**4.502 bayesian questions.**

I am wondering if it is possible to re-calculate the normalizing constant of the posterior distribution for example the following
$$\pi(\theta|\boldsymbol{Y}) = \frac{L(\boldsymbol{Y}|\theta)\pi(\...

I'm using MCMC to simulation the distribution of some parameters in a Bayesian hierarchical model, which has the following form:
$$\gamma_{ik} \sim Ber(\omega_{ik}).$$
Then I make a logit-...

I'm trying to fit this simple varying intercept model with brms:
Weight ~ Height + (1|Gender)
However sampling is slow (>10mins), effective sample size is low, autocorrelation is large. Although the ...

I'm taking an Intro to Bayes course and I'm having some difficulty understanding predictive distributions. I understand why they are useful and I'm familiar with the definition, but there are some ...

I am trying to implement Gaussian Mixture model with stochastic variational inference, following this paper.
This is the pgm of Gaussian Mixture.
According to the paper, the full algorithm of ...

all. I am asking this question in not necessarily a "subjectively recommend something for me" approach, but with a clear focus on just an accessible beginner's reference. My situation is I have been ...

I am doing a Bayesian updating for housing construction defects. But the observed data is very limited and incomplete.
My model is beta binomial. beta (a1, a2) is my prior for defect rate for roof ...

One merit of hierarchical Bayesian modeling is to incorporate random coefficients relatively easily (i.e., in panel data, the regression coefficients can be individual specific).
However, when I ...

I am curious for myself, but also trying to explain this to others.
The beta distribution is often used as a Bayesian conjugate prior for a binomial likelihood. It is often explained with the example ...

I’m having difficulties dealing with a time series of relations between two numbers.
I have two time series, essentially a count of "successes" and "trials". What I'm interested in, though, is the ...

I have a linear regression model $\bf Y=\bf{X}\bf{\beta}+\epsilon$. I want to assign a prior on $\bf\beta$ in order to derive the posterior predictive model $p(y_{predictive}|\bf{y},\bf{X},\beta)$. ...

I am trying to interpret the regression coefficients of a covariate in a Bayesian linear regression problem. More specifically, I am trying to determine if the regression coefficient have an important ...

I'm trying to build a simple Bayesian regression model to test Edward. However, I notice significant different between Edward's PPC results and PyMC3's.
Common code to generate a data set.
...

I'm trying one of the examples in the textbook Statistical Rethinking by Richard McElreath. My graph looks wrong:
According to the textbook, it is sampling from the posterior & then ...

In the following paper found here and reference below, the author suggests that "if the model is true or close to true, the posterior predictive p-value will almost certainly be very close to 0.5" . ...

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 ...

I was reading this article in wikipedia related to MAP http://en.wikipedia.org/wiki/Maximum_a_posteriori_estimation. However, I had this confusion when it says
MAP estimation is a limit of Bayes ...

I understand that the Jeffreys prior is invariant under re-parameterization. However, what I don't understand is why this property is desired.
Why wouldn't you want the prior to change under a change ...

I am new to Bayesian statistics, and I just came across MAP.
When our prior is a continuous distribution (pdf) on $\theta$ how can we calculate $g(\theta)$ in the numerator?
Edit:
I assumed $g(\...

I have a couple of questions, so I hope it is ok that I ask them here.
Before that, here is some background information on my data:
Outcome variable (1): categorical, 6 categories, N=168
Predictor ...

I've the following situation.
I've a binary classifier which classifies input feature vectors into either of two classes '$y$' or '$n$', along with the probability of it being in either of the ...

The documentation for BSTS says the following about coefficients
If object contains a regression component then the output contains matrix with rows corresponding to coefficients, and columns ...

Which is the best introductory textbook for Bayesian statistics?
One book per answer, please.

Background: I am building a framework to analyze a type of experiment called protein microarray. The basic idea is that you can affix a bunch of different proteins on a microarray chip and then apply ...

I need help with the following question:
Consider $m$ observations $(y_1; n_1); ... ; (y_m; n_m)$, where $y_i \sim Bin(n_i; θ_i)$ are binomial variables.
Assume that $θ_i \sim w_1Beta(α_1; β_1) + ...

