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

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Can quadratic constraints be handled by Bayesian methods?

I want to solve a regression method whose parameters are under quadratic constraint a'*a=1. Is there any method in Bayesian statistics to handle this constraint? Thank you in advance.
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compute Expectation Propagation messages for sum

Can anyone help me in understanding how Expectation Propagation updates are computed when we have a function on several variables? Like this example: ...
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54 views

How to write up and report a Bayesian analysis?

Bayesian Estimation Supersedes the t-Test for John K. Kruschke is one of the most important papers that I had read explaining how to run the Bayesian analysis and how to make the plots. But the ...
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22 views

Systematic change of proposal density of metropolis algorithm - still a markov chain?

The problem is that I have a Gibbs-Sampler where one of the parameters has to be sampled via a Metropolis-Step from the respective FCD. I have problems finding a suitable scale for the Gaussian ...
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35 views

why we need trace plot in MCMC

i am reading papers and i see most of the papers gave trace plots.why we need trace plots in Monte Carlo Markov Chain. what the trace plot of the parameters indicates ?i understand MCMC but i dont ...
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14 views

what is the difference between RJMCMC and Birth and Death Process?

what is the difference between RJMCMC and Birth and Death Process ? how both works for model selection ? Can we use RJMCMC for non-nested Model ? i read the paper of Green, but i am not clear about ...
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12 views

Bayesian calculation of parameter multiplying normal

I am interested in a model like: $y_{i} = \sum_{k\in K}{\beta_{k} z_{k}}$, with $z_{k} \tilde{} N(\mu_{k}, \sigma_{k})$. where $\beta \equiv(\beta_{k})_{k\in K}$ is not known, but all else is. I ...
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15 views

Pymc: Does this model call for Index, and if so, how would I use it?

I'm working on speeding up the mcmc for a hierarchical pymc model that is taking .2 seconds per iteration. It's the second model from this paper, modeling a soccer league using team-specific attack ...
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388 views

Why should we use t errors instead of normal errors?

In this blog post by Andrew Gelman, there is the following passage: The Bayesian models of 50 years ago seem hopelessly simple (except, of course, for simple problems), and I expect the Bayesian ...
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25 views

Bayesian Network

I am preparing for midterm exam and need to know what is the step by step solution to this question? Answer is shown in red. Also any external related link is very much appreciated.
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77 views

Bayesian Data Analysis [closed]

I started recently studying the Bayesian Data Analysis. I installed R studio, BEST and JAGS. I ran this analysis on two groups of means (...
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Which naive Bayes?

I am attempting to use a naïve Bayes classifier in python (using scikit-learn), with two examples. The first example has 6 classes and 2 hypotheses, the 2nd example has 2 classes and 6 hypotheses. ...
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Bayesian Data Analysis, 3rd edition: Problem 8.8

I'm self studying with the 3rd edition of Bayesian Data Analysis by Gelman et. al. Currently reading through Chapter 8 and trying out some of the problems. Question 8.8 has me baffled on how to solve ...
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23 views

Combining Posterior Distributions of Separate Models

I am running Bayesian models to estimate the number of fruits on a plant, given the presence/absence of herbivores. I get a posterior distribution on each mean. I then run a separate model to estimate ...
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1answer
27 views

What is the commonly used conjugate distribution for this type of problem

I have in mind a Bayesian Learning model . The idea of the model is described as the following. The probability of an event (A) happening is ...
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1answer
26 views

How to specify a hierarchical bayesian model with sum-to-zero constraints?

I'm working on the first model described in this paper ("Bayesian hierarchical model for the prediction of football [soccer] results"). The gist of the model is: The model includes two sum-to-zero ...
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2answers
117 views

What makes a GLM Hierarchical?

