# Tagged Questions

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

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### Defining low frequency and substantial frequency events [on hold]

I have some frequency data and I would like some objective definitions for "substantial" and "rare" or "low frequency" events. For example, if Event A happens less than 5 percent of the time, could I ...
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### Think Bayes Book - The M&M Problem - How is Normalizing constant calculated?

In his book this problem is given for M&M's as an example of Bayes. The M&M problem M&M’s are small candy-coated chocolates that come in a variety of colors. Mars, Inc., which makes ...
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### In Bayesian networks does hard evidence make P(evidence) = 1?

I've been attempting to understand how Bayesian networks work when evidence is applied to them, and in the book I'm currently reading, there are what appear to be contradictory statements, and I don't ...
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### Applying Bayes rule

This is probably almost standard textbook Bayes rule, but I wanted to double check a formula that I am applying: $P(A | B,C) = P(A|C) \cdot \frac{P(B|A,C)}{P(B|C)}$. Is this correct?
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I want to do Metropolis Hastings sampling of a tree structure $\mathcal{T}$ (in the space where the tree size is fixed) from a posterior distribution: $p(\mathcal{T}|X) \propto p(X|\mathcal{T})p(\... 0answers 4 views ### Conditional Probability Example Problem [duplicate] This is a question that came up on Udacity's "Intro to Statistics" course, and I'm having trouble interpreting the problem. This is a classical Bayes problem where we're looking at probabilities of ... 1answer 32 views ### Bayesian networks and weird probabilities I have to solve the following problem: Suppose we have a bayesian net in which we have the following variables: R, PA and PR Let: P(R) = 0.1, P(PA) = 0.5, P(PR|R, PA) = 0.6, P(PR|¬R, PA) = 0.4, P(... 2answers 55 views ### Transition probabilities - Markov chains I have a homogeneous Markov chain with transition matrix I want to compute$P(Y_1 = 1| Y_2=2)$where$Y_t, t=1,2$is the observation at time$t$and$Y_0=3$. I tried with Bayes' rule, so $$P(Y_1 = ... 0answers 59 views ### Think Bayes - Chapter 7 Exercice 7.4 I'm reading this book by Allen B. Downey and trying to do the exercises http://greenteapress.com/wp/think-bayes/ I am a bit stuck at this one, 7.4. I tried looking for blogs and stuff like that where ... 2answers 78 views ### Question involving Bayes' Theorem and Law of Total Probability Usually I know how to do these problems, but this one stumped me. This is what the problem says: "Let D denote the event that a person selected randomly from a population has a disease, and suppose ... 1answer 20 views ### Bayes Rule for Random Samples? Suppose I have M samples from unknown distributions F(X) and F(Z|X). Is there a way from these two vectors to get samples of F(X|Z)? I understand Bayes rule, but I only know how to apply it ... 2answers 159 views ### Intuition of Bayesian normalizing constant In the commonly mentioned mammography screening problem with a screening likelihood of 80%, a prior of 10% and a false positive rate of 50%, or its variants, it is easy to explain that the conditional ... 3answers 270 views ### Monty hall problem, getting different probabilities using different formulas? In my Monty hall problem, I am computing what is the probability that P(H=1|D=3) i.e. price is behind door 1 and the 3rd door is opened. P(H=1|D=3) = p(H=1) * \frac{p(D=3|H=1)} {p(D=3)} = 1/3 * 1/... 1answer 52 views ### Hidden Markov Model and Naive Bayes similarity I understand Naive Bayes classifier and already have made a few implementaions. What i dont understand is, considering that i have a train set with all the X observations and Y states, what stops me ... 1answer 130 views ### allocating degree belief to forecast value We have a number of providers for a forecast of wind power generation per country per date. Values are forecast up to one week ahead. Forecasts may be compared with actual values of reported wind ... 0answers 40 views ### Bayesian Approach To Combine Multiple Weighted Inputs I'm beginning to learn about Bayesian theory but I'm stumped on the ideal approach for combining multiple weighted inputs. Here's an example to make this more concrete. Let's say that I want to ... 0answers 18 views ### Marginalizing versus optimizing the nuisance and hyper parameters In a Bayesian setting, the classical approach when studying a given variable of interest (here \theta_0) consists of marginalizing the full posterior over nuisance and hyper parameters (here \... 2answers 59 views ### What am I doing wrong in this Baye's theorem equation I have to find the probability that that a woman does not have cancer, given that her mammogram came back positive. Facts needed: 0.1% of all women have breast cancer probability of a positive ... 0answers 21 views ### 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 ... 0answers 8 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 ... 1answer 42 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) + P(W|S,\bar{R}... 1answer 33 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 ... 0answers 45 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 ... 1answer 54 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 \... 0answers 56 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 ... 1answer 23 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 ... 0answers 31 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. ... 0answers 17 views ### 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 ... 1answer 19 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 ~\eta(... 1answer 45 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$$I know all the conditional ... 1answer 33 views ### Bayes theorem with unknown model I have a book on applied statistics that uses a result I don't understand. The example in the book begins with Bayes' theorem applied to hypothesis H and data D:$$P(H|D) = \frac{P(D|H) P(H)}{P(D|... 1answer 123 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 ... 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} ...
I'm trying to fit a linear model to describe student performance in 2 different schools. My response variable is $$Yij= X{ij}*\beta+Z_{ij}*\gamma_j + \epsilon_{ij}$$ . $$i = 1,...,n$$ $$j = 1,2$$...