Linked Questions

93
votes
11answers
56k 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.
12
votes
4answers
2k 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 ...
25
votes
3answers
5k 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 ...
16
votes
3answers
15k 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 ...
11
votes
2answers
17k 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 ...
4
votes
2answers
293 views

What are the econometric 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-...
2
votes
2answers
4k 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 ...
8
votes
1answer
5k 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 became is about Bayesian Linear Regression. I wonder if it's both the same things because the formula look quite similar
7
votes
1answer
915 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?
4
votes
1answer
712 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 ...
3
votes
1answer
900 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
1k 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
1answer
142 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 =...
1
vote
1answer
2k 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 ...
1
vote
1answer
48 views

Extra information at prediction time when using a Bayesian logistic regression vs. normal

I have a binary classification problem (i.e. is observation positive or negative) and I'm interested in what information I can obtain about observations in my test set. I don't care about the model ...
0
votes
1answer
17 views

Placing constraints on linear model coefficients

I have this bit of data : ...
0
votes
1answer
402 views

Bayesian smoothing using Dirichlet prior : why not MAP?

I am reading about smoothing methods for language model ( I am working on unigram model). If you are not familiar with unigram model, it is closely related to multinomial distribution (with the ...
0
votes
1answer
41 views

what is the posterior in the case of regression

I am having trouble "mapping" the variables in the Bayes equation onto the case of regression. As notation, say $$ P(\theta|D) = \frac{P(D|\theta) P(\theta)}{ P(D) } $$ I have come to think of $\...