For questions about how to parameterize some statistical model, or comparisons between different ways to parameterize.

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How the process parameters changes with the length of data aggregation?

Is there any general relationship for a process(e.g. ARMA, O-U process) applied to financial data over different time intervals. e.g.In this question there is an answer telling the O.P. to aggregate ...
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1answer
18 views

parameter tuning using nested cross validation

Parameter tuning in SVM has been performed using a nested cross-validation(CV) approach with 45 folds(outer loop) and 13 folds(inner loop). In this process, the outer loop will have 45 prediction ...
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0answers
12 views

Modelling of distribution

I have faced with the following distribution (it is truncated at $0.03$ for clarity): It takes values in $(0, \infty )$, unimodal (with mode around $0.0001$), heavy-tailed, and has regular "hills". ...
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0answers
22 views

Estimating a parameter which itself is a sample from a parametric distribution

I am trying to model an engineering problem in the following way: Suppose $\theta_1$ is an unknown parameter lying in some set $A$, and let $\mathcal{P} = \{P_{\theta_1}: \theta_1 \in A \}$`be a ...
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5answers
791 views

What's in a name: hyperparameters

So in a normal distribution, we have two parameters: mean $\mu$ and variance $\sigma^2$. In the book Pattern Recognition and Machine Learning, there suddenly appears a hyperparameter $\lambda$ in the ...
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0answers
10 views

In factor analysis what is more stable sample to sample: regression coeffients or structural coefficients?

In Which matrix should be interpreted in factor analysis: pattern matrix or structure matrix? ttnphns remarks "Weak side of pattern matrix is that it is less stable from sample to sample (as usually ...
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0answers
37 views

MCMC efficiency and nonlinear reparametrizations

The efficiency (e.g., effective sample size per density evaluation) of most MCMC methods depends on the parametrization. However, so far I have come across little work in the MCMC literature that ...
4
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0answers
42 views

How to parameterize coefficient matrix to restrict eigenvalues?

Consider the $r-$dimensional autoregression $$ y_t = Ay_{t-1} + v_t, v_t \overset{iid}{\sim}N(0,\Sigma). $$ It is well known that if all eigenvalues of $A$ have modulus less than unity then this ...
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3answers
289 views

GLMs must be 'linear in the parameters'

I am experiencing some cognitive dissonance about what 'linear in the parameters' means. For example, here and here. For example, my understanding is $y_i = \beta_0 + \beta_1\beta_2x_1 + ...
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0answers
58 views

What is a parameter in Bayesian analysis?

In any case study, when we use Bayesian analysis to solve our problem we consider a model parameter which is sometimes known and sometimes unknown. And using this parameter(and of course prior data) ...
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0answers
28 views

Support of distribution (distribution fitting)

This might be a weird question. I want to know why Matlab still run to produce estimated parameter whenever I input data which doesn't belong to the support of the distribution? E.g. I want to ...
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0answers
11 views

Splitting of parameter space when using random mutation hill climbing

I have developed an agent-based model in NetLogo, and to calibrate the model and its parameters I want to use the random mutation hill climbing method. However, since my model is computationally ...
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0answers
25 views

Choosing the good initial value of the Newton-Raphson iteration method for Maximum Likelihood Estimation

I want to estimate the four parameters of Exponentiated Modified Weibull Extension (EMWE) distribution introduced by Sarhan and Apaloo (2013) with the Maximum Likelihood Estimation. Because the first ...
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0answers
12 views

Improving convergence of simulated annealing

I have a complex curve that I need to approximate with a parametric model (5 parameters). The parametric model itself is highly non-linear, and small changes in parameters can lead to big changes in ...
2
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1answer
33 views

Justification of simulated annealing versus random search

I have a set of 16 integer parameters to optimize. The parameter space is too big for an exhaustive search, so I am using simulated annealing instead. I think my simulated annealing works - it finds ...
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1answer
38 views

Hierarchical Weibull model: choice of parameterization

I am experimenting with fitting a Bayesian hierarchical model using right-censored and Weibull distributed time-to-first-event data. However, I have some issues that might be related to the ...
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0answers
41 views

Help: Random Forest optimization (image classification)

I'm having trouble classifying images using a random forest. The images all have a very similar scale, but they may be rotated arbitrarily around a fixed point in the image. The core problem is ...
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0answers
40 views

Completely understanding the Confidence Interval - how is it not a probability of containing a population parameter?