I'm trying to understand Bayesian Networks and am attempting to apply it to solve some problems in the world of marketing, most notably search engine marketing. I have a data on each in click to a ...

My model is as follows :
With $y\in\mathbb{C}^{40},A\in\mathbb{C}^{40\times10},x\in\mathbb{C}^{10},b\in\mathbb{C}^{40}$ :
$$y=Ax+b$$
$y$ and $A$ are known and I have a normal prior law on the module ...

I've been asked to perform a statistical analysis at my work and report on the results. I'm using a 2-sided t-test comparing 2 groups where H0=0 and Ha≠0 at a significance level of .05. For my results ...

I am a new user to WINBUGS. I am running a model with 2 chains. When my model has finished running I have the following posterior density plot of my parameter:
The plot only shows one distribution (i....

I am new to Bayesian inference and Gaussian Processes. I am writing to ask what is the difference between MAP (maximum a posteriori) and MML (maximum marginal likelihood). They both seem to enable us ...

(A cross post after finding more appropriate tags here.)
My question is on Bayesian inference of partitioned multivariate Gaussian. To make things easier, suppose there is a 2-dimensional Gaussian,
$$...

I'm very new to Bayesian statistics, but I've found myself in a situation where they might be able to help. I'll be running the same experiment repeatedly and analyzing the data every few months. The ...

Solomonoff's universal prior for models is based on the algorithmic complexity of a computer program $p$ which executes that model. Where $l$ is the length of the computer program, the prior is ...

I'm attempting understand, and use, the population Monte Carlo algorithm found here https://arxiv.org/abs/0805.2256 for approximate Bayesian computation. However I think this is a general SMC question,...

The problem I want to solve:
Lets imagine that I have two factories A and B, where each factory produces coins. What I suspect is that the probability of tails (denoted as $\theta$) varies ...

I want to better understand the step for calculating the message from the game factor $h_{g}$ down to the difference variable $d_g$ on the TrueSkill factor. Such message is shown in the Rasmussen's ...

There is something that is confusing me about max-likelihood estimators. Suppose my I have some data and the likelihood under a parameter $\mu$ is
$$
L(D|\mu) = e^{-(.7-\mu)^2}
$$
which is ...

I know that WinBugs uses precision as a parameter in dnorm instead of variance
...

I have data D_k and different models M_i, and I would like to calculate a goodness-of-fit statistic for undertaking model comparison between the different M_i's, in the case of unknown uncertainties ...

I am looking for a way to solve this problem
I have run k-means to obtain a set of clusters with elements, some of this clusters have 1 or 2 elements in them.
I use the hypergeometric function to ...

I am reading Judea Pearl's "Causality" (second edition 2009) and in section 1.1.5 Conditional Independence and Graphoids, he states:
The following is a (partial) list of properties satisfied by the ...

I have a general query regarding informativeness of priors, since my laptops gone down and not able to run this on Stan to check (but from previous runs I think this was the case). If the priors used ...

In general we say that the likelihood function is defined as some $L(\theta|x)$, so that it is a function over some parameters: $\theta$ given some data: $x$. That is, $\theta$ is free to vary whilst $...

For numerical Bayesian inference we have Posterior~Prior*Likelihood. In MCMC we do not need to calculate the denominator in Bayes rule.
My question is that can I multiply the Likelihood by a large ...

Overview: Suppose I have a log which records the time at which customers visit a store. For the sake of this example, say I have 10 stores in the dataset.
Example data for Store 1:
Customer 828: 9:...

This is a task where I think bayesian statistics can help, but as I only know the basics about it and the question is rather complex I have troubles to get started...
Assume a machine where some ...

I have implemented Bayes multinominal and Bernoulli's model and my question is does the smoothing have any impact of the performance of both models (Laplace’s law of succession
or add one smoothing)?

Text: Bayesian Data Analysis 3E by Gelman, section 3.6
Let $y | \mu, \Sigma \sim \text{MVN}(\mu, \Sigma),$ where
$\mu$ is a column vector of length $d$
$\Sigma$ is a $d \times d$ symmetric, ...

For example, we always assumed that the data or signal error is a Gaussian distribution? why?
I have asked this question on stackoverflow, the link: https://stackoverflow.com/questions/12616406/...

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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