# Questions tagged [prior]

In Bayesian statistics a prior distribution formalizes information or knowledge (often subjective), available before a sample is seen, in the form of a probability distribution. A distribution with large spread is used when little is known about the parameter(s), while a more narrow prior distribution represents a greater degree of information.

833 questions
Filter by
Sorted by
Tagged with
135 views

### pymc3: Updating the standard error prior

I am estimating a Bayesian multiple regression using continuous data on both the dependent variable and the regressors. My goal is to iteratively estimate the coefficient distributions as more data ...
59 views

### Why do the non-informative a priori distributions give better results than the frequentist estimate?

For example, in the specific case of Markov-Switching GARCH models why is a non-informative prior distribution chosen for GARCH models with Bayesian estimation and why is this approach better than the ...
22 views

228 views

### Generating data from the posterior distribution

Let $$p(D \mid \mu,\sigma^2) \sim \mathcal{N}(\mu,\sigma^2)$$ where $D=(x_1\ldots x_n)$ is my data. I imposed a normal prior on the mean as $$\pi(\mu) \sim \mathcal{N}(\mu_0,\sigma_0^2)$$ Using Bayes, ...
135 views

### Is assigning an inverse-Wishart distribution to a diagonal matrix problematic?

I'm reading the paper Bayesian Vector Autoregressions by Thomas Wozniak. He considers the model $$y_t = \mu + A_1 y_{t-1} + \cdots A_k y_{t-k} + u_t$$ where each $y_i$ is a $N$-vector, each $A_j$ is a ...
105 views

### Finding the posterior distribution of a Bayesian analysis prior

I have a prior distribution $f(x)=\pi cos(\pi x)$ where $x$ is the probability of getting tails in a coin toss. Should a coin toss result in tails, how would this be reflected in the posterior ...
111 views

### Posterior as prior for correlated parameters [closed]

I want to use the posterior distribution of the model parameters $\theta$ given data in the time frame $[0,t]$ days, $P(\theta|y_{0:t})$; as a prior for the parameters in the time frame $[t+1, t+n]$ ...
216 views

### Significance of parameterisation invariance of Jeffreys prior

I often hear it said that the Jeffreys prior is well-motivated because it is invariant under reparametrization. The proof of this is quite straight-forward (I know the proof on e.g., wiki). I'm a bit ...
304 views

### Explanation of the Posterior Derivation of the Gaussian Distribution

I'm reading through my notes and I don't quite understand this bit: I understand how the likelihood was calculated but no more than that.Can anyone explain the steps and exactly how they go from one ...
91 views

### Formal Bayesian justification of conditional modelling

I'm having some trouble following the logic of this passage from Chapter 14 in Bayesian Data Analysis, A. Gelman: The numerical 'data' in a regression problem includes both $X$ and $y$. Thus, a ...
40 views

### Constraints on choice of marginal distribution and likelihood

For some time I have been reading into Bishop's Pattern Recognition and Machine Learning. Coming back to some earlier chapters the following got me confused and I am interested where, formally I go ...
31 views

### 1D Bayesian Inference clarification

I'd like some help making sure I understand a 1D Bayesian inference problem. Say I have a data vector which is an array of the number of flu cases reported weekly in California for the past 10 years. ...
105 views

### Crew selection: ranking rowers by letting them race against each other

Seat selection is a common practice in competitive rowing and I would be curious about more solid statistical underpinnings: there are more rowers in a team than the 8 seats in the crew boat. So the ...
79 views

### How do Bayesian hierarchical models adaptively learn the prior?

It seems the main difference between a hierarchical and a non hierarchical model is that the hierarchical model learns the prior. That is it adaptively comes up with a regularizing prior to be applied ...
14 views

### Automatic selection of plot bounds for Normal pdfs in a combined chart

Suppose an app's user specifies several Normal priors by setting the mean and variance for each. I'd like to display a combined plot with the prior pdfs, like that on the figure. . Q: What is a good ...
30 views

### How to set a Bayesian prior on a set with a large but unknown number of elements?

Let us suppose that we are trying to analyze a given starfish. We would like to know which species does the starfish belong to. We have a list of 1000 starfish species, but we know that there is an ...
80 views

### Compute conjugate prior from the sample distribution

I feel like this question might be marked as duplicate because I see many similar incurring in that fate but I'll try anyway. I would say I did not find anything similar. I have been thought a ...
310 views

### What is the posterior distribution of a Bernoulli prior that gets updated with a continuous uniform signal?

I'm trying to figure out what the distribution of the posterior is after I update a Bernoulli prior with a continuous uniform signal, say: P(D=G|u)=x where D{G,I} and u is uniformly distributed on ...
126 views

### How does L2 penalize large weights

The L2 regularization term is useful because it penalizes large weights over smaller weights which is good to prevent overfitting. I'm having a hard time understanding how exactly it does this. This ...
38 views

### In a Hierarchical Bayesian Model, how can we sample and see how a prior distribution looks like if it contains hyperparameters with hyperpriors?

I have a Bayesian Hierarchical Model that looks like: Y_i \sim N(\mu, \sigma^2) \\ \mu \sim N(\mu_0, \sigma_0^2) \\ \sigma^2 \sim Gamma(1,1) \\ \mu_0 \sim N(0,1) \\ \sigma_0^2 \sim ...
53 views

### Valid highly informative prior for proportion

I am trying to find a prior distribution for a proportion $\theta$ that is highly informative i.e. it is almost point mass at $\theta$ but I am not able to find such distribution that is valid for a ...
47 views

### In a Multi-level Bayesian Hierarchical Model, would higher level parameters be affected by how they are jointly modeled in lower levels?

Suppose we have a Multi-level Hierarchical Model where:  Y_{0i} \sim Bin(\theta_{0i}, n_{0i}) \\ Y_{1i} \sim Bin(\theta_{1i}, n_{1i}) \\ \theta_{0i} \sim Unif(0,1) \\ log\left(\...
30 views

### Plot Scaling Problem

I am trying to implement the following code in R $\theta \sim Beta(a=1,b=1)$ $x|\theta \sim Bin(N=5,\theta)$ $\theta|x \sim Beta(a+\sum x_{i},b+\sum N-\sum x_{i})$ ...
85 views

### How many missings are too many to impute data with the AMELIA II package?

I have a very large longitudinal dataset. I only want to impute 3 variables individually using the AMELIA package in R. The problem is that some individuals have a lot of missing values, so I want to ...
56 views

### Understanding the Bayesian question [closed]

I have a Bayesian question here: In a drug experiment, patients with a chronic condition are asked to choose between two drugs, C (control), and T (new treatment). (You may assume for the purpose ...
1k views

### Learning prior distribution from data

Suppose I have a dataset. How can I learn the prior distributions of the parameters of a model from this data? I want to learn the prior from this data in order to use them in a Bayesian model. Sorry ...
A classical example of Bayesian model averaging (BMA) is the regression setup where the choice of different sets of covariates corresponds to different models $\mathcal{M}_k$, $k = 1, \ldots, K$, ...
I am attempting to approximate the posterior $\tilde{\pi_{G}}(z|\theta,Y)$ which is the Gaussian approximation to the full conditional of $z$, and in order to do this I need to find the mode \$z^{*} \...