Questions tagged [parameterization]

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

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3answers
358 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 + \exp(\beta_3)...
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0answers
66 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
56 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 know ...
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0answers
142 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 ...
2
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2answers
621 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 ...
2
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1answer
191 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 Weibull-...
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0answers
396 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
57 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 ...
2
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1answer
157 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
22 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
22 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 &...
5
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2answers
4k 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 ...
8
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1answer
3k 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 ...
1
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1answer
448 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
302 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, ...
0
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1answer
83 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 ...
1
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1answer
72 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
1k views

Calculating parameters for a mixture of beta distributions

I have two beta distributions with known parameters: ...
8
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1answer
1k 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
236 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 $f(x)$ $\nabla_{f(x)}...
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2answers
615 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. hat ties directly into the question. Although the ...
2
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0answers
111 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 ...
2
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1answer
50 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
345 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
280 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
23 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
782 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
512 views

Count Data Model, Poisson Distribution and Rounding?

In doing a count data model using a Poisson distribution, should the estimate (output) be rounded (or the ceiling) if your target variable is always a whole number in the input training target data ...
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1answer
43 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
150 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
159 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 ...
5
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1answer
151 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 ...
2
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2answers
576 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
1k 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 ...
1
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1answer
402 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'': $f\left(x;\alpha,\beta\right)=\frac{\beta^{\alpha}}{\...
1
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1answer
41 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 $\theta=1$)...
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0answers
120 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 ...
7
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1answer
2k 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 ...
9
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2answers
1k 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} \...
4
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1answer
6k 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 \right)\beta^{\alpha}}exp\left\{{-\frac{x^2}{2\sigma^{...
3
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0answers
53 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 $\min_{\...
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0answers
85 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 ...
2
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1answer
2k views

Likelihood ratio test for comparing two exponential distributions

I am trying to use a likelihood ratio test to compare the parameters of two exponential distributions. by this thread Likelihood Ratio for two-sample Exponential distribution I found that I can use ...
0
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1answer
670 views

Point estimation MLE and MME

Consider the family of probability mass functions given by f(x;k) = 3(4^(k-x)) x = k + 1, k + 2,.... and indexed by parameter k E Z. For a random sample of size n, derive with justification: a) ...
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1answer
310 views

How do models, parameters, specifications, restrictions and assumptions relate?

So this has been something I've been struggling with for a long time: The specification of a particular model is subjective. However, there seems to be objective ('true') values of the parameters we ...
4
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2answers
2k views

Confusing Holt-Winters parameters

I have got a model for forecasting using holt-winters. However the parameters confuse me... The parameters show that there is no trend or seasonality even though there is definite trend and ...
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0answers
71 views

Do assumptions for estimators affect population parameters?

TL;DR: Specifying a model (a collection of restrictions over a sample space) specifies the model parameters. Specifying an estimation procedure adds additional number of restrictions (assumptions?). ...
0
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1answer
195 views

Calibrating Generalized Hyperbolic distribution in R - which parameters are valid and allow for a numerical calculation of absolute moments

I am using the R-package ghyp in order to calibrate and model. In fact my coding is based on this paper. I know that I could do quite a robust fit using ...
1
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1answer
115 views

Stable Distribution Log-likelihood and AIC values

I have used the stableFit function from the fBasics package to come up with parameters (alpha, beta, gamma, and delta) for a stable distribution as you can see below: ...
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1answer
1k views

Definition of Parameters [duplicate]

I imagine this either extremely simple or extremely complex. I am trying to understand the interpretation of the term 'parameter'. A couple of quick online searches deliver an intuitive understanding ...