Questions tagged [parameterization]
For questions about how to parameterize some statistical model, or comparisons between different ways to parameterize.
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24 views
Can someone explain the concept of parameter didactically to me? [closed]
Let $\mathcal{P}$ denote a family of probability distributions on $\textbf{R}^{n}$. We then use a parametrization to describe $\mathcal{P}$, that is, a map $\theta\rightarrow\mathcal{P}_{\theta}$ from ...
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0answers
20 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
23 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
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1answer
22 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
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1answer
35 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
56 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 ...
4
votes
1answer
47 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 ...
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0answers
12 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
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0answers
30 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
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2answers
111 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 ...
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0answers
50 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
41 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
212 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 ...
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0answers
34 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
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1answer
77 views
How to identify a Bayesian SEM parameter in R package blavaan
I have fit a Bayesian SEM using the R package blavaan.
...
1
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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
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1answer
82 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 ...
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1answer
33 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
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0answers
16 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
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1answer
43 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 ...
0
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0answers
58 views
Fitting a reinforcement model to reaction time
I have a data set of reaction times in a simple reward/punishment task, in which the rate of feasible trials is probabilistical (around 2/3). After having a look at the reaction times, it seems ...
3
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0answers
75 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, ...
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0answers
80 views
MCMC/Bayesian Inference Model Fitting: Parameters over-fitting to a sharply peaked data point. How can I fix this?
I am trying to fit three models to a data set:
Method:
Each measurement has some measurement uncertainty
Generate X samples from a gaussian with mean of the measurement and std of the measurement ...
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. $$
Supposing $X$ to be so distributed, one has
\begin{align}
& \mu = \...
2
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0answers
40 views
Linear combination of two non-independent random variables
I would like to check if the slope coefficients retrieved from two separate regression models are significantly different. Both models have the same independent variables. The dependent variable (DV) ...
3
votes
1answer
62 views
Sampling parameters from exponential family
So suppose PDF $f_{X|\theta}(x_1,...,x_n;\theta_1,...,\theta_m)$ is from the exponential family. Is there any theory or general guidelines for sampling parameters from this PDF?
This question is not ...
-1
votes
1answer
37 views
use data of table in R [closed]
I have a table of data that I have already imported in R as variable Dataset and I want to apply the function fitdistr() to my ...
0
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0answers
12 views
Parametrization of a model with data-sheet's sensor information or with empirical data
When working with a 3D laser sensor (LiDAR), the volumetric point density versus distance $\rho_r$ can be theoretically worked out taking into account the physical properties of the laser (number of ...
1
vote
1answer
54 views
Anyone seen this parametrization of Weibull?
My lecturer uses a parametrization of Weibull that I can't find any where else so I'm wondering are they mistaken. Can anyone confirm if this is legitimate pdf of a Weibull?
$$\lambda\theta y^{\...
0
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1answer
48 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
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1answer
228 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 $\theta_4=3\theta_2^2$, ...
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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
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1answer
121 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=...
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1answer
48 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 ...
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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
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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 = \...
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1answer
111 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
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0answers
119 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
169 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
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0answers
191 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
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0answers
26 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
32 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:
$$
GB2(y;a,b,p,q) = \frac{|a|...
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0answers
68 views
Basics of Akaike's Information Criterion in GIS/Hydrology
I have been asked to use the AIC to assess the relative fitness of various terrain wetness index (TWI) methods for predicting soil moisture in a specific study site.
The TWI is calculated from a ...
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0answers
46 views
What set of parameters should I choose for Naive bayes and GBM models so that it creates minimal fitting error?
I understand that different set of parameters has to be chosen for each model so as to avoid under or over fitting. But is there is a 'safe set' of parameters which can be used for the widest range of ...
1
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2answers
132 views
Parameter estimation of exponential distribution depending on multiple factors/attributes
for a simulation I’ll need to simulate project delays.
I’ve data on 20k projects with delays in quarters. Some of them were finished ahead of plan (i.e. neg. delays) others with a delay of 1-16 ...
1
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1answer
1k views
GARCH vs ARCH models - which is more parsimonious?
As I understand the inclusion of the GARCH term, $\sigma^2$, in a GARCH model allows for an infinite number of time series terms, $\epsilon^2$, to influence the conditional variance. Is this the case? ...
2
votes
1answer
159 views
Merits of reparameterizing the Gamma and inverse Gamma
Wikipedia states that the PDFs for the Gamma distribution is:
$$
f(x|\alpha,\beta) = \frac{\beta^\alpha}{\Gamma(\alpha)}x^{\alpha-1}\exp(-\beta x)
$$
However, in Rasmussen 2000, the pdf for the ...
-1
votes
1answer
71 views
Optimize a regression forest (Better parameters and how to obtain them)
I'm currently working on sales forecasting.
I'm using a Regression Forest to make my forecast. (with MLLib from Spark on Databricks)
I'm trying to find what features are useful in my forecasting.
...
0
votes
1answer
50 views
Is this sensible: $P(y_{1}<Y\le y_{2}\mid Y\sim\mathcal{D}(\mu))$
I want to write:
$$P(y_{1}<Y\le y_{2}\mid Y\sim\mathcal{D}(\mu))$$
to say:
The probability of $Y$ being between $y_1$ and $y_2$
given that $Y$ is a random variable distributed according to ...
