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Questions tagged [bayesian]

Bayesian inference is a method of statistical inference that relies on treating the model parameters as random variables and applying Bayes' theorem to deduce subjective probability statements about the parameters or hypotheses, conditional on the observed dataset.

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Bayesian inference on mean of statistic from population

Suppose that a collection of time intervals $t_i$ have occurred, for $i=1,...,n$. These should be considered as samples from a population governed by some distribution. During these time intervals, ...
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295 views

Coin flip experiment with biased coins (and analogy to real-life problem)

In order to determine if a coin is fair by an experiment I flipped it 20 times and received 7 heads. Since the cumulative probability to have 7 or less heads is 13% with a binomial distribution I ...
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Hierachical Bayesian Linear Regression using PyMC3 is super slow [migrated]

I am trying to write some code for implementing HBM in the case of logistic regression using the adults dataset from the UCI repository. I have already written the code, but sampling is super slow, ...
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Bayesian estimation of weighted proportion

Having bayesian estimates of a proportion is relatively easy. You model that proportion as a binomial variable, you choose a beta-binomial prior and by using the likelihood you obtain a beta-binomial ...
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Regression when dependent and independent variables come from different datasets

I am trying to figure our the most robust way to combine two different sets and run a regression. The first dataset gives me an outcome value for each of several categorical treatment variables, each ...
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19 views

meaning of posterior distribution and credible internal

In Bayesian method, we can get a posterior distribution of a parameter. Now I want to do some simulation to know if the posterior distribution is the same as the true distribution. For example, mean ...
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14 views

Heuristic vs Bayesian [on hold]

I'm aware Heuristics and Bayesian methods are two separate things, but I'm attempting to choose between them for a task. As input, I take a sentence of fixed words (so all the words are in a small ...
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30 views

Normal-Gamma: Metropolis-Hastings on log-scale, but no Jacobian?

I am reading the paper by Griffin and Brown (2010) where at one step in their MCMC procedure they need to sample from the following conditional posterior: $$ p(\lambda|\gamma, \Psi)\propto \pi(\...
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Rigorous Bayesian Model Selection

I am learning Bayesian Model Selection. I want to understand the rigorous mathematics behind the idea of encompassing model. To be more specific, suppose we want to compare M models: Model $\mathcal{...
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Bayesian batting average prior

I wanted to ask a question inspired by an excellent answer to the query about the intuition for the beta distribution. I wanted to get a better understanding of the derivation for the prior ...
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1answer
177 views

Specifying correlations among random effects in brms package in R

For this example, I am using the data "appendix_example1_wide.SUPP.FINAL.csv" posted here. In the paper, the authors use the to MCMCglmm package fit a multivariate multilevel model. Of particular ...
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1answer
305 views

The Bayes credible interval / Bayes credible region of the posterior distribution of a multinomial Dirichlet conjugate pairs

I have a posterior distribution of Dirichlet form with new parameters (alpha1, x1), (alpha 2, x2) and (alpha 3, x3) and the posterior mode of each dependent variable as the Bayes estimator. I wish to ...
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Randomization testing in Bayesian spatial scan statistics

I was reading about Bayesian Spatial Scan statistics paper. I have this confusion about why randomization testing is not necessary in this approach. The paper says that it is by construction. But, I ...
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Treating Word Embeddings as Samples From Random Variables

Suppose I want to specify some probabilistic clustering model (such as a mixture model or lda) over words, and instead of using the traditional method of representing words as an indicator vector $z$, ...
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In the fully supervised case, provided we have contingency matrices, is Bayesian inference the optimal method?