Wikipedia defines a Hierarchical GLM as: Hierarchical linear models (or multilevel regression) organizes the data into a hierarchy of regressions, for example where A is regressed on B, and B ...
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2answers
90 views

2-Gaussian mixture model inference with MCMC and PyMC

The problem I want fit the model parameters of a simple 2-Gaussian mixture population. Given all the hype around Bayesian methods I want to understand if for this problem Bayesian inference is a ...
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122 views

How to apply Bayes' theorem to the search for a fisherman lost at sea

The article The Odds, Continually Updated mentions the story of a Long Island fisherman who literally owes his life to Bayesian Statistics. Here's the short version: There are two fishermen on a ...
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Estimating correlation hyperparameters of a Gaussian Process

I have an actual function that I need to simulate using a GP model. I've not done this before so I'm unclear of the steps. I have used the true function at different values of the inputs ($\vec X1, ...
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42 views

Correct numerical result in Bayesian model comparison

I was wondering how to calculate the following Bayesian model comparison. Suppose you have a couple of models: $$M_{1}: x \sim Bin(n, \pi); p \sim Be(1,1)$$ $$M_{2}: x \sim Bin(n, \pi); p \sim ...
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32 views

Calculation of the expectation of a posterior distribution using numerical integration methods

I want to calculate the expectation of the following posterior distribution: $$E( \theta \mid {\bf u} ) = \int\limits_{ - \infty }^\infty \theta \cdot g(\theta \mid {\bf u} )\,d\theta $$ and if ...
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1answer
56 views

How to interpret autocorrelation plot in MCMC

I am getting familiar with Bayesian statistics by reading the book Doing Bayesian Data Analysis, by John K. Kruschke also known as the "puppy book". In chapter 9, hierarchical models are introduced ...
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24 views

Recursive Bayesian Estimation, $p(C_k|\mathbf{x})$ as (discrete) likelihood

I''ve been struggeling with this problem for the last couple of days. The main goal is to use the probabilistic classification output $p(C_k|\mathbf{x})$, from for example a logistic regression, to ...
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25 views

Turning categorized output into continuous

I'm using a NaiveBayes algorithm that generates categorized probabilities as output instead of continuous values, which is what I need for this webapp I'm working on. Unfortunately I can't switch ...
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Growing number of Gaussians in a mixture

Let I have a Gaussian mixture consisting of $n$ Gaussians that is already fitted (e.g. using EM algorithm) with respect to a given data set. Now I want to add one more Gaussian to make the mixture ...
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How to simulate a prior for a Poisson distribution? [closed]

I would like to simulate random variates from a Poisson distribution to act as prior for a predictive model, but I fail to do it correctly. Here is my attempt: ...
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prior predictive distribution negative binomial in R

I have a prior distribution Gamma(1.71,1.05) from a Poisson(2.2), and I know that the prior predictive distribution will be a Negative-Binomial of Gamma parameters i.e. Neg-bin(1.71,1.05). I would ...
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to find the values of gamma distribution knowing the parameter value of a poisson

I have a variable X, and information available to me is that the parameter $\theta$ is around 2.2 $X\sim \mathbf{Poisson}(\theta)$ How can I determinate the value of the parameters $\alpha$ and ...
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About Bayesian formula and rating system

I'm building a scoring system with score from 0 to 5) and I would like to sort products according to the number of reviews and their scores. After some research on the Internet I have found two ...
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16 views

Popularity Index

I'm constructing a website related to food consumption behaviour of travellers. For example, when a group of people, say 5000, is travelling from New York to Tokyo, some of them has sushi, some has ...
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Is my OpenBUGS / WinBUGS model well specified?

I've just started trying to use OpenBUGS for Bayesian analysis of stochastic volatility models. In particular, I'm trying to calculate stochastic covariance, similar to the DC-MSV model specified by ...
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1answer
54 views

Can someone explain to me the Bayesian classification model?

I often read about converting from a normal classification model like logistic regression and then using an equivalent Bayesian model. As I understood, it's somehow the same model but with a different ...
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Values for the parameters of a Gamma in a Gamma-Poisson distribution

I need values for the parameters $ \alpha,\beta$ of a Gamma distribution that represent the parameter $\theta$ in a Poisson distribution,so its expected value. I'm using these distribution to ...
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Recursively updating the parameter of a Beta function in a bayesian way?

