# Tagged Questions

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 ...

31 views

### Calculate probability using Naive Bayes Classification

I'm having problem calculating the probability using Naive Bayes approach Problem First I calculate \begin{align} P(\text{No})P(\text{Sunny}|\text{No})P(\text{Cool}|\text{No})P(\text{High}|\text{...
13 views

### Likelihood of an autoregressive model

I have the following autoregressive model: $Y_I=\lambda_t + \alpha_t(Y_t-\lambda_{t-1}) + \epsilon_t$ where $\lambda_t=\beta_1+\beta_2cos(\pi t/6)+\beta_3sin(\pi t/6)$ and $\epsilon$ has a ...
27 views

### Finding likelihood for an event using Bayesian Inference

A spacecraft carrying two female and three male astronauts makes a trip toMars. The plan calls for a two-person detachable capsule to land at site A on the planet and a second one-person capsule to ...
60 views

### Finding probability of a sample using Bayesian Inference [closed]

In a particular water sample, ten bacteria are found, of which three are of type A. What is the probability of obtaining six type A bacteria, in a second independent water sample containing 12 ...
12 views

### Convergence t-student distribution a posteriori

Good afternoon. I want to show that when n goes to infinity, the predictive distribution converges to distribution of $x_{n+1}$. To do this, I need to know the density limit of $x_{n+1}$. So I'm ...
33 views