BACKGROUND Imagine that we have contingency matrices, i.e., counts or frequencies, linking the features (say, columns) and targets (rows). One could then compute the posterior probabilities, i.e., ...
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1answer
58 views

Bayesian A/B testing with parameters other than success rate

If I have certain number of clicks and conversions for a group of ads, I can do Bayesian A/B testing following this method http://ucanalytics.com/blogs/bayesian-statistics-to-improve-ab-testing-...
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54 views

Another round of some simple Bayesian probability questions

Following questions like this one, I have some very simple probability questions for which I guess that Bayes theorem is the tool to answer. I think that Bayes theorem is the tool because each ...
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38 views

Time series forecast with probability

I have historical data for a particular metric for each month for the last 3 years for different categories. The metric is a percentage and its heavily skewed towards 1 with more than 75% of values ...
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19 views

The posterior distribution of Bt is Bernoulli

I'm trying to follow the math of Estimating Heston's and Bates’ models parameters using Markov chain Monte Carlo simulation in Journal of Statistical Computation and Simulation, but I'm having trouble ...
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14 views

Estimating state covariance with the Unscented Transform and diffuse prior

I have a set of measurements (assume additive Gaussian noise on each), a non-linear measurement model, and a diffuse prior. The state covariance estimate: $P = (H^T R^{-1} H)^{-1}$ where $H$ is the ...
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1answer
45 views

Value of using a better normal distribution

I tried to derive this on my own, but my stats education proved too far back… (This is a problem in Bayesian decision theory – if that makes you uncomfortable, feel free to reformulate it) Let's say ...
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'Randomizing' Gradient method for the proposal of Metro-Hastings step

In my problem, I've used a gradient method for the mean of the proposal. Let my proposal be $q(\mu_n,\Sigma)$, where $\mu_n = \mu_{n-1}+s\frac{\partial}{\partial \theta}\log(f(y,\theta))$ and $s$ is ...
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Determining the optimal number of clusters using plots of Bayesian Information Criterion

I am having trouble interpreting the results from an Expectation Maximization clustering using mclust and the Iris flower data, Using R. Reproducible example If ...
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55 views

Binary logistic regression with brms

I've run a binary logistic regression in R, using brms. I have one independent variable (Age) and 3 dependent variables, Y1, Y2, and Y3. These dependent variables are all pass/fail tasks. For each ...
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1answer
283 views

Why classifiers report the class with maximum posterior probability as the predicted class?

When we train a classifier to predict $y \in \{1, \dots, K\}$ given an input $x$, classification is done by reporting the class with the highest posterior probability as the prediction; that is: $$ \...
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How to choose the parameters of a prior distribution based on a range for the variance?

How can I use R to calculate the parameters of a prior distribution if I want the variance to fall within a specific range? For instance, I have a variable that follows the inverse gamma distribution ...
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Uniform prior 3 sided dice marginal probability [closed]

Given a 3 sided dice with a uniform prior what is the probability of observing ordered data $D = \{n_1, n_2, n_3\}$ where $n_1$ is the number of observed 1s? For example rolls $1,2,3,1$ have $D = \{2, ...
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Uniform prior 3 sided dice marginal probability equation [duplicate]

Given a 3 sided dice with a uniform prior. What is the probability of observing ordered data $D = \{n_1, n_2, n_3\}$. Where $n_1$ is the number of observed 1s. Denoting the bias on the dice by $\...
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1answer
267 views

Determining conserved features using a Bayesian approach

I would like to perform some sort of binary classification, and my data set consists of 100 examples (for each class), which are vectors with 2500 elements. Ideally, I would like to determine which ...
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Computing marginal probability and Bayes factor of structural model

I have a Bayesian structural model of the following format: $Y1 = X \alpha +\epsilon$ $Y2 = S \beta + \eta $ $\epsilon = \gamma \eta + \chi $ where Y1 and Y2 are linked by the error terms. I ...
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Bayes factors in R for correlated proportions (such as a “Bayesian McNemar's test”)

Is there any way to get Bayes factors in R for correlated proportions (i.e., paired sample)? For example, the same group of 90 people is measured with one technique, then with another; once there are ...
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1answer
317 views

Obtaining a Bayes Factor for the difference between two proportions (R code provided)

Below (in R code), I'm showing the Bayesian estimation of the Difference between two proportions resulted from two binomially distributed groups (groups) of scores (...
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What is the difference between Naive Bayes & AODE (Average One Dependent Estimator)? [on hold]

I am trying to increase my knowledge about kinds of algorithms and am stuck at this point as I can't find much useful information about AODE.
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Distribution to model Binomial distribution with parameter p in trial n dependent on result from trial n-1?

