a method of estimating parameters of a statistical model by choosing the parameter value that optimizes the probability of observing the given sample.

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6 views

Distribution for modelling return times with inflated zeros

I have data on people's return times which I wanted to fit a distribution to using maximum likelihood estimation. I was planning on using a Weibull or Gamma but there are a high number of return ...
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3 views

Help in parameter estimation using MLE for time series data

I have training data $\mathbf{X}$ that consists of $N$ time series as examples where each time series $\{\mathbf{x}_i\}$ is of length $n$. The values of the elements of the times series are binary. ...
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1answer
12 views

Fisher's information for multiple binomials

I am trying to quantify error of the MLE for the following model using Fisher's information: $Y_{j} \sim Binomial(n_{j}, p_{j})$ $logit(p_{j}) = \eta + \gamma_{j}$ where the $n_{j}$'s and $\gamma_{j}$'...
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15 views

Sparsity as missing data + MLE

I just had this "funny" idea: what about a classifier that not only tries to learn weights for predicting y but actually works with "deleted" data (as in sparse ...
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25 views

Help in unsupervised problem formuation for parameter estimation

In the supervised learning problem, the goal is, given a training set, to learn a function $h : X \mapsto Y$ so that $h (x)$ is a “good” predictor for the corresponding value of $y$. If $y$ takes ...
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1answer
24 views

Is EM feasible when there is no closed form maximization of the expectation of log likelihood?

In every example I've seen of expectation maximization, the E step concludes with an expression of the expectation of log likelihood ( $Q(\theta | \theta^{(t)})$ ) for which a maximum w.r.t. $\theta$ ...
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27 views

Finding a Scalable Approach to a modified coin-flip problem using MLE model

and thank you in advance for your help! I am interested in applying MLE to estimate parameters in a "modified" coin flip model, but have been having difficulties scaling the solution. The problem ...
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33 views

Maximum likelihood estimation, how to derive the hessian

I am reading a paper and trying to understand how the authors estimated the standard errors of a set of parameter estimates $[\delta \ \ \phi \ \ \Sigma]$. Below is the loglikelihood function (sorry I ...
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22 views

Setting up maximum likelihood estimation with multi-response data

I was trying to fit the parameters of a time-dependent system coupled of ODES related to a kinetic experiment with multi response data. Example: A->B+H A+H->C+H A->D dcA(t)/dt=-k1Ca(t)-k2Ca(t)*Ch(t)-...
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1answer
37 views
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1answer
29 views

Variance of maximum likelihood estimator in R

In different sources there is an algorithm how to calculate the variance of MLE in R. To keep it short: construct the negative log likelihood function. minimize it via nlm or optim with hessian=TRUE ...
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1answer
26 views

How can standard logistic regression model fractional response variable while denominator is available?

I have X and Y variables, as well as a cluster variable (State). X and State are derived from Database A, while Y and State are derived from Database B. X is a sentiment score ranging between -1 and ...
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9 views

Application of Barndorf-Nielsen Formula for Maximum Likliehood Inference and Confidence Intervals

I've seen various forms of what is called the $p^*$ or Barndorff-Nielsen formula for the conditional distribution of the MLE. The most general form I've found is here. I'll reproduce it below: $$ f(\...
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1answer
139 views

How do iterative methods for solving maximizing likelihood problems work?

Does anyone know about the computational iteration processes for maximum likelihood estimation? If these set of equations cannot be solved practically then how does the computer solve them?
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154 views

Is frequentist conditional inference still being used in practice?

I've recently reviewed some old papers by Nancy Reid, Barndorff-Nielsen, Richard Cox and, yes, a little Ronald Fisher on the concept of "conditional inference" in the frequentist paradigm, which ...
3
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1answer
28 views

How to implement MLE of Gumbel Distribution

I'm trying implement the Maximum Likelihood Estimation in R to Gumbel distribution, but the algorithm doesn't converge. I'm using this parametrization to gumbel: $${\frac {1}{\sigma}{{\rm e}^{{\...
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1answer
48 views

What is maximum likelihood PCA?