I ask, because it is very hard to find information regarding the beta distribution and the bayesian inference, where the beta distri is NOT the prior. My goal is to identify or to improve the two ...
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adaptive surveying for a maximal income that depends on a parameter

I have a product that I would like to price for the highest income. The income $I$ from this product will depend on the asking price $c$: $$ I(c) = N \cdot E(c)$$ where $E(c)$ is the expected ...
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1answer
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A non-i.i.d observations in a Bayesian inference problem

Suppose we have a simple Bayesian network which has two variables $x$ and $y$, $x$ is the parent of $y$. We sample $M$ $x$s independently based on $P(x)$, named $x_1,\ldots,x_M$, and for every $x_i$, ...
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Picking noninformative priors using pivotal quantities

In 'Bayesian Data Analysis' (Gelman, Carlin, Stern and Rubin) on page 64 it reads: "If the density of $y$ is such that $p(y-\theta|\theta)$ is a function that is free of $\theta$ and $y$, say $f(u)$ ...
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1answer
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Is there an article/book reviewing different methods for constructing posterior point/interval estimates?

Given a one-dimensional posterior distribution it is often the case that you want to calculate a point estimate and a credible interval for the corresponding parameter. There are, of course, many ways ...
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Selecting priors based on measurement error

How do you calculate the appropriate prior if you have the measurement error of an instrument? This paragraph is from Cressie's book "Statistics for Spatio-Temporal Data": It is often the case ...
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32 views

Using interaction terms in an MCMCglmm

I am using MCMCglmm models in R, with hierarchically nested data. The basic structure of the data is as follows - each dyad is a unique combination of focal/other: ...
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22 views

How do I define the number of parameters needed to specify this Bayesian network?

If it is known that Bayesian network has one root node, one node with a single parent, two nodes with two parents and the remaining nodes with 3 parents, indicate how many parameters would be required ...
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168 views

Implementation of hierarchical bayesian model produces errors with PyMC

I'm trying to solve an exercise from this book in which I'm supposed to fit data on temperature and elevation in Colorado to this model: \begin{equation} \boldsymbol{Y} = \boldsymbol{\mu} + ...
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31 views

Rstan model for a simple mixture of normals

This blog post from Rbloggers describes how to code a simple three-part normal mixture model with known mixing coefficients, means and standard deviations. While it describes the procedures in some ...
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1answer
44 views

R Bayesian prediction of a Gaussian process

I have a Gaussian model with mean zero, variance is arbitrary constant, and correlation function $e^{-\theta(x-x')^2}$ where $\theta$ is again an arbitrary constant. I've plotted some realizations of ...
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How to use Bayesian statistics to estimate mean and a covariance matrix given structured observations

I have a real-world problem in which the observations are linear combinations of elements in a vector $\bf{c}$. However, there exist correlation between different element in $\bf{c}$. For example ...
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1answer
36 views

Bayesian models vs Bayesian network models

I'm new to statistical modeling and working on applications in spatial property prediction. Can you help me understand the difference between a hierarchical bayesian model and a bayesian network ...
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38 views

Informative prior for a binomial proportion close to one (or zero)

I want to do inference on a binomial proportion, which I have reason to believe a priori is close to one. Let's say my prior expectation is 0.98. I'd like to do incremental updating of my beliefs as ...
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Posterior autocorrelation in Pymc. How to interpret it?

I started learning Bayesian inference by reading "Probabilistic Programming and Bayesian Methods for Hackers". I found something that is not really clear for me in the third chapter. Lets look at the ...
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Hypergeometric: how do I construct a credibility interval around K (population successes) in R?

I have a problem for which I believe I should use the hypergeometric distribution, but I can't figure out how to do it in R. Say I have a bag of marbles with known number ($N$) of marbles, but the ...