Maximum Likelihood Estimate Puns

Basically, I am doing MLE on a 1024 normal vector with a matern covariance matrix. I want to do mle to estimate the parameters of the matern covariance function but using autograd.grad(negloglik) and then plugging in a value for the first parameter, I get the following error:

‘ufunc 'kv' not supported for the input types, and the inputs could not be safely coerced to any supported types according to the casting rule ''safe''’

The function kv is the modified bessel function of the second kind or order v. It is imported from scipy

hi guys... so, i know what a loss function (like mean squared error) is, and if i understand correctly, we use a linear regression function to classify data in a problem of linear classification... but where does maximum likelihood estimation fits? does it take the place of the mean squared error function?

I have a task which goes as follows:

>Suppose that you know that a random variable has density 1/𝛼 𝑒^(−𝛼𝑥) for some value 𝛼. You obtain a single observation from the random variable which is the number 3. What is the maximum likelihood estimate for 𝛼?

Here's my solution. Is it correct?

Thank you in advance!

Hello you beautiful, I'm trying to increase my engineering toolset and robust parameter estimation considering errors in inputs and outputs for arbitrary functions is not something easy to find in the wild, but applicable to many cases in the practical engineering life. There is this paper from the Royal Society of Chemistry, whose reference is too dense for my poor engineering applied math skills. Does someone has a reference or a scheme I could use to implement it in excel and use solver to maximize the log-likelihood?

I’m not a statistician, but I’m trying to suggest that maybe TMLE is better than propensity score matching for a retrospective observational cohort study. I read that it is, but I’m not really understanding how TMLE (with machined learning) works. Lots of stats jargon and stuff. Hope one of y’all experts can help me. Ty in advance!

For my Econometrics project I am doing a probit model, but part of the report requires me to explain the economic model of my project. I don't understand at all what I am meant to put here wrt to the Probit model or MLE This is my first research project I have done so apologies if I am missing something simplistic here.

What should I put down for this section?

Two of the widely used linear regression methods for finding parameters are ordinary least square (OLS) and analytical methods. In these two methods which is considered as a maximum likelihood estimate(MLE)? Are they both MLE?

Can we say that, any method which estimates parameters is a MLE?

Hi, could someone please give some advice on this code? Why is it not working?

My dataset: a fair coin that was tossed 30 times first (p=0.5) then switched to a biased coin and tossed another 70 times (p=0.2)

coin_toss <- c(rbinom(30, 1, 0.5), rbinom(70, 1, 0.2))

I want to create the function of log-likelihood so I could optimise my dataset in optim()

mix_2bin_nll <- function(switch, obs, prob){

sum(log(switch*dbinom(obs, size=1, prob=prob[1]) + (1-switch)*dbinom(obs, size=1, prob=prob[2])))

}

mle_100 <- optim(par=c(0.51, 0.24), fn=mix_2bin_nll, switch=0.3, obs=coin_toss)

summary(mle_100)

My problems:

1. lots of warnings, such as " NaNs produced"Warning message in dbinom(obs, size = 1, prob = prob[2]):
2. outputs are non-numeric

Thank you!

Why we cannot use Sum of Least Squares??

I am absolutely DESPERATE. I've been looking for HOURS on how to calculate MLE for Non-Linear Multiple Regression in 4 ways (Manual Calculation, Excel, EVIEWS, SPSS). If you know any books, websites, or vides that could help with this, please do share it. You don't even have to explain it to me. I'm willing to do the work. I just want to know if there's any suggested readings or viewings that could help me learn it on my own.

Thanks everyone and have a great day :)

Is it possible to do "Analysis of Maximum Likelihood Parameter Estimates" in R like in SAS?

I did logistic regression on both but they produce similar coefficients

https://preview.redd.it/aaowexqc39u41.png?width=1920&format=png&auto=webp&s=4c0a4abbc8780cf3f5d6fbc623824dc5eee6e88d

https://preview.redd.it/ioyvkwu439u41.png?width=1920&format=png&auto=webp&s=e9be23c8bd6995283c62da69637071467ec28b95

I created the following Jupyter notebook that illustrates maximum likelihood estimation in Jax:

Maximum Likelihood in Jax

Any questions, comments, or corrections are appreciated. Also, any advice on what other forums that would be interested would be appreciated.

Thanks!

We are learning this concept in a statistical programming course for research methods, and the professor couldn't be less clear if he tried. Can someone explain the maximum likelihood estimate (MLE) like I'm five?

I am still quite a beginner in statistics and i do not have a good command over calculus and LA. I would prefer a resource which is relatively easier

Hello! I haven’t used R in years and am having some difficulties getting back into it.

I was reading an article and noticed they had maximum likelihood estimates presented in the paper. I have watched a few videos on YouTube and read articles as well.

I am find the gap from overly simplistic to very complex examples a bit daunting.

I have attached the information here for reference. Can anyone assist with how these numbers were produced for Anaplasma spp.

If you could post your code that would be appreciated as well. I have gotten stuck since the only information provided is the positive pools and I am uncertain how to calculate p.

If I am doing this entirely wrong, please correct me and enlighten me.