I've been doing data analysis for a while, but recently I questioned my understanding of the oft-misunderstood confidence interval. So, I read multiple sources. Many of them say explicitly that the ...
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0answers
11 views

Estimating a Mixture Model from incomplete datasets

I would like to figure out the best way to estimate a univariate mixture model from an incomplete dataset. For example, generate a mixture of two normal distributions and then crop the dataset below ...
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1answer
34 views

what is the relationship between covariance matrix and its variance parameter in linear mixed model

In parameter estimation for linear mixed model for unknown variance, I met some statements saying that "we assume G (as variance) is only known up to its variance ...
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0answers
16 views

Get level set from 3D dataset obtained exploring a 2D space parameter

I am exploring a 2 parameter space performing simulations. As a result I get a surface as a function of these 2 parameters. I know this is probably simple but I don't know how to look for it. Now I ...
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0answers
6 views

estimating correlation of estimated parameter from windows

Say you have a process $x[n]$ for which you estimate a parameter $\theta$. You want to know how stationary is the parameter $\theta$ over time. So, you take $x[n]$ and divide it to windows of duration ...
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0answers
20 views

Find Parameters from regression coeffiecients

I have Set of data, defined as follows: $$ \begin{array}{c|lcr} x & Y_1 & Y_2 & Y_3 \\ \hline 1 & 0.24 & 1.2 & 1.5 \\ 2 & 0.56 & 1.89 & 5.8 \\ \vdots & \vdots ...
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0answers
99 views

Probability Distribution and Likelihood for Deterministic Dynamical Systems

Using MLE to fit data to a deterministic non-linear model, say, a system of ordinary differential equations (e.g. Lotka Volterra,without stochastic elements besides measurement errors), how do I ...
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0answers
135 views

Question about reparameterization and setting up a 'noninformative' hyperprior distribution

When I read Bayesian Data Analysis, 3rd ed. by Andrew Gelman, et al., I can not understand the problem of "choosing a standard parameterization and setting up a 'non-informative' hyperprior ...
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2answers
400 views

How to interpret slope parameter estimates for linear models in R?

I wish to analyse a simple lab experiment. I have 8 fish. Four are fed on diet A, and four on diet B. I measure their Nitrogen (N) over 5 time periods (so 5 repeated measures per fish). I wish to know ...
5
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1answer
303 views

Can I get the parameters of a lognormal distribution from the sample mean & median?

I have the mean and median values for a sample drawn from a lognormal distribution. Note that this is not the mean and median of the logs of the variable, though I can of course calculate the logs of ...
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0answers
25 views

Directional 1D Variogram by BME Analysis

I participated in a discussion where one speaker had applied oil-drilling's math-balance equations into 1D signals by the directional 1D variogram. I understood that the most important thing is to ...
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1answer
84 views

Using K-fold cross validation as a hint for number of neurons in hidden layer. Possible flaws?

I have a dataset of 14 continuous variables and would like to predict one (say y) using all the remaining ones (say X). I decided to use a neural network with linear output (since I am doing ...
2
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1answer
86 views

Parameter estimation for Kumaraswamy distribution

I'm interested in estimating the shape parameters of a Kumaraswamy distribution from sample data. The closest research I can find is Jones' paper from 2009 which analyses a maximum likelihood method, ...
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1answer
29 views

Gibbs sampling: ancillary and sufficient parametrization

After asking a question about Gibbs sampling earlier, I have another one for you. I have not been able to find laymen's background on this, the only referenced use I've found for this is in ...
0
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0answers
32 views

nls model parameter compare

I am doing nonlinear regression using a same sigmoidal model for different treatments. for each treatment, I got a set of estimated parameters (a1, b1, c1 for treatment 1; a2, b2, c2 for treatment ...
1
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1answer
46 views

Ways to stabilize OLS betas [closed]

I am estimating the parameters of a system of OLS equations in Matlab. $y=X\beta+\epsilon \to \hat \beta=(X'X)^{-1}X'y$. My $X$ is a $5\times 5$ matrix and $y$ is a $5\times 1000$ matrix, so $\beta$ ...
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1answer
90 views

Calculating parameters for a mixture of beta distributions

I have two beta distributions with known parameters: ...
3
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1answer
137 views

What is the point of graphical models?

