Questions tagged [parameterization]
For questions about how to parameterize some statistical model, or comparisons between different ways to parameterize.
193
questions
0
votes
0answers
10 views
Parameter Tuning for auto-regressive Neural networks (NNETAR)
I am analyzing time series data on electricity prices using a variety of methods (ARIMAX, TBATS, STLM) including the auto-regressive feed-forward neural network NNETAR, which is implemented in the ...
0
votes
0answers
42 views
What to do when the meaning of a variable has changed over time?
I have dataset of a company with 2014 data with 15 variables then 2018 data with same 15 variables.I want to combine both the datasets however the meaning of 1 variable has changed meaning that ...
0
votes
1answer
20 views
What’s the difference between k-theta and alpha-beta parameterization for gamma distribution?
In my book “Mathematical statistics with Applications”, written by Wackerly, it’s stated that there are two methods for parameterization of gamma distribution. The first one is k-theta and the second :...
0
votes
0answers
26 views
Changing a conditional probability to a deterministic function
Suppose that we have a conditional density function $p(y|x;\theta^*)$, where $\theta^*$ represents distribution parameters and are assumed to be deterministic. Is it possible that we write this ...
0
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1answer
29 views
Different notions of over-parameterization
While reading a paper, I came across the statement
This prediction function will be
parameterized by a parameter vector $\theta$ in a parameter space
$\Theta$. Often, this prediction function ...
0
votes
0answers
15 views
Confused by “mean” and “median” of $\alpha$ parameter in Lognormal Distribution
I read a book and find the following content (Fig.1). It is about lognormal distribution. What confused me is in the red box.
In Fig.1, $\alpha$ is said "the mean of $z$ on the log scale". Then I ...
2
votes
0answers
10 views
Is there a formal relation between weight regularization and compression?
In my understanding, compression, strictly speaking, means that we diminish the amount of data required to describe something, such as a model. E.g. compressing an image file means to create a file ...
0
votes
0answers
22 views
Estimation of covariance over a range of independent variable
I have a set of data that comprise 2 dependent variables (let's call them $x_1$ and $x_2$) evaluated at different temperatures, T.
There is an assumption that for a range of T ($T_0<T<T_1$) ...
0
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0answers
24 views
Mixed parameterization of sample from normal distribution
I am studying exponential families and mixed parameterizations. Now, I am told that
$$
\mathbf{\theta} = \begin{bmatrix}\mu\\ -\frac{1}{2\sigma^2}\end{bmatrix}
$$
is the parameter in a variation-...
1
vote
1answer
23 views
How can I write an asymmetric-BEKK(1,1,1) model
To write a BEKK(1,1) model, I would write something like this,
$$H_t=C^*C^{*'}+A_{11}\varepsilon_{t-1}\varepsilon_{t-1}'A_{11}'+ B_{11}H_{t-1}B_{11}' $$
How could I extend this to write the BEKK(1,...
3
votes
1answer
52 views
good terminology for the parameters of a lognormal distribution?
Is there any good short terminology for the two parameters of a lognormal distribution?
I have been using mean-log for $\mu$ and volatility for $\sigma$, where the lognormal variable $X$ has $\ln(X)$ ...
2
votes
1answer
86 views
Understanding the definition of a location parameter
In some probability distributions, like normal or (non-standard) t distributions etc, there are location parameters such that a change to this parameter leads to the distribution moving rigidly to the ...
3
votes
1answer
53 views
Formula for cross-classified (a.k.a., crossed random factors) mixed effects model with interaction between two “second level” variables
I have a crossed-classified (Hox, 2010) mixed effects model—also known as crossed random factors (West, Welch, & Galecki, 2015), but I am struggling with how to write the formula for an ...
0
votes
0answers
15 views
Convert regression parameter standard error estimates to standard deviation estimates
Lets say I fit a linear model (in R), of y ~ x:
x <- runif(100,0,5)
y <- x*0.5 + rnorm(length(x))
summary(lm(y~x))
The summary output returned is:
...
2
votes
1answer
163 views
Some questions about exponential families
Regarding the book The Bayesian Choice I understand most of chapter three on exponential families, but there are two parts I have trouble understanding.
The first is
Consider$$f(x|\theta)=h(x)\...
2
votes
0answers
31 views
Choosing Gaussian PDF basis bandwidth depending on number of bases and range of data
Summary (details below!)
I have a basis expansion of $m$ (univariate) Gaussian PDFs to model the density of a sample $X$. The means of these PDFs are spaced equidistantly through the domain of $X$ ...
