Questions tagged [posterior]

Question 1

I am working on a Bayesian hierarchical model of a plant physiological process written in Stan. Basically it can be broken down to a multilevel piecewise regression model with a species-specific ...

Question 2

Background Consider the following recursive Bayesian classifier \begin{equation} p_{t}(c)=\frac{\ell(y_t\mid c)p_{t-1}(c)}{\sum_{\nu=1}^C \ell(y_t\mid \nu)p_{t-1}(\nu)}, \qquad c=1,\dots,C \tag{1} \...

Question 3

Bayesian updating is sometimes described by the following equation: \begin{equation*} \text{Posterior}=\sigma \times \text{Signal}+(1-\sigma )\times \text{Prior} \end{equation*} This expression treats ...

Question 4

Suppose $X$ is a random variable taking values in $\{-1, 0, 1\}$. Say that a priori I know nothing about $X$ so my prior distribution for $X$ is $\Pr(X = x) = 1/3 \quad(x = -1, 0, 1)$. Now suppose I ...

Question 5

I’m fitting a mixture model in Stan to strictly positive data. Each component distribution has a mean that can be expressed by some summation of a and b. (a and b are two “factor” parameters shared ...

Question 6

Low Acceptance Rate in Independent Metropolis-Hastings with Jeffreys Prior Model Specification Implementing an Independent Metropolis-Hastings sampler for: Likelihood: $$ f_X(x \mid \theta) \propto ...

Question 7

I am trying to estimate a posterior distribution and specifically its entropy using a Sequential Monte Carlo (SMC) sampler. Given a prior $p(x)$ and a likelihood $p(y|x)$ I am using SMC with adaptive ...

Question 8

I am practicing some concepts from my graduate stats class and trying to derive the Bayes rule for the squared loss function $L(\theta,a)=(\theta-a)^2$. I have a Laplace distribution with location ...

Question 9

There is a similar question that was asked here: Gaussian processes: posterior vs. predictive distributions but it never received any attention and so I am re-asking the question although the emphasis ...

Question 10

Using a Dirichlet prior and a multinomial likelihood model, one can derive the posterior distribution for the estimation of the frequency of discrete events. A technique of pseudocounts can be applied ...

Question 11

Inspired by this twitter thread, posting this question: I have two children, (at least) one of whom is a boy born on a Tuesday what is the probability that both children are boys? Via Joel Grus, ...

Question 12

I have got a question that I am not sure how to answer on it, and I would like to get some clarification, or to point me out where is the problem in my understanding. We got a logistic regression ...

Question 13

This question is around clarification for whether the posterior distribution and posterior predictive distribution can be used to create an interval estimate for a quantile. Consider the following ...

Question 14

Currently i'm estimating HR splines using mgcv::gam::coxph. My spline is nonlinear and has one turn, so i'd like to divide my spline into two sections given the turn and get conditional estimates for ...

Question 15

Question: I am performing importance sampling (IS) for a Bayesian inference problem with the following setup: 1. Data and Model My data has ( D = 1300 ) dimensions. The log-likelihood, $ \log p(x \...

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Questions tagged [posterior]

Population mean of combinations of parameters from a joint posterior distribution

Dealing with an overconfident likelihood

Learning About Higher Moments in Bayesian Updating

Conditional probability given expectation

Wide intervals and oddly-shaped posterior densities of mixture‐model weights and means in Stan—should I be concerned?

Low Acceptance Rate in Independent Metropolis-Hastings with Jeffreys Prior

Posterior entropy estimation using Sequential Monte Carlo

Posterior of a Laplace distribution with a Laplace prior

Difference between the posterior and posterior predictive of a Gaussian process

Finding posterior of Multinomial likelihood and Laplace Prior

Understanding intuition of the Two child problem

Problem in understanding how to find posterior (logistic regression)

Bayesian interval estimate for a quantile

How to aggregate confidence interval from spline into intervals correctly for Cox model?

Title: Handling Skewed Importance Sampling Weights for High-Dimensional Log-Likelihoods

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