There are many papers on this topic, such as this one (pdf). However, I could not find out what exactly maximum likelihood PCA is, how it is applied and for which purpose. Can anyone explain it?
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42 views

Layman explanation of Cramér–Rao bound [closed]

I am trying to understand Cramér–Rao bound, but I have a problem understanding the formula in Wikipedia. Can somebody tell me the intuitive way of it?
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11 views

PyMC: Using maximum a posteriori on vector/matrix-valued variables

I am using PyMC to find a maximum a posteriori estimate for some data. The data is all vector-valued. I am trying to estimate my variable x based on a matrix-valued ...
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1answer
58 views

AIC only applicable to maximum likelihood fit (not least squares)?

When I read about AIC I see that it is calculated for maximum likelihood model estimation. For example, R function arima0 estimated by ...
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1answer
25 views

Conditional distribution (on N) of arrival times in a nonhomogenous poisson process

Conditional on $N(t)$, given some $\lambda(t)$ characterizing some Nonhomogenous poisson point process, the distribution of an arrival time $t_i$ is $\lambda(t_i)/\int_{A}\lambda\left(t\right)dt$ ...
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1answer
22 views

MLE of exponential distribution

Let $Y\sim Exp(1)$ and $T=\mu+Y,\ \mu\in \mathbb{R}$. Let $t_1,\dots,t_n$ be a simple random sample from $T$ with $\mu$ unknown parameter. How can I find MLE for $\mu$? I know that the likelihood ...
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0answers
24 views

Find MLE on custom density function

Let $y_1,\dots,y_n$ be i.i.d. random variables from $$p_{Y_i}(y_i;\alpha,\beta)=exp\{y_i(\alpha+\beta x_i)-ln(1-e^{\alpha+\beta y_i})\},\ y_i=0,1$$ $\alpha, \beta$ are unknown real parameters ...
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10 views

Maximization of a special log-likelihood function

I'm clear on how you found the likelihood function by multiply the pdf of all observations and then do the log to help when you derive. But here I don't understand the (2). Is it in a tobit censored ...
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33 views

Residual standard error difference between optim and glm

I try to reproduce with optim the results from a simple linear regression fitted with glm or even ...
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26 views

Are Maximum Likelihood Estimators asymptotically unbiased?

I can follow the proofs in which the asymptotic normal-distribution of a maximum likelihood estimator $\tilde{\theta}_n$ is derived. however, does this already imply that the maximum likelihood ...
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3answers
51 views

Maximize response for input params clusters from a blackbox function

I have a blackbox function which takes finite number of integers V1, V2, Vn parameters and based on time series variable produce a scalar response. I would like to ...
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30 views

Maximum Likelihood Methods and derivate

I have an exercise about ML, I have some ideas but I can't go through. Here is what I need to answer and what I think I should do. Consider the following econometric model: $$y = \max(y∗, 0) \tag 2 $$...
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1answer
45 views

Confused about logistic regression equality

Problem: Prove that: \begin{align} \Delta E(in) &= -\frac{1}{N} \sum_{n=1}^N \frac{y_n x_n}{1 + e^{(y_n w^t x_n)}} \\[10pt] &=\frac{1}{N} * \sum_{n=1}^N - y_n x_n \theta (-y_n w^T ...
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1answer
127 views

95% confidence intervals on prediction of censored binomial model estimated using mle2 / maximum-likelihood

I am working on a problem in which I have multiple pairs of currently living males i that each have a presumed paternal ancestor ...
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13 views

factor analysis using Maximum likelihood or Principle axis factor to extract factors for 6 point likert type questions?

We have a questionnaire, which have many questions on 6-point likert scale. So these variables are ordinal, not normally distributed. In performing factor analysis, there are two major methods in ...
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54 views

MLE of heteroscedastic model

I'm doing some practice questions for an upcoming exam and am unsure whether I've understood the problem correctly. Can anyone confirm what I've done or point out where I've gone wrong? My final ...
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1answer
32 views

Learning just a decoder (autoencoder without encoder)

I am trying to do something quite unusual: learning a latent representation of some data just by optimizing a decoder. Basically, a probabilistic model of a neural network autoencoder without the ...
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18 views

How to calibrate REGARCH model? (Finding MLE)

I have a model whose specification is $$R_{t+1} = \sigma_{t+1} \varepsilon_{t+1} \text{ with } \ \ \ \ \varepsilon_{t+1} \sim N(0,1)$$ $$r_{t+1} \sim N(0.43 + \log \sigma_{t+1}, 0.29^2)$$ $$\log\...
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23 views

How to measure clustering algorithm performance? [duplicate]

For supervised learning, both regression and classification have ground truth. The model performance can be measured against ground truth. For example, $R^2$ in regression or accuracy (0-1) in ...
3
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1answer
74 views

What r parameter is used in a negative binomial regression?

