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

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5 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
18 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
10 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 ...
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1answer
27 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
22 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
25 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
35 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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7 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
28 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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15 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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5 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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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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89 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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66 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
179 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 ...
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1answer
159 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
20 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
65 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 ...
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1answer
53 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
23 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 ...
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29 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 ...
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1answer
45 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
60 views

Calculating parameters for a mixture of beta distributions

I have two beta distributions with known parameters: ...
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1answer
127 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
104 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 $f(x)$ ...
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1answer
94 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 ...
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0answers
23 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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96 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
43 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 ...
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66 views

Multivariate normal: from canonical parameterization to mean parameterization (or vice versa)

In their book (https://www.eecs.berkeley.edu/~wainwrig/Papers/WaiJor08_FTML.pdf) Wainwright and Jordan consider two types of parameterizations in the exponential family, the canonical parameterization ...
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1answer
52 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
65 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
18 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\ ...
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1answer
219 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
35 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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33 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 ...
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1answer
65 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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0answers
24 views

Implementing evolutionary algorithms

We're trying to to minimize the following functions using Multi Objective Evolutionary Algorithms : $\mathrm{minimize}~\lambda_q(1-a)E(N)E(X)+\lambda_xE(N)E(\max(X/a-R,0))$ ...
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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
111 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 ...
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1answer
182 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 ...
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1answer
45 views

Prior for gamma distribution in “mean form”

I need to specify priors for the parameters of a gamma distribution. Normally the gamma distribution is parametrized in either the "rate-form'': ...
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1answer
17 views

Is there a family of processes centred on the Poisson process?

I am looking for a model, characterized continuously by a single parameter, to describe the arrival times of buses with unit expected interarrival time. At one extreme of the parameter (say ...
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0answers
70 views

What have I done wrong implementing this Bayesian method for fitting a circle to noisy data?

I have noisy measurements of movement along a circle. I want to fit a circle to these measurements. I tried two methods, a straight forward moment fit, and then an ODR fit (described here. However ...
3
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1answer
236 views

CV for model parameter tuning AND then model evaluation

I have a basic question on using cross-validation for model parameter tuning (model training) and model evaluation (testing) similar to this Model Tuning and Model Evaluation in Machine Learning I ...
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2answers
307 views

Fisher information matrix determinant for an overparameterized model

Consider a Bernoulli random variable $X\in\{0,1\}$ with parameter $\theta$ (probability of success). The likelihood function and Fisher information (a $1 \times 1$ matrix) are: $$ \begin{align} ...
3
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1answer
1k views

Find the mode of a probability distribution function

I am trying the find mode of a probability distribution function given by \begin{equation} g(x/\alpha,\beta,\sigma)=\frac{1}{\Gamma \left( \alpha ...
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0answers
74 views

Parameter estimation using lmom package

As a part of my risk management job, I need to try to fit various distributions to loss data. I have been using the lmom package in R for estimating parameters for ...
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0answers
34 views

Verification of an optimal parameter from an empirical CDF

Suppose we have the following model for the variable $V_5$: $$V_5 = \prod_{k=1}^5(e^{\mu + 0.2X_k}+0.05e^{0.05Y_i - 0.00125}), X_i,Y_i\sim N(0,1)$$ What I wish to do is to solve the problem ...
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49 views

forcing certain parameters to be skipped during optim in R

I have a code which tests each possible order of ARIMA and selects the best model by choosing the one with the absolute minimum sum of lags from the PACF graph. The code then proceeds to add weight to ...