Bayesian inference is a method of statistical inference which uses Bayes' theorem to find probability estimates of parameters or hypotheses.

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multiple imputation for categorical data question

How do i design the use of Multiple Imputation based on Bayesian Inference when I am dealing with categorical data and my dataset does not contain complete prior observations at every combination ? ...
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MCMC of a mixture and the label switching problem

I generated some data according to a mixture of two lognormals: $f(x) = p \cdot \mathcal LN(\mu_1, \sigma) + (1-p) \cdot \mathcal LN (\mu_2, \sigma)$. given $p$ and $\sigma$, this is my code to find ...
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Bayesian estimation of $N$ of a binomial distribution

This question is a technical follow-up of this question. I have trouble understanding and replicating the model presented in Raftery (1988): Inference for the binomial $N$ parameter: a hierarchical ...
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Estimating $n$ and $p$ for Binomial distribution, repeated counting of partly hidden population

A brief motivation: $n$ critters live in an aquarium, where sadly they often hide in, under or behind things. When the aquarium is observed, each critter is only seen with probability $p$ ...
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what to chose for prior and proposal function for MCMC of a mixture

I generated some data according to a mixture of two lognormals: $f(x) = p \cdot \mathcal LN(\mu_1, \sigma) + (1-p) \cdot \mathcal LN (\mu_2, \sigma)$ Now I want to use MCMC to find the parameters $p, ...
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How can we combine learnings from multiple experiments in a single causal model?

I would like to use a causal network modelling to model the interaction of several variables and the effects of interventions. I have measurements for all priors of the model, that is without any ...
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bayesian panel vector autoregression bugs / stan code? [on hold]

Does anyone have or know of a nice clean example of panel VAR (vector autoregressive model) code that I can use to help me get started in a bayesian direction? A panel var is for estimating auto / ...
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Posterior distribution of proportional difference of two binomial variables

Can somebody point me in the right direction for a treatment of the following problem? I imagine this should be a fairly common problem in medical statistics... Given two binomial random variables ...
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Fisher information metric for hierarchical Bayesian model is negative-definite?

I'm strungling at the computation of Fisher information matrix for the hierarchical Bayesian model. For simplicity, consider theta following hierarchical Bayesian model: $$X|\sigma \sim ...
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24 views

Posterior predictive checking in Hierarchical logistic model

I'm fitting a Bayesian Hierarchical logistic model with a random intercept, having data at two levels: subjects and hospital, ...
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107 views

Do Bayesians believe in Fixed Effect Models? [duplicate]

Given the Bayesian paradigm, is there actually such a thing as a fixed effects model since Bayesians treat all parameters as random variables?
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Finding the most “uniform” or “least concentrated” density function, subject to moment constraints

Background I want to find a probability measure for a continuous random variable, subject to moment constraints, that is maximally "uniform", as defined below: Definition: Maximally Uniform ...
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SVM versus Bayesian regression example(s)?

I am trying to track down examples where some basic problems have been tackled via both classical Machine Learning algorithms and more formal statistical methods. In particular, I'm interested in ...
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Evaluating the $H_0$ of a contigency table

I have a 2 way contigency table with variables $A=\{a_1,a_2\}$ and $B=\{b_1,b_2\}$. I have the observed cell frequencies $O_1=a_1b_1$, $O_2=a_1b_2$, $O_3=a_2b_1$ and $O_4=a_2b_2$. My null hypothesis ...
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General theoretical properties of empirical Bayes estimates

I was wondering if someone could provide reference (if such exists) for the theoretical properties of empirical Bayes(EB) point estimates, in the sense of what can we say about their risk under ...
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21 views

Estimating parameters and latent variables in a split Poisson distribution using R and JAGS

I am trying to estimate parameters and latent variables in a split Poisson model that describes observable and unobservable counts in time assuming the split probability is $\pi$. An observable event ...
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44 views

Understanding a measure of convergence of MCMC simulations

I am trying to better understand better the Gelman/Rubin measure of convergence of MCMCs. The method starts off by defining two quantities: $B$ and $W$. $B$ is said to be the between chain variance ...
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1answer
68 views

In Bayesian hypothesis testing, do the prior model probabilities have to be equal?