From my understanding of the negative binomial regression, we have $Y_i|X_i; \theta$ is distributed $Neg Binom (r_i, p_i)$, where $r_i$ is known and fixed (analogous to a fixed $\sigma^2$ when we ...
3
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1answer
42 views

Removing undefined (NaN) values during log-likelihood maximization

I am trying to maximize a Poisson likelihood function for an array of values, of the form llhij = -mij + kij*ln(mij/kij). (where I use the numerical approximation ln(k!) ~ k*ln(k)). For my ...
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21 views

Specifying the initial values of likfit function of geodata in R

I have a geostatistical data. For analysis, I am using geoR. I want to estimate the parameters. But likfit or ...
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1answer
24 views

Consistency and asymptotic normality of two-dimensional parameter

In a textbook exercise, for a sequence of iid variables, I have calculated the score function to be $$\begin{bmatrix} - \frac{n}{2\lambda} + \sum_{i=1}^n \frac{( x_i - \mu)^2}{2\mu^2 x_i}& \sum_{i=...
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21 views

Expectation of infinite sum of random wishart matrices

I have problem figuring out how to find the expectation for an infinite sum of random matrices. More explicitly, my problem is: Let $\mathbf{S}_i$ be the maximum likelihood estimator of the sample ...
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11 views

Maximum likelihood of gaussian with right censoring

I'm trying to fit the mean $\mu$ of right-censored gaussian data ($n$ samples) in a toy example (let's assume $\sigma^2=1$ is known), and the censoring happens always at the same value $s$. As far as ...
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0answers
40 views

Find Bayesian estimator with random sample from poisson and prior distribution from exponential distribution

Let $X_{1}$ .....$X_n$ be a random sample from Poisson distribution, prior distribution with parameter $\pi(\lambda) = \beta e^{-\beta\lambda}$. Find Bayesian estimator I couldn't take integration ...
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1answer
58 views

Properties of conditional maximum likelihood estimators

I am trying to find a source that describes the properties of conditional likelihood estimates like those obtained from conditional logistic regression?
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24 views

mle for the binomial distributed data

For example i have folowing dataset of number of boys in families that have 5 kids: 0 boy - 34(number of such families) 1 boy - 128 families 2 boys - 233 families 3 boys - 267 families 4 boys - 144 ...
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30 views

Maximum likelihood estimation for non-stationary time series

I want to estimate how the taxes influence the retail price of alcoholic beverages. The price function is tricky because in EU countries there is excise duty and also VAT. The non-linearity (which is ...
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1answer
23 views

What is the mode of Dirichlet-Multinomial (Polya) distribution?

What is the ML estimate of the parameter $e_i$ for the Dirichlet-Multinomial (Polya) distribution defined below? $p(\mathbf{x}|\mathbf{e}) = \frac{N!}{\prod_i^d x_i!}\frac{\Gamma(A)}{\Gamma(N+A)}\...
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2answers
34 views

Minimising MSE of $\sigma^2$ estimator of specific form

I have found a past exam question for a statistics course and can't seem to find the required result. Part A is fine but my working for part B must be incorrect [see below]. Can anyone figure out ...
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26 views

Model comparison via AIC or BIC for different likelihood maximization procedures

Maximum likelihood estimation of different models (which all model the same variable and assume the same likelihood function) is done by a different method for each model. Simple numerical ...
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10 views

MLE estimators given score and information

I want to find the MLE estimators of $\lambda>0$ and $\mu > 0$ in a distribution with score vector $$\left[ \frac{-n}{2\lambda} + \sum_{i=1}^n \frac{ (x_i - \mu)^2}{2\mu^2 x_i} \ \ \ \ \ \ \...