum\limits_{c} ...
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50 views

Prior Parameters in Bayesian Hierarchical Linear model

I'm trying to fit a linear model to describe student performance in 2 different schools. My response variable is $$Yij= X{ij}*\beta+Z_{ij}*\gamma_j + \epsilon_{ij}$$ . $$i = 1,...,n $$ $$j = 1,2 ...
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1answer
18 views

Problem using continuous bayes theorem on multivariate normal distribution

Given three correlated normally distributed variables $ x$, $ y$ and $z$ such that: $ p\left(\begin{bmatrix} x \\ y\\ z\end{bmatrix}\right) \sim \mathcal{N}\left(\begin{bmatrix} 0 \\ 0\\ ...
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42 views

Bayesian Inference reference to self-study

I need a reference request for bayesian inference for self-study, I'm look for something containing: 1-Fundamentals about prior and posterior distribution, conflict between prior and posterior 2- ...
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54 views

Bayes' theorem problem

Three companies supply same type of products. Company A supplies 30 % more products than company B. Company C supplies the same as A. Fraction of defective products produced by company A is 4 %, by ...
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31 views

How to evaluate probabilistic classification of multi-class problem

I have 3 classes $c = \{A,B,C\}$ and use a bayesian formulation to achieve a probabilistic outcome $p(c \mid x)$ based on some observation $x$. I know there is some bias in there which I haven't ...
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1answer
48 views

Bayes theorem applied correctly on client churn?

Here is a table selected and grouped from table where i store information about client - if he churned(TRUE - he churned, FALSE he stayed) and how many refund he got. CNT counts number of rows per ...
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20 views

JACKMAN: ordered logit model, how do I get proper thresholds?

I'm working on a logistic regression model, using as a reference this Jackman lesson http://jackman.stanford.edu/classes/BASS/ch8.pdf . I implemented his jags function on my data (student scores ...
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Probability of non recurrence given a particular time of non-reccuring

I've been having a cardiac problem that may (or may not) be linked to alcohol consumption. If its happening about once a week on "social use", how long do I have to be completely alcohol free and ...
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1answer
58 views

Can frequentists use Bayes theorem?

I understand that Bayesians interpret probability as belief, which can be updated with evidence. We happen to compute the posterior with Bayes theorem. What is the difference between Bayes Theorem ...
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21 views

Calculating conditional probability through time

Suppose I can obtain non-parameteric estimates of a probability distribution at different horizons, e.g. $\rho(x, \tau)_{t=0}$ is the probability density seen at time $t=0$ for the variable to have ...
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30 views

Posterior from a Poisson likelihood and prior

I have the following Poisson mass function: $$p(y| \theta) = \frac{\theta^y e^{\theta}}{y!} $$ Which has a corresponding likelihood for n independent realizations of y as follows: ...
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47 views

Question on how to apply Bayes Theorem realistically

So I'm new to Bayes Theorem and am trying to understand it. For simplicity I'll refer to the usual example of testing for cancer. ...
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44 views

How Do I choose parameters of prior on regression coefficients in a Bayesian linear model?

I'm trying to perform a linear regression in a Bayesian way. The response is normal,the prior I would like to put over Beta (vector of regression coefficients) and Sigma^2 (variance of the error ...
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24 views

When is BIC reasonable approximation to evidence?

I've recently seen a few papers in physics using the Bayesian information criterion (BIC) to evaluate models. I'm much more familiar with Bayesian evidence, $p(x|M)$. I've read in a few places, e.g. ...
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Classic medical Bayes Theorem question with a twist [duplicate]

Typical statistics question about taking a test to detect a deadly disease and what are the chances that you have the disease given a positive result. Now I ask what happens when you take the test ...
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36 views

What is the Bernoulli class conditional distribution?

What is the Bernoulli class conditional distribution? I am trying to implement a procedure for computing a naive Bayes classifier for binary features with a Bernoulli class conditional distribution. ...
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35 views

Find Bayes rule/action under given prior

I am able to solve for Bayes actions/rules with no data and am able to follow problems with simple data. However, I'm not sure how to solve a question where the data, $X$, is conditional on the state ...
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32 views

How to calculate $P(A)$ given only $P(A|B)$ , $P(A|B')$ and $P(B)$?