I spent the day learning about the bnlearn package in R only to discover that Bayesian models do not work with undirected graphs. I'm trying to learn about the Markov Random Field Network, and so far ...
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1answer
114 views

How should I parametrize a nonlinear increasing function?

I want to learn a nonlinear monotone increasing function $f$ parametrized using a set of weights $w$. Given an input $x$, I can calculate the gradient of the loss with respect to $f(x)$ ...
1
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1answer
133 views

Spherical Parameterization of Variance-Covariance Matrix in Mixed-Effects Regression

I wonder if someone can please help me with a passage on the article by José Pinheiro and Douglas Bates on unconstrained matrix parametrization. I have been slowly working through it, and getting ...
2
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0answers
28 views

how to find the aleatory uncertainty in parameter using Bayes?

Generally, the uncertainty can be categorized into aleatory and epistemic according to whether it can be reduced or not. In Bayesian statistics, one "true fixed parameter" is presumed as discussions ...
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0answers
126 views

How to constrain higher-order interaction terms in hierarchical bayesian regression models with multiple categorical and metric predictors

Greetings Statistics Wizards! I am building a hierarchical bayesian regression model in which the predicted (y) variable is metric (numerical, continuous) and the predictor variables are both ...
2
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1answer
45 views

Objective interpretation of a parameter

In the following model equation (purely statistical / descriptive model, no mechanistic information involved): $$ Y = a \times X^b $$ considering that $Y$ and $X$ are two measurements, say, $Y$ is ...
0
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1answer
58 views

Log likelihood for inverse gamma

For a gamma distribution, the answer to this question shows that you can just use the log of the gamma distribution density function. Is the same true for inverse gamma? It is the same as the log of ...
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1answer
81 views

Questions regarding interpretation of item parameters: inconsistent results between classical item analysis and item response analysis

I was not trained as a psychometrician, so my questions may be concept-related. If you know different resources, books, or articles that can clear my confusions, please let me know. Thank you very ...
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0answers
19 views

p-test for parameter

Statisticians, number magicians, I was wondering what the best way is to check for the equality of two parameters including possibly a confidence interval and p-value. $$H_0:\beta_1=\beta_2\vert\ ...
4
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1answer
268 views

Questions Regarding Item Response Models – the 3PL model vs. the mixture of 2PL and 3PL model

I currently work on an item analysis for an assessment. The assessment consists of 25 multiple-choice questions. Each question has 4 choices with one correct answer. I used different IRT models to ...
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1answer
37 views

OLS parameter estimation of an expression?

During my research for a class, I came across a paper that said they estimated an equation using OLS. But the parameter they were estimating appeared to be an expression that looked like this (not the ...
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0answers
35 views

Under what assumptions can parameter estimate uncertainty be estimated from the Hessian?

Given a model with some parameters, some data it's attempting to reproduce, and a distance function to quantify how well the predictions correspond to the data, I can fit parameters via a general ...
1
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1answer
75 views

Beta binomial mean different from actual mean

I have data that I am fitting a beta binomial distribution to. The VGAM package for R is being used to do this. However, the the mean of the fitting beta binomial distribution is vastly different from ...
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1answer
50 views

Parameters in a non-parametric model

I have not understood this Wikipedia statement: The difference between parametric model and non-parametric model is that the former has a fixed number of parameters, while the latter grows the ...
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2answers
162 views

Estimation of probability mass function using finite samples [closed]

Suppose $X_1, X_2, \dots, X_N$ are $N$ random samples of a discrete probability distribution such that $X_i \in \{1, 2, \dots, K\}$. The probability distribution $p$ used for sampling is ...
0
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1answer
221 views

Beta distribution vs beta binomial distribution: alpha and beta

I have been attempting to estimate alpha and beta from a beta binomial distribution given my data. There are R packages like VGAM to do this. I am wondering if there is a difference between estimating ...