The posterior odds is the product of the Bayes factor and prior odds: $\frac{p(M_1|data)}{p(M_2|data)}=\frac{p(data|M_1)}{p(data|M_2)}\times\frac{p(M_1)}{p(M_2)}$. I was under the impression that ...
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39 views

Bayes' factor vs. Bayes' Discriminant Rule

When we are comparing two models against some data, will we obtain the same (set of) posterior odds for the models both when we use the Bayes' factor and when we use the discriminant rule? If not, ...
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HPD interval for the mean

Suppose we have iid observation with the following model $ Y_t \sim \mathcal{N}(\mu,1/\mu) , t=1,2,..T$ The question is " Assuming a flat prior on $(0 ,\infty )$ find a 95% HPD interval for $\mu"$ ...
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about the definition of bayesian network

In this PDF http://people.csail.mit.edu/yks/documents/classes/mlbook/pdf/chapter2.pdf page 5 says: Given a set of functions $f(x_i,pa(x_i))$ non-negative and sum to 1, we define a joint probability ...
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Bayesian fitting - multiplying two probabilities with differing orders of magnitude

I am fitting a model to data using Bayesian inference. This is my first time of using this method. My posterior is $P = P_{prior} + P_{photometric} + P_{spectroscopic}$. Value of $P$ is negative and ...
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PyMC – Calculate Evidence (Bayes' Theorem denominator)

I have one simple model and one more complex model (both are PDEs that describe displacement, when different kind of forces and thermal effects take place). From those, given some data, I calculate ...
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40 views

multivariate dirichlet for multiple imputation

I dealing with 3 covariates {x1, x2, x3} all three are discrete and contain missing data. ...
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How to update probabilities where datasets and analysis methods differ

Any help would be appreciated, as I'm not sure how to proceed. I have a dataset with binary data and have been able to fit a logistic regression model to it (presence of disease, for example, as a ...
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Bayesian probabilty [migrated]

I need to know how to find the Bayesian probability of two discrete distributions. For example the distributions are given as follows: ...
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127 views

How to compute this conditional probability in Bayesian Networks?

I met a problem related to conditional probability from the article "Bayesian Networks without Tears"(download) on page 3. According to the Figure 2, the author says $$P(fo=yes|lo=true, ...
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Problem with Finding Likelihood: Bayesian

I am really unfamiliar with Bayesian methods particularly parameter estimation. Suppose I have a test to find a parameter, theta which is the number of packaged bag for retail sale that could contain ...
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65 views

Bayes Theorem - Is this Marketing Example Correct?

I'm new to whole concept of Bayes Theorem and its applications to marketing. I've been trying to learn this on my own but unsure if I'm making dumb mistakes or if I'm applying the formula correctly - ...
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Does the parameter change during data generation in Bayesian Inference?

Let's assume that we have the following graphical model: This graph encodes the joint distribution $P(p,x_1,x_2,x_3,x_4) = P(p)\prod_{i=1}^{4}P(x_i|p)$. In the Bayesian inference, if we know ...
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Integrating multiple tests Bayes factors

I have been using an Bayesian-centric R package for some genomics analysis to detect mutations in 3 individuals from the same family. I have to do each analysis for each individual separately due to ...
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Is my interpretation of Bayesian probability and inference correct?

I have the following interpretation of the Bayesian probability and inference (without referring to Measure Theory, I am still at the very beginning of learning it): Let's say we have five random ...
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39 views

Question about the Bayesian Inference of a parameter

In order to understand the difference between the Frequentist and Bayesian inference, I was reading the presentation at: http://www.stat.ufl.edu/archived/casella/Talks/BayesRefresher.pdf . In order to ...
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detect line in geocoordinates

I have repeated samples of geocoordinates of activities in a city. In most of these samples positions will simply be random. In some samples, however, some percentage of the data will be arranged -- ...
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Is there a desription in the literature of a Normal hierarchical model with hyperparameters for both the mean and the standard deviation?