12 views

30 views

I read a paper that assumes a prior distribution on the Fourier components of a 3D model--specifically that the components are independent and normally distributed: $$p(\Theta) = \prod_{l=1}^L \frac{... 0answers 14 views ### What is a parameter in Bayesian analysis? In any case study, when we use Bayesian analysis to solve our problem we consider a model parameter which is sometimes known and sometimes unknown. And using this parameter(and of course prior data) ... 3answers 30 views ### What is the probability a piece of clothing was made by person 1 if it is defective Person 1,2 and 3 produce the following proportions of clothes: Person 1: 10% Person 2: 30% Person 3: 60% The probability they make clothes that are defective are: Persion 1: 4% Person 2: 3% ... 0answers 24 views ### I(X,Y,Z) and I(X\bigcup Y,Z,W) \ge I(X,Y,W) I am trying to prove if I(X,Y,Z) and I(X\bigcup Y,Z,W)=> I(X,Y,W). I know that I(X,Y|Z)=I(Y,X|Z) and I(X,W|Z\bigcup Y) and I(X,Y|Z) \Rightarrow I(X,Y\bigcup W|Z), unable to use the above ... 0answers 18 views ### How to find convergence with a learning rule that depends on the outcome of a game? my first post here and really excited about the community. In a game theory set in which agents choose from a finite set of actions with a probability distribution, how can I look for convergence ... 1answer 33 views ### Bayesian Expected loss integral Thanks. I don't understand how to calculate the integral for a Bayesian Expected Loss. The problem is from Berger 1985 Stat Decision Theory and Bayesian Analysis page 8. Example 1. Assume no data is ... 0answers 9 views ### How to incorporate p-values into Bayesian classification? I'm interested in using data from multiple studies to assess cancer risk in a patient. Each study has different p-values for the confidence of their result. When assessing an individual's cancer ... 1answer 32 views ### Elementary book for Bayesian statistics I need to study the applications of Bayesian statistics in environmental sciences. For that I need a good book which can explain concepts from basics. I do have sufficient knowledge in probability but ... 0answers 19 views ### Why can prior be swamped? (given a data set, any prior will go to the same posterior) [closed] Is there any mathematical proof for that? 0answers 14 views ### How can I properly define G_0 in Chinese Restaurant Processes clustering? I would like to implement a generative model for clusters as defined in section 2.2 of 1. Assuming I already have the procedure for assigning tables, I would like to now assign each "table" with a ... 1answer 53 views ### Predictive Distribution with Normal Prior Given \Theta = \theta, let X_1, X_2, \dots, X_n, X_{n+1} \sim \mathcal{N}(\theta, \sigma^2) be independent. \Theta \sim \mathcal{N}(\theta_0, \tau^2). What is the easiest way to find the ... 1answer 33 views ### How to derive mean and variance for a Bayes estimator? Let X_1,...,X_n \sim iid \mathcal{N}\left(\theta , \sigma ^2\right), where the variance is known. Also, suppose the prior distribution \theta \sim \mathcal{N}\left(\theta_0,\frac{\sigma^2}{\... 2answers 22 views ### Survival bias and probability Imagine the following situation: A new virus is discovered that is believed to have infected 20% of the population. Anyone infected with the virus has a chance of 50% of dying in their sleep every ... 1answer 51 views ### An explanation of how this solution is derived I am having difficulty understanding the solution to this problem. Since the solution is in the form of Bayes theorem I expected something along the lines that looked similar to Bayes theorem. ... 1answer 34 views ### Determine how likely it is that a set of boolean data is produced by a distribution Suppose we have a collection of independent Boolean random variables X_i and Y_i (for 1 \le i \le N), and are told p_i = P(X_i = 1) for all i. We are now given a set of values x_i that was ... 0answers 30 views ### Nando de Freitas' Machine Learning Homework 2 Questions 1 & 2 Solutions I've been following Nando de Freitas' Machine Learning course from UBC. While I have been enjoying the course I thought it would be good to see if I could do the homework along with it. So I'm on ... 2answers 56 views ### A priori probability in Bayesian inference problem The problem A psychic uses a five-card deck to demonstrate ESP, claiming to be able to guess a card correctly with 0.5 probability (of course, ordinary guessing is 0.2). A single experiment ... 1answer 275 views ### Hillary Clinton's Iowa Caucus Coin Toss Wins and Bayesian Inference In yesterday's Iowa Caucus, Hillary Clinton beat Bernie Sanders in six out of six tied counties by a coin-toss*. I believe we would have heard the uproar about it by now if this was somehow rigged in ... 1answer 12 views ### Prior that incentives dissimilarity of 2 parameters I have some binary data. I have a proposed partition of this data into partitions 1 and 2. I want to test whether the data in models 1 and 2 were generated by two Bernoullis such that their ... 1answer 32 views ### Bernoulli Naive Bayes Classification I am having trouble understanding the following text regarding Bernoulli Naive Bayes. Specifically, the author mentions that i is a feature. However, what is the difference between x_i and i? 0answers 28 views ### Bayesian estimation of x_m for Pareto distribution The Pareto distribution has pdf$$f\left(x\right)=\alpha x_m^\alpha x^{-\alpha-1}$$for x\geq x_m with \alpha,\,x_m positive parameters. I've been researching maximum-likelihood and Bayesian ... 1answer 49 views ### How to solve conditional probability problem using bayesian algorithm I am trying to solve An agent learning to categorise news articles in two topics, World (W) and Finance (F). Out of 100 articles, 40 were classified as W, and 20 of the articles were ... 0answers 15 views ### How to sort list with Bayesian inference? I have long list of Instagram accounts with the following data: number of followers of the account (N); number of users, who follows both this and mine accounts (n). I would like to get list of ... 1answer 37 views ### Conditional Probability with two subsets Question: A man plans to ship six boxes. Two of the boxes are insured, while the other four aren't. Each package that is shipped has a 10% chance of being damaged. What is the probability that: ... 0answers 33 views ### P(A=0, B=0) is what given the following graph? Graph and Probabilities Given this graph and respective probabilities, what would be the value for P(A=0, B=0)? I computed P(A=0, B=0)=P(A=0)P(B=0)=0.24 because A & B are independent of D. ... 0answers 17 views ### How to find the conjugate prior of a probability distribution? I am looking for a procedure for finding the conjugate prior, given a probability distribution. I am more interested in the exponential family of distributions of the form$$ F(x|\theta) = A[x]exp(B[...
I'm reading the book Causality - Models, Reasoning and Inference (Second edition). On page 11 the Decomposition property uses the notation $YW$, which is not defined before. What does $YW$ mean, ...