Questions tagged [parameterization]

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

74 questions with no upvoted or accepted answers
Filter by
Sorted by
Tagged with
10
votes
0answers
407 views

Asymptotic property of tuning parameter in penalized regression

I'm currently working on asymptotic properties of penalized regression. I've read a myriad of papers by now, but there is an essential issue that I cannot get my head around. To keep things simple, I'...
4
votes
1answer
189 views

Normalize a periodic parameter

I am using inverse modelling software (PEST) to estimate a periodic parameter for the direction of anisotropy, $\hat{\theta}$, which is somewhere in $[0^{\circ}, 180^{\circ})$ (i.e., has a wavelength ...
3
votes
0answers
30 views

Why are these 2 ARIMA formulations equivalent?

In the "Understanding constants in R" section of his book, Hyndman & Athanasopoulos textbook "Forecasting: Principles and Practice" claims that the following AR processes equations are equivalent: ...
3
votes
0answers
99 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
0answers
47 views

Family of flexible parametric mappings $f_\theta:(0,1) \rightarrow \mathbb{R}$?

For the purpose of reparameterizing a model (mostly with the goal of improving MCMC efficiency), I am looking for a family of flexible parametric mappings $f_\theta:(0,1) \rightarrow \mathbb{R}$ such ...
3
votes
0answers
56 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 ...
3
votes
0answers
54 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_{\...
2
votes
1answer
28 views

How to parameterize a bivariate Normal distribution output for a neural network?

For a neural net where the output is a Gaussian distribution, the output is usually parameterized as $(\mu=O_1, \sigma^2=e^{O_2})$. That is to say, the neural net will output the mean, and also output ...
2
votes
0answers
11 views

Alternative to plug-in estimation for log-tranformed linear model

I want to estimate a relationship of the form: $$y=ax^b\times\epsilon$$ If I log this model i get: $$\log(y)=\log(a)+b\log(x)+ \log(\epsilon)$$ If I then proceed and estimate this model using a ...
2
votes
1answer
27 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 ...
2
votes
0answers
36 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
0answers
58 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) ...
2
votes
0answers
151 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 ...
2
votes
0answers
48 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|...
2
votes
0answers
724 views

glmnet returning lambda that gives all-zero coefficients as optimal lambda

Before I start, I have already looked at the answers for related questions: How to interpret all zero coefficients in the results of cv.glmnet? Why is cv.glmnet giving a lambda.min that is ...
2
votes
0answers
241 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 ...
2
votes
0answers
117 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
votes
0answers
980 views

Rejection sampling from a Gamma distribution using a Cauchy proposal

i'm trying to find the parameters $ \gamma,x_0$ of a standard Cauchy distribution : $$T(x)= \frac{1}{(\pi \gamma (1+(\frac{x-x_0}{\gamma})^2))} $$ To perform rejection sampling from a gamma ...
1
vote
1answer
41 views

Why is it easier to estimate $P(X|Y)$ rather than $P(Y|X)$ in terms of number of parameters?

In chapter 3 of the book by Mitchell ("Generative and discriminative classifiers: Naive Bayes and logistic regression") he states that "accurately estimating P(X|Y) typically requires many more ...
1
vote
0answers
23 views

Strategies for analyzing the functional relationship between two time series?

Suppose we have time-dependent survey data about name recognition for a political campaign. We're interested in learning how campaign spending effects that name recognition. My interest is in ...
1
vote
1answer
25 views

Expected value without complete sample space

The book way: Suppose, we have a bag with 8 balls numbered 1-8, we want to estimate the population parameter mean. we note down the entire sample space. (1,1)(1,2).. (8,8) calculate mean of each ...
1
vote
0answers
17 views

Hypothesis test practice question

" Prof. J conducts a hypothesis test on whether the proportion of all students who bike to school (denoted as p) equals 30%. Specifically, Prof. J has H0: p=0.3 versus HA: p≠0.3. He obtains a P-value ...
1
vote
0answers
8 views

How do I create error bounds after parameter calibration?

I have a power transform $f$ I am applying to an Ornstein-Uhlenbeck stochastic process $\{X(t), t\geq 0\}$: $$dX(t) = \kappa (\mu - X(t)) dt + \sigma dW_{t}.$$ From here, I was able to plug in my ...
1
vote
1answer
44 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 = \...
1
vote
0answers
229 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
30 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 ...
1
vote
0answers
82 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 ...
1
vote
1answer
52 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 ...
1
vote
0answers
178 views

Parameters estimation in custom chi-squared distribution

For modeling purposes, I need to add a parameter (denoted by $\alpha$) allowing us to control the location of a Chi-squared distribution (instead of always beginning at 0). The probability density ...
1
vote
0answers
27 views

No loss of generality

Let $$ \underset{n \times n}{\Sigma_t} = \underset{n \times m}{A} \underset{m \times m}{\Sigma_t^f} \underset{m \times n}{A'}, \qquad m <n. $$ In this model $A$ is the parameter matrix. The authors ...
1
vote
0answers
47 views

What are some interesting parameterizations of $4 \times 4$ correlation matrices, and also perhaps their associated jacobians?

I am studying (mainly using Mathematica) some constrained integration problems in which the six-dimensional convex set of $4 \times 4$ correlation matrices plays a central role. In light of this, I ...
1
vote
0answers
175 views

Data simulations for SVM : study of parameters

I'm studying SVM for classification. The first step of my work consists in making a data simulation in order to study the influence of the cost parameter C, the choice of the kernel, for examples. Do ...
1
vote
0answers
87 views

Identifying the parameters of a linear state-space-model using Kalman Filter

I have a linear state space model (SSM) that looks like this \begin{align} {\dot {x}} & = {\rm \textbf{A}}{x} + {\rm \textbf{B}}{u} \\ {y} & = {\...
1
vote
0answers
98 views

Is it justified to estimate residual error by sample variance of residual in bayesian parameterization?

I'm using Bayesian inference to estimate the parameters of a dynamical system which is comprised of several ordinary differential equations (ODEs). I use a gaussian error model. I would like to know ...
1
vote
0answers
18 views

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 ...
1
vote
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) ...
1
vote
0answers
60 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 ...
1
vote
0answers
149 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 ...
1
vote
0answers
422 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 ...
1
vote
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 ...
1
vote
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 ...
1
vote
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\ \...
1
vote
0answers
151 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
vote
1answer
48 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 $\theta=1$)...
1
vote
0answers
122 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 ...
1
vote
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?). ...
1
vote
0answers
118 views

Assumptions implied by “pairwise marginal” parameterization of MRF

I'm trying to understand the assumptions of different parameterizations in a Markov network. In this case, I'm trying to understand the assumptions (and effects) that result from parameterizing ...
1
vote
0answers
38 views

Floor effects in Bayesian estimate, can I reparameterize?

I'm replicating an old study and I have two sets of existing estimates which measure a similar effect, namely the presence of a studied item in memory over time: ...
1
vote
0answers
637 views

Parameters estimation of ODE system

I have all the data and an ODE system of three equations which has 9 unknown coefficients (a1, a2,..., a9). ...
0
votes
0answers
14 views

How to implement the estimation of parameters in negative binomial distribution in python?

Assuming the negative binomial distribution, How can I implement the estimation to parameters(r & p) especially by MLE? Which function or package should I use? scipy.stats, sympy?