2
votes
2answers
112 views
Testing whether the conditional correlations/covariances differ between two groups
I have two samples of variables $\{y_{1i},y_{2i},x_i,s_i\}$. Where $y_1$ and $y_2$ are binary variables, $x$ is a continuous variable and $s$ is a sample indicator, taking the value 0 in one sample ...
0
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0answers
82 views
How to find parameter $k$ from a negative binomial distribution in R?
I want to find the value of parameter $k$ from my data set. The data set is composed of several populations. Should I calculate the parameter $k$ for each subpopulation, or for the population at large?...
2
votes
1answer
45 views
Can every parameter $\Theta$ in Bayesian modelling be explained via De Finetti`s representation theorem
My question is the following: I recently got to know (and love) De Finetti`s representation theorem and I now started to read a Book an Bayesian statistics. However this book simply takes as the ...
4
votes
1answer
241 views
Correct understanding of De Finetti`s representation theorem
I am currently interestend in understanding De Finetti`s representation theorem. As I am only familiar with Frequentist thinking I have some problems to understand its meaning. I have already read the ...
0
votes
0answers
35 views
How to test for differences between model parameter estimates for different datasets?
Description of analysis
I am considering grain yield response to available nitrogen with a linear-plateau piecewise regression model for two different field studies, denoted by the variable ...
1
vote
1answer
81 views
How to identify a Bayesian SEM parameter in R package blavaan
I have fit a Bayesian SEM using the R package blavaan.
...
1
vote
1answer
29 views
Why are mixed effect methods more effective when data are limited
In the study in here, it is said that mixed effects models are better in estimating parameters of a ODE system when there is only very small number of data to estimate the parameters. So, in a ...
1
vote
1answer
83 views
From OLS to semi-parametric GAM: parametric vs no-parametric
I am quite new to this kind of topic, but for my master thesis i built an multiple linear regression with OLS. Now I want to control for non-linear relationships using a semi-parametric GAM. My ...
0
votes
1answer
38 views
GLMMs, stable isotope distribution analysis
I am currently working with a set of samples of stable isotopic concentrations obtained from a group of individuals.
I am trying to process this data through a glmm() from the package lme4 to ...
0
votes
0answers
19 views
How to Interpret Parameter Estimate Output from SPSS [duplicate]
Dear Community Members,
Given the outputs of the SPSS analysis, how can the exp (B ) and Beta values be interpreted in terms of odd ratio ? and in relation to how the independent variable affects the ...
0
votes
1answer
44 views
Calibration of an individual-based model of an epidemic
I am currently developing an individual-based (or agent-based) mathematical model (IBM) of an epidemic. I want to calibrate the transmission parameters in my IBM to match empirical data (epidemic ...
3
votes
0answers
80 views
Probability distribution over shapes (or: How to parameterize arbitrary polygons)
Has there been work on modeling variations of a 2D shape? E.g., say you want a distribution over 5-sided polygons, or over ellipses, or curved shapes? For simple shapes, like circles, rectangles, ...
3
votes
1answer
26 views
Is there a standard name for a certain parameter for the beta distribution?
The beta distribution is $$ (\text{constant})\times x^{\alpha-1}(1-x)^{\beta-1} \, dx \quad\text{for } 0\le x\le 1. $$
Supposing $X$ to be so distributed, one has
\begin{align}
& \mu = \...
2
votes
0answers
41 views
Linear combination of two non-independent random variables
I would like to check if the slope coefficients retrieved from two separate regression models are significantly different. Both models have the same independent variables. The dependent variable (DV) ...
3
votes
1answer
64 views
Sampling parameters from exponential family
So suppose PDF $f_{X|\theta}(x_1,...,x_n;\theta_1,...,\theta_m)$ is from the exponential family. Is there any theory or general guidelines for sampling parameters from this PDF?
This question is not ...
-1
votes
1answer
38 views
use data of table in R [closed]
I have a table of data that I have already imported in R as variable Dataset and I want to apply the function fitdistr() to my ...
1
vote
1answer
63 views
Anyone seen this parametrization of Weibull?
My lecturer uses a parametrization of Weibull that I can't find any where else so I'm wondering are they mistaken. Can anyone confirm if this is legitimate pdf of a Weibull?
$$\lambda\theta y^{\...
0
votes
1answer
49 views
Parameters in a neural tensor network
I am reading the paper of "Reasoning With Neural Tensor Networks for Knowledge Base Completion". I read it many times but I couldn't understand the parameters that are used especially the parameter U. ...