Assume $A$ and $B$ are two dependant events with only the following details provided $P(A|B)$, $P(A|\neg B)$ and $P(B)$ How to calculate the value of $P(A)$?
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Calculating elasticities from spatialprobit Bayesian coefficients

I have run a model in R using the spatialprobit package and would like to calculate elasticities with respect to some of my coefficients of interest. I am a bit ...
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39 views

Why is Bayes Classifier the ideal classifier?

It is considered the ideal case in which the probability structure underlying the categories is known perfectly. Why is that with Bayes classifier we achieve the best performance that can be achieved ...
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1answer
40 views

What is the difference between a Naive Bayesian Classifier and Bayesian Linear Regression?

The difference between linear regression and Bayesian regression is that: Linear regression: You are trying to minimize (y-bx)^2 Bayesian regression: You are trying to do similar given a prior on ...
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Assign the direction and sign (+,-) of an arrow using Bayes rule [duplicate]

Being two vertex: A,B and one arrow -> that can be positive or negative, (i.e, it can activate or desactivate). How I can compute the associated probability of each posible combination: A->+B (A ...
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37 views

Buckets of dice - Binomial probabilities of either event occuring

I'm doing a bit of analysis on a dice rolling mechanic for a role playing game. This is a buckets of dice system where the result is based on the count of the number of dice rolling a given target ...
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1answer
28 views

Bayes Rule clarification

On page 12 of this tutorial, it states $$P(\pi \mid \mathbf{L}; \gamma_{\pi1}, \gamma_{\pi0}) = P(\mathbf{L} \mid \pi) P(\pi \mid \gamma_{\pi1}, \gamma_{\pi0})$$ I'm having some trouble seeing why ...
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56 views

Bayesian Hierarchical Clustering with mixed data

I want to perform Bayesian hierarchical clustering in R. I have 4 variables that 3 of them are nominal and 1 is discrete. So my data are mixture of nominal and discrete data. Data are: ...
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1answer
41 views

How to calculate prior probabilities

I have two possible events $A$ and $B$ that could lead to $n$ possible consequences $X_1, X_2, \ldots , X_n$, $P(A) + P(B) = 1$, $P(X_1) + P(X_2) + \ldots + P(X_n) = 1$. I know all conditional ...
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1answer
54 views

MCMC advice: Ignoring some parameters in a MCMC scheme?

I am after some general advice regarding my MCMC scheme, which is causing me some grief. Essentially, I have a large (2N + 9 parameters) MCMC scheme which works great. However, the problem is that ...
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For each x, I observe A and know P(C). What can I say about E(A|C)?

For each subject x in a population, I observe x's age, A(x). I can calculate the probability that x has some property of interest c, $P[C(x) = 1]$, where C(x) is a binary variable indicating ...
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1answer
611 views

Bayes Theorem with multiple conditions

I don't understand how this equation was derived. $P(I|M_{1}\cap M_{2}) \leq \frac{P(I)}{P(I')}\cdot \frac{P(M_{1}|I)P(M_{2}|I)}{P(M_{1}|I')P(M_{2}|I')}$ This equation was from the paper "Trial by ...
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2answers
51 views

Strange election results and probability of election fraud

Suppose an election is held for the leadership position in a major political party. Four candidates are running. After the election, the following results are announced: ...
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30 views

Making inferences from Bayes networks and CPTs

So I'm practicing working with Bayes Networks and conditional probability tables and I feel like some of my numbers simply don't make sense. Here's the situation: I have a bag of three different ...
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84 views

Practical Bayes Theorem - how to use it?

I am testing a variant of LDA (Latent Dirichlet Allocation) algorithm on some text data. Given some documents $d$ where each document is expressed as a distribution over words $w$, the algorithm ...
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5answers
209 views

Interpretation of Bayes Theorem applied to positive mammography results

I'm trying to wrap my head around the result of Bayes Theorem applied to the classic mammogram example, with the twist of the mammogram being perfect. That is, Incidence of cancer: $.01$ ...
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2answers
82 views

Different Confidence vs. Credible Interval (Continuous case, noninformative prior) [duplicate]

Okay, so, credible intervals aren't the same as confidence intervals. We all know that. In fact, they're only guaranteed to be the same when they're about a location or a scale parametre with a ...
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Inferring intermediate probabilities in a real-time system if the ending distribution is known?

For example, Let's say I have a bar of 4 LED lights that light sequentially, as below: [1] [2] [3] [4] Meaning that if [3] is lit, both [1] and [2] are also lit, etc. During some period of time - ...