# Bayesian updating normal distribution

For $X_, X_,..., X_$ iid $\mathcal(\theta,\sigma^2)$, and a priori distribution $\theta\sim\mathcal(\mu,\tau^2)$, you should obtain posteriori distribution $\mathcal(\mu_,\tau^2_)$, where: $$\mu_=\frac\quad\text\quad\tau^_=\left(\frac \frac\right)^$$ As for the Bayesian estimator - well, I believe that that would depend on your risk function; with a MSE function, you should obtain $\theta^_=\mu_$.Suppose we observe one draw from the random variable $X$, which is distributed with normal distribution $\mathcal(\mu,\sigma^2)$. (Interpretation: we get noisy signals about $\mu$, which are known to be normally distributed with known variance---this is the draw of $X$.Here is a ten-minute overview of the fundamental idea. But there's a catch: Sometimes the arithmetic can be nasty.On your way to the hotel you discover that the National Basketball Player's Association is having a convention in town and the official hotel is the one where you are to stay, and furthermore, they have reserved all the rooms but yours.) hypothesis while on the other hand very religious people for example have 0 in their priori when it comes to possibility of their religion being made up so they are forced to ignore evidence to the contrary (because bayesian updating breaks for them due to division by zero and mind's way to signal this exception is denial).

The prior information $\pi$ on $\theta$ is given by an $N(0,\tau^2)$ distribution.The whole idea is to consider the joint probability of both events, A and B, happening together (a man over 5'10" who plays in the NBA), and then perform some arithmetic on that relationship to provide a updated (posterior) estimate of a prior probability statement.Once you figure out simple examples you slowly start thinking this way about the world. Take people for example: Someone with open mind has a priori with at least slight probability assigned to unlikely (for them!We assume learners in this course have background knowledge equivalent to what is covered in the earlier three courses in this specialization: "Introduction to Probability and Data," "Inferential Statistics," and "Linear Regression and Modeling."In this week, we will discuss the continuous version of Bayes' rule and show you how to use it in a conjugate family, and discuss credible intervals.

By the end of this week, you will be able to understand and define the concepts of prior, likelihood, and posterior probability and identify how they relate to one another.

I have to calculate the posteriori distribution on $\theta$ and the Bayes estimator.

## Bayesian updating normal distribution comments

• Bayesian Updating - Statistical Engineering

## paulette60

We use Bayesian Updating every day without knowing it.…
• Bayesian Inference in a Normal Population - StatSci

## paulette60

From a Bayesian perspective, it is. Find the conditional posterior distribution µ. Bayesian Inference in a Normal Population – p.12/18. Data 100 200 300 400…
• Bayesian Inference for Normal Mean - University of Toronto

## paulette60

Bayesian Inference for Normal Mean. Simple updating rule for Normal family. posterior distribution is Normal and thus symmetric.…