Example: 2/52 pools positive Pathogen: Anaplasma spp. MIR 0.8% (0.0,1.8) 95% CI MLE 0.8% (0.1,2.5) 95% CI

Say I want to find out the probability of success p of an experiment. So I carry out the experiment n times and obtain k success. Then the simple Monte Carlo estimate gives p=k/n.

The other way ia using the likelihood function. Given the outcome, the probability of that outcome for p \in [0,1] will be my likelihood function L(p). If I look at the value of p for which L(p) is maximum, it will be my maximum likelihood estimate of p.

My question is, are both of these estimates equal? And if so, is there a way of proving it?

The third way to estimate is by taking expected value of p assuming p is a random variable with PDF c*L(p) where c is some scaling constant. Is this estimate better than previous ones? Is there a way to prove this?

And a last question, how to obtain the confidence interval for the estimate obtained from likelihood function?

I have felt unconvinced by the explanations I've read, or when they were more mathematical, I felt I didn't quite follow exactly what they were doing to grasp the significance of the proof.

Is it simply an artifact of defining variance as the squared error? I've read that the least squares method minimizes the variance of the errors.

If I defined the variance as a third moment,

Var(x) = E( |x - mu|^3 ), would the least absolute cubes estimate be the best linear estimator in terms of minimizing the "variance"?

What if I made my "variance" function simply the absolute deviation?

Or are my thoughts simply off completely, and these properties come out of the behavior of the Gaussian distribution?

What are the prerequisites for learning Parametric Inference and Maximum Likelihood Estimation and what is the gradual order so that no detail is vague while learning? There are a few lectures on Youtube but they mostly went over my head, maybe because I omitted few important chapters. I need some help.

Hi. so I'm a 3rd year CS student and I'm really struggling to understand this topic. I can't even understand the simple purpose of these two methods or what they mean. Can someone explain it to me in a very easy way? even if it superficial and not mathsy, I just want to know at the top level of abstraction what these two things are for and what their difference is.

hi. can someone please show how one can use maximum-likelihood theory to find an estimate for the volatility in BS model? Wikipedia has an equation here but I cannot derive it.

Hi I have a problem regarding the MLE of a negative binomial distribution. It has the pdf: f(Z)=((z-1)Choose(j-1))(0.75^j)(0.25)^z-j. I have to find the MLE of j. I made the log likelihood function and tried to derive it but I am not sure how to derive all of the terms in the derivative. Specifically, I do not know how to derive ln((z-1)Choose(j-1)). Could anyone help me out?

I'm searching for a reference on large deviations of maximum likelihood estimators.

Specifically, I'm searching for a theorem that says that under some regularity conditions, the probability that the MLE deviates from its limit decreases exponentially with the distance.

I want the upper bound, and it would be even better if the upper bound is uniform in n.

I've search in van der Vaart's book without success ...

Does anyone have any recommendations for resources showing that the iteratively reweighted least squares maximum likelihood estimator for the logit model can be expressed as:

b = (X'VX)^(-1)X'VY^*

where y^* = Xb + V^-1(y − p)

Thanks! Any resource recommendations would be appreciated.

Hi all,

I've been working on a personal project where I try to make a pairs trading strategy based on conditional probabilities computed from a t-copula. I've been coding everything from scratch (more or less) and done several sanity checks using the "copula" package for R and I know that I am computing the correct copula density for my pseudo observations.

I am, however, struggling to estimate the degrees of freedom of the copula. I essentially have two datasets: Return series of two assets sampled daily and return series of the same two assets sampled at 6H intervals.

I am "somewhat" able to estimate the degrees of freedom using the daily data, but not at all able using the 6H data. I've used the estimated degrees of freedom and maximized log likelihood produced by the copula package in R as a benchmark for my own estimation. With the daily data, I get quite close but for the 6H data, the log likelihood I calculate for seemingly any degrees of freedom is "inf" in Python.

I also noticed that R estimates the degrees of freedom on the daily data a lot faster than my Python implementation does. I very inexperienced with optimization, so I don't really care about these kind of performance issues, I just want to get close to the benchmark estimates I get in R.

This is how I compute the log likelihood and how I estimate the degrees of freedom:

1. For a given degrees of freedom, compute the copula density for each pair of pseudo observations
2. Take the cumulative product of these densities
3. The log of this cumulative product and multiply by -1. This returns "-inf" in Python. (Would taking the log of the densities before taking the cumulative product make a difference for Python? I am using numpy.cumprod() )
4. Use scipy.optimize.minimize to find the degrees of freedom that minimizes the negative log likelihood

I didn't use the "actual" log likelihood function because I do not trust myself to derive it correctly (the copula density function is already quite nasty-looking) and I have not been able to find the log likelihood function for a d-dimensional t-copula online.

My question is firstly, how can I get a closer to the benchmark estimates of the degrees of freedom from R and secondly, what do I need to change about my approach in order to even get an estimate for the 6H data.

Thanks!

Given a likelihood L(\theta) and the \theta* MLE solution, is there a way to approximate the expected value of L(\theta)? I have the ability to calculate the gradient and Hessian of L(\theta). L(\theta) is the non-linear least squares likelihood so the expected value is not necessarily the same as the MLE.