# Questions tagged [posterior]

In Bayesian statistics, the term 'posterior' refers to the probability distribution of a parameter conditioned on the observed data.

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### BayesDCCGarch Model Code to analise Stock index Data and MCMC Simulation [closed]

MCMC Simulation and bayesian approach of estimating parameters of BayesDCCGarch Model
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### Posterior Distribution in a Bayesian Multivariate Normal Model

I am currently working on a Bayesian inference problem and would appreciate some help on computing the posterior distribution of a hyperparameter within a specific multivariate normal model. Below, I ...
1 vote
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### Estimating expected value with respect to posterior

I have a neural network and I need to calculate the following: $$\mathbb{E}_{P(\theta|D)}[f(\theta)]=\frac{\sum_\theta P(D|\theta)P(\theta)f(\theta)}{\sum_\theta P(D|\theta)P(\theta)}$$ Where $f$, ...
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### prior and posterior predictive distributions, Bayes Theory

Consider the binomial sampling model with a Beta prior on $\theta$ and the prior predictive distribution. Let $n$ be the binomial sample size. \begin{align} p(y^{new}) &= \int_{\theta}f(y^{new}|\...
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### Confusions modeling times of related events

I am currently interested in modelling the time of related events, and I am currently confused as to how to incorporate all different sources of information in a single model. Consider a toy example ...
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1 vote
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### Why do T prior and likelihood make a bimodal posterior?

In this post, the author shows that when a likelihood and prior are both T-distributed with $2$ degrees of freedom, the posterior is bimodal. The given reason is that The two modes persist - the ...
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### Is it acceptable to take the mean of a bunch of median values?

I use a Bayesian latent variable model to construct a time series cross-sectional measure of corruption for all countries in the world from 1960 to 2010. For each country-year observation, I obtain a ...
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### How do we obtain the posterior of a beta binomial mixture of continuous and a discrete density?

In section 3.6 of Jim Albert's 2009 book "Bayesian Computation with R" he describes a test of whether a coin is fair using a mixture of priors. The coin tossing follows a binomial ...
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### Correction variance estimation from the posterior in a Bayesian framework

My question is quite basic, I have posterior distributions for some parameters derived from an arbitrary Bayesian framework. Since I know that the posterior variance under-estimates the true variance, ...
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### Estimating posterior of proportion of positives in population from per-observation probabilities

I have a sample from some population of 0s and 1s and need to estimate the posterior of the proportion of 1s in this population. But the catch is: for each observation in the sample I only have ...
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### How do I evaluate correlation of model parameters using MCMC posterior samples from a rstan fit?

Is there a better way to do so than simply by taking posterior parameter estimates and calculating the Spearman or Pearson correlation between them? Anything specific to having posterior samples from ...
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### Is it correct to use the posterior distribution from a Bayesian model in other analysis?

I have written a Bayesian model in JAGS that I use to calculate the growth rates of several plant populations as well as their variance while taking into account the observation error during the ...
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### Some Problems in Auxiliary Particle Filter

recently I am studying PF. And I am stuck in APF for a few days, though I derived many times. Here is my question: I followed the framework of this paper. The APF is defined in Algorithm 1: The ...
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### Why the Pitman estimator is given by the sample mean of X and Y?

Let $(X,Y)$ be bivariate normally distributed with $E[X] = E[Y] = \theta$, $Var[X] = Var[Y] = 1$ and $cov[X, Y] = \rho, |\rho| < 1$, where $\rho$ and $\theta$ are unknown. Find the minimum risk ...
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### Maxdiff Approach - Claims comparison , how to compare product claims of two different surveys Maxdiff gives Preference shares or count based analysis

My business objective: I want to create a MAX diff approach where I will have multiple surveys my output will be Claims and its Posterior Probability , count of best and worst selection. For more ...
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### How informative should a Gaussian Process prior to be?

I recently started learning about the Gaussian Process for a GP machine learning project so my understanding is relatively limited. However, from what I have read/watched so far you have a prior GP ...
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### Logistic vs. linear regression for "inherently continous" variable - comparing probability

This is a situation that arises commonly in my area (medicine). Suppose there is an inherently continuous variable $y$ Suppose there is some normal range for this variable, say 80 - 120 Suppose there ...
1 vote
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### Gaussian Process posterior distribution

I'm trying to find a way to get the posterior covariance function for a mgcv::gam fit. Assuming I have a simple model y ~ s(x), ...
Assume the simple, well-known scenario: Data = $(x_j, y_j)_{j=1}^{n}$, and that, as usual, the $n$ data points are drawn iid. The $x$'s may be considered non-random, but the $y$'s are observations ...