# bayesian's questions - Chinese 1answer

4.442 bayesian questions.

### State space model with third or more order trend

1 answers, 20 views bayesian state-space-models
In state space model, a system model with first order trend is represented as $$x_{t} = x_{t-1} + e_{t},$$ where $x_{t}$ is system model, $e_{t}$ is system noise. Also, a system model with ...

### 7 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 ...

### 5 Bias induced from model selection

I'm trying to understand the following sentence «Cross-validation and information criteria make a correction for using the data twice (in constructing the posterior and in model assessment) and ...

### Bayes rule and logistic regression [closed]

1 answers, 120 views probability logistic bayesian
Some context: I want to explain a risk scores to students. These students are familiar with concepts such as “prevalence” of disease, where prevalence = (#people with disease) / (# people with ...

### 4 What's the relationship between Laplace approximation and Variational Bayes methods?

1 answers, 79 views bayesian laplace-approximation
To be precise, I'm checking this presentation https://kaybrodersen.github.io/talks/Brodersen_2013_03_22.pdf, but I don't understand what is the connection between Laplace method and variational bayes? ...

### 1 Conditional probability of posterior distribution for bayesian linear regression

1 answers, 31 views regression bayesian
In Deep Learning Chapter 5.6, Bayesian Linear Regression is introduced. I'm confused by the following formula: $$p(w | X, Y) \propto P(Y | X, w) P(w)$$ $X$ is a sample vector input data. $Y$ is the ...

### The implementation issue of Adaptive Metropolis-Hasting [closed]

0 answers, 23 views r bayesian mcmc metropolis-hastings
I'm trying to implement the Adaptive Metropolis-Hasting (AM) algorithm. I know there are many AM algorithms out there. The one I want to use is proposed by Haario et al. (2001) and later restructured ...

### -1 How can I calculate the conditional probability? [closed]

Could you inform me please, how can I calculate conditioned probability of several events? I have this example: How can I calculate P ( X2 | X4 ) and P ( X5, X3 | non( X4 ) ?

### 19 Is there any difference between Frequentist and Bayesian on the definition of Likelihood?

Some sources say likelihood function is not conditional probability, some say it is. This is very confusing to me. According to most sources I have seen, the likelihood of a distribution with ...

### 3 Why do we use inverse Gamma as prior on variance, when empirical variance is Gamma (chi square)

Let $$X_i\sim \mathcal{N}(0,\sigma^2)$$ than we know that $$\sum_{i=1}^N\frac{X_i^2}{N}\sim\Gamma(\frac{N}{2},\frac{2\sigma^2}{N})$$ that the empirical variance follows a Gamma distribution. How do ...

### 1 How to define the Lee-Carter model and its constrains in Bayesian setting

1 answers, 20 views bayesian jags mortality
I'm running the Bayesian version of Lee-Carter model on jags, using rjags R package. Given a matrix of data $M$ such that $M_{x,t}=\log m_x(t)$ where $m_x(t)$ is ...

### 101 Help me understand Bayesian prior and posterior distributions

3 answers, 120.867 views distributions bayesian prior posterior
In a group of students, there are 2 out of 18 that are left-handed. Find the posterior distribution of left-handed students in the population assuming uninformative prior. Summarize the results. ...

### 3 To show that Bayes classifier has best error rate

Show that the bayes classifier will achieve the best error rate, defined as: $$E(f) = \int \int \mathbb{I}(y = f(x)) \cdot p(x, y) dxdy$$ where $$f(x)$$ is the classifier, and $$p(x, y)$$ is the ...

### 1 Estimating probability of winning for each player based on ranking data of previous tournaments

The question could also be: "estimating the true ability of each player", though I think that already implies some assumptions. In this paper I saw some references to Rankade and TrueSkill used by ...

### 1 Updating Gamma conjugate prior

2 answers, 611 views bayesian prior
I've got some data that looks like it is Gamma distributed. I've constructed the prior distribution from mean=232 and standard deviation = 150, which yield the Gamma distribution parameters: a_prior (...

### 1 multinomial distribution aggregation property

1 answers, 34 views bayesian multinomial marginal

### 3 Gibbs sampler examples in R [closed]

1 answers, 5.511 views bayesian mcmc gibbs
How can I implement Gibbs sampler for the posterior distribution, and estimating the marginal posterior distribution by making histogram?