6
votes
1answer
233 views
Generalized Normal Distribution
Is there a known distribution, $f(x|\theta_1,\theta_2,\theta_3,\theta_4)$, with the following properties:
$E(X^n)=\theta_n$ for $n \in \{1, 2, 3, 4\}$.
If $\theta_3=0$ and $\theta_4=3\theta_2^2$, ...
0
votes
0answers
36 views
Special cases of distributions under different parameterizations
Suppose you have two instances of a distribution that are parameterized differently, and for one of them a certain restriction on the parameter values of the pdf or CDF results (perhaps after some ...
2
votes
1answer
130 views
Are the Feller-Pareto and the generalized beta distributions really the same?
The Feller-Pareto distribution was originally is defined in terms of a transformed beta distribution. If $Y\sim \beta(\gamma_1, \gamma_2)$ then $W=\mu + \sigma\left(\left(1/Y\right) - 1\right)^\gamma=...
0
votes
1answer
53 views
How to calculate the probability of the parameters?
I am reading the Wikipedia article on posterior probability and I note the expression:
$$P(\theta|X) = \frac{P(X|\theta)P(\theta)}{P(X)}$$
I understand that $\theta$ represents the parameters of the ...
1
vote
0answers
24 views
Parameter estimation of 3d model
Suppose we have cost data on some product line, let's say clothing. A simple model of the true cost of the clothing could look something like this:
C$_{i,j,k}$ = c$_i \cdot \alpha_j \cdot \beta_k $,
...
1
vote
1answer
43 views
How to select optimal observation number n from two marginal distributions?
I have two marginal distributions $(Y_1,Y_2)$ that follow distributions $N(\mu_1,50)$ and $N(\mu_2,100),$ respectively. I can allow for a total of 100 observations to estimate the parameter $\theta = \...
0
votes
1answer
125 views
Normalizing Flows, Real NVPs and Inverse Autoregressive Flows - Used for Probabilty Density Approximation or for Sampling?
Suppose we have a parametric family $g(x;\theta)$, where $\theta$ are the parameters. As far as I can tell, there are two ways we can use this family to model a probability distribution:
Probability ...
1
vote
0answers
127 views
How to fit parameters of a stochastic model applied to agent modeling?
I have a network of agents, these are modeled roughly according to the paradigm of "Agent_Zero: Toward Neurocognitive Foundations for Generative Social Science". The main feature is that the equations ...
1
vote
1answer
185 views
Finding a closed-form solution of nonlinear function for parameter estimation
I've come across this problem of estimating parameters of nonlinear model using closed-form solution. I've read that logarithms can be used for certain forms, but they can't be applied to everything. ...
1
vote
0answers
205 views
Degrees of freedom of a hierarchical model
I have a nonlinear regression model that has two independent parameters, $a$ and $b$, and one dependent parameter, $c$, which is dependent on the independent parameters $\alpha$ and $\beta$ estimated ...
1
vote
0answers
28 views
How to map 2 vectors on the hyper plane to a similarity metric?
I am working on a face recognition application and one of the features I want to include is to compare if two pictures of $2$ people is the same. I have written code (Convoluted neural network) to ...
2
votes
0answers
37 views
How could one prove that b in the GB2 distribution is a scale parameter?
In the Generalized Beta distribution of the second kind (GB2), where a, p, and q are shape parameters and b is a scale parameter, the pdf is defined on $\mathbb{R}_+$ by:
$$
GB2(y;a,b,p,q) = \frac{|a|...
1
vote
0answers
72 views
Basics of Akaike's Information Criterion in GIS/Hydrology
I have been asked to use the AIC to assess the relative fitness of various terrain wetness index (TWI) methods for predicting soil moisture in a specific study site.
The TWI is calculated from a ...
0
votes
0answers
49 views
What set of parameters should I choose for Naive bayes and GBM models so that it creates minimal fitting error?
I understand that different set of parameters has to be chosen for each model so as to avoid under or over fitting. But is there is a 'safe set' of parameters which can be used for the widest range of ...
1
vote
2answers
138 views
Parameter estimation of exponential distribution depending on multiple factors/attributes
for a simulation I’ll need to simulate project delays.
I’ve data on 20k projects with delays in quarters. Some of them were finished ahead of plan (i.e. neg. delays) others with a delay of 1-16 ...
1
vote
1answer
1k views
GARCH vs ARCH models - which is more parsimonious?
As I understand the inclusion of the GARCH term, $\sigma^2$, in a GARCH model allows for an infinite number of time series terms, $\epsilon^2$, to influence the conditional variance. Is this the case? ...