I'm wondering how one can model a Binomial distribution as described in question. E.g., p = 0.5 for trial n = 0; p(n+1) = p(n) + 0.01 if for trial n Bernoulli(p(n)) samples to 1, else p(n+1) = p(n) - ...
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Why is the bayesian information criterion called that way?

The word "Bayes" suggests that we are updating a distribution using data, to get a posterior distribution. The fact that the Bayesian information criterion (BIC) is used to select a model from a set ...
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1answer
182 views

PyMC3: Mixture Model with Latent Variables

I have a rather basic knowledge of Bayesian inference and I'm somewhat new to MCMC and PyMC3. Can I model data that looks like this? ...
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DIC to compare models with different numbers of parameter?

I am interested in comparing hierarchical Bayesian models based on the same dataset but differing in their spatial and temporal resolution. In short, I am looking at animal population changes over ...
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1answer
362 views

Using Gaussian process regression with non Gaussian data

I have a question about practiacal implementation and interpretation of the Gaussian process regression model given by Rasmussen & Williams (http://www.gaussianprocess.org/gpml). The regression ...
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1answer
19 views

Understanding of conjugation relationship in Bishop book

Referring to Pattern Recognition and Machine Learning by Bishop(Page 367, Section 8.1): Such models have particularly nice properties if we choose the relationship between each parent-child pair in ...
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Approximating 1D integral with Metropolis - Hastings Markov Chain Monte Carlo

I've been asked to approximate the integral of a one dimensional unnormalised posterior with a flat prior, using a Metropolis Hastings Markov Chain Monte Carlo, I realise that this isn't a practical ...
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Bayesian Estimation of a Mean and Standard Deviation (2D)

(Originally Posted at: https://stackoverflow.com/questions/56399700/bayesian-estimation-of-a-mean-and-standard-deviation-2d) I'm currently following Think Bayes, an introductory text to Bayesian ...
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1answer
29 views

Bayesian updating - update probability that measurement is real

I have a sequence of observations, which are either a measurement of 'active' or 'inactive'. These measurements are not necessarily accurate, with false negatives being more unlikely than false ...
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41 views

Gaussian process regression model for comparing two groups

I have a data set consisting of functional observations, where $Y_{mi}$ is the response of the $m^{th}$ functional observation from the $i^{th}$ group, $m=1,...,M$ and $i=1,2,$. The observations are ...
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Is Variational Bayes (VB) and Mean-Field Approximation Useful In practice

I have just had a course in Bayesian Inference, and I am left puzzled about what method should I actually use in practice. Assume I have a multivariate model with multiple parameters $\theta$, where ...
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2answers
373 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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What is the correct way to write the elastic net?

I am confused about the correct way to write the elastic net. After reading some research papers there seems to be three forms 1) $\exp\{-\lambda_1|\beta_k|-\lambda_2\beta_k^2\}$ 2) $\exp\{-\frac{(\...
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Probability of a player being skilled given results observed

Let's say we have a player playing a game. The player is either completely unskilled at the game, or is an expert at the game. We want to find out the probability that the player is an expert given ...
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How do I sample from the posterior distribution with gamma likelihood with unknown alpha and beta?

I realize that this Wikipedia page provides the proportional form of the conjugate prior to the gamma distribution with unknown $\alpha$ and $\beta$ parameters, as well as the posterior values of $p$, ...
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Difference between two dimensions sampled from Dirichlet distribution

Say I'm doing Bayesian inference on a Dirichlet-Multinomial model: $$ x \in [1,2,3]; \\ x \sim Multinomial(p_1, p_2, p_3); \\ p_1, p_2, p_3 \sim Dirichlet(\alpha_1, \alpha_2, \alpha_3); \\ \alpha_n =...
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1answer
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Using a simulation to show sceptics that t-test gives the right answer, and how to do the same for a bayesian inference case

I want to demonstrate to sceptical colleagues and friends that statistical analysis works. And there’s a follow-on question regarding doing the same with bayesian inference. Suppose that I want to ...