I'm looking for a comprehensive description of and justification for a Normal hierarchical model where both the means of the groups and the standard deviation are modelled. It is common to find ...
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41 views

Normal prior for Binomial likelihood [closed]

Pardon my ignorance, i am new to Bayesian Analysis. I am trying to use Normal prior for a binomial likelihood, which of these are most likely candidates ( $\bar{x} $, $ \mu $, $ \sigma $ ) ...
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80 views

Prior on a non identifiable parameter-MCMC integration

To introduce the problem I will explain the Projected normal distribution. Let $\mathbf{z}_i=(z_{i1},z_{i2})$ be a bivariate vector distributed as a bivariate normal with vector mean ...
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Setting up this generative model for inference: uniform priors

I am trying to set up a generative model where I have two images $x$ and $y$ and it is assumed that $y$ can be generated by applying some unknown transformation to $x$ i.e. $$ y = t(x, w) + e $$ ...
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Zero trick in WinBUGS for truncation

I am using the Zero-trick to create a prior for correlation parameter. Data y is a bi-variate normal with covariance matrix with same diagonal elements and ...
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1answer
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AB testing vs testing the null hypothesis

I'm trying to understand the difference between testing the null hypothesis (i.e. testing that the probability of a "goal" is the same across 2 different populations, similar to prop.test in R) an ...
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Concern with using the DIC to compare Bayesian models

The deviance information criterion (DIC) is a very popular tool for Bayesian model selection, due, in part, to its support by the BUGS platforms. However, there are some remaining limitations as ...
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Sampling methods and parallelization

A couple of years ago I learned about recent work in parallelizing slice sampling methods. More recently, I have read great things about NUTS and Hamiltonian Monte Carlo methods (HMC) in general (e.g. ...
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MCMC algorithm to generate samples

I read that MCMC algorithm is used to draw samples from a distribution. The example mentioned in the text book is about a 6x6 matrix which after 1000 iterations will converge to a steady state 1x6 ...
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1answer
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Is Slice Sampling a special case of Gibbs Sampling?

I read on this thread the following: If you can use both the gibbs sampler and slice sampling to sample from a posterior I would use the Gibbs sampler as the slice sampler seems unnecessary to ...
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Basic Bayesian reasoning question — what is wrong with this “equational” argument?

Let's say that we have a model: $y + x = \epsilon$, $\epsilon \sim N(0, 1)$. After observing a value for $y$, we can write $x$ as: $x = \epsilon - y$ Since $y$ is just a constant, and $\epsilon$ ...
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identifying latent variables in this model

I have been trying to understand EM and I am having a hard time understanding what a latent variable is. In particular, I am having issues in identifying whether in a particular model that I am using, ...
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MAP estimate of posterior parameters

I have a setup where the joint posterior is written as: $$ P(w, \lambda, \phi \vert y) = P(\phi) \times P(w \vert \lambda) \times P(\lambda) \times \prod_{i=1}^{N}P(y_i \vert w_i, \phi, \lambda) $$ ...
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Why is Gamma(0,0) equivalent to the Jeffreys prior

I'm trying to use some code that includes Gamma priors for Poisson (rate) and Exponential (rate) distributions. I want to make the priors noninformative. I read that using a Gamma(0,0) is equivalent ...
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how to set key for deterministic variable in pymc [migrated]

I'm trying to plot the difference between two variables. I'm following the example set here (search for true_p_A and it will be in the right section) Here is my code ...
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Priors for discriminative methods?

Say we want to build a classifier for a binary classification problem using a discriminative method (e.g. SVM) and be able to impose a prior on the classes. For example, let's assume that we want to ...