Linked Questions

97
votes
12answers
61k views

Maximum Likelihood Estimation (MLE) in layman terms

Could anyone explain to me in detail about maximum likelihood estimation (MLE) in layman's terms? I would like to know the underlying concept before going into mathematical derivation or equation.
27
votes
3answers
7k views

Do Bayesian priors become irrelevant with large sample size?

When performing Bayesian inference, we operate by maximizing our likelihood function in combination with the priors we have about the parameters. Because the log-likelihood is more convenient, we ...
18
votes
3answers
19k views

Bayesian updating with new data

How do we go about calculating a posterior with a prior N~(a, b) after observing n data points? I assume that we have to calculate the sample mean and variance of the data points and do some sort of ...
13
votes
2answers
19k views

Bayesian logit model - intuitive explanation?

I must confess that I previously haven't heard of that term in any of my classes, undergrad or grad. What does it mean for a logistic regression to be Bayesian? I'm looking for an explanation with a ...
12
votes
4answers
3k views

Why I should use Bayesian inference with uninformative prior? [duplicate]

I am a Ph.D. student and currently I am studying Bayesian inference concerning vector autoregressive models. A lot of researchers when talking about uninformative prior, conclude that the results of ...
11
votes
1answer
7k views

Is Bayesian Ridge Regression another name of Bayesian Linear Regression?

I searched about Bayesian Ridge Regression on Internet but most of the result I got is about Bayesian Linear Regression. I wonder if it's both the same things because the formula look quite similar
8
votes
1answer
1k views

What exactly is a hyperparameter?

Title says it all. I have seen both "the hyperparameter of the Dirichlet distribution" and "the parameter of the Dirichlet distribution" What are the differences?
7
votes
2answers
1k views

What are the assumptions in bayesian statistics?

So, for OLS there are 3 assumptions regarding the DGP, which are (from Stock & Watson): Independence of error terms (+ Homoskedasticity?) IID of variables Large outliers are unlikely, meaning non-...
5
votes
1answer
944 views

Questions on Bayesian Softmax Regression [closed]

My question is about how to actually do this both rigorously and practically. Allow me to elaborate. Suppose that we have data $(x_1,y_1),...,(x_N,y_N) \in \mathbb{R}^p \times \{0,...,k-1 \}$. I'd ...
4
votes
1answer
3k views

Posterior vs conditional probability

When talking about events, there is the following formula called Bayes' rule, where $A$ and $B$ are random events: $$P(A|B)=\frac{P(B|A)P(A)}{P(B)}$$ Now let's say that for now only $A$ happened. I ...
3
votes
1answer
1k views

What is the real-life benefit and application of Bayesian regression [closed]

Question What is the real-life example of the benefit and application of the benefit of Bayesian regression? Having read the items and it looks having the range of inference (possible values and ...
3
votes
1answer
2k views

Estimation of Bayesian Ridge Regression

According to scikit-learn, by using a probabilistic model : $p(y|X,\omega,\alpha) = \mathcal{N}(y|X\omega,\alpha)$ with $\omega$ given by a spherical Gaussian: $p(\omega|\lambda) = \mathcal{N}(\...
2
votes
2answers
5k views

Sum of squared difference and Gaussian noise model

I have been reading that when the underlying error is distributed normally, then minimising the sum of squared difference between the observed data and the model is the appropriate cost function to do ...
2
votes
1answer
335 views

Implementing Bayesian Linear Regression using PyMC3

I am learning a Bayesian Approach towards implementing Linear Regression. The motivation is that Bayesian Approach gives you a range on predictions which might be useful when investing money in ...
2
votes
1answer
184 views

Intuition on simple linear regression signal plus noise model

I'm currently studying linear regression on this book "F.M. Dekking - A Modern Introduction to Probability and Statistics: Understanding Why and How" where the signal+noise model is presented: $Y_i =...

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