Questions tagged [parameterization]

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

Filter by
Sorted by
Tagged with
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?
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 ...
0
votes
0answers
28 views

Starting values for an nls model in R [duplicate]

I'm trying to fit an exponential model using nls, but I don't know how to select the starting values for the parameters. I know this question has been answered multiple times, but I spent some days ...
3
votes
4answers
1k views

Fitting SIR model with 2019-nCoV data doesn't conververge

I am trying to calculate the basic reproduction number $R_0$ of the new 2019-nCoV virus by fitting a SIR model to the current data. My code is based on https://arxiv.org/pdf/1605.01931.pdf, p. 11ff: <...
0
votes
0answers
29 views

parameterize distribution of subsets

Suppose there is a set $S=\{1, 2, 3, ..., n\}$, then I need a distribution of its subsets with fixed size k, which can be denoted as $A=\{x_1, x_2, ..., x_k\}$ where $x_1$ to $x_k$ are from 1 to n. ...
0
votes
0answers
26 views

What is the definition of a scalar parameter?

I'm having trouble understanding what explicity is a scalar parameter. I understand what a location parameter and scale parameter represent but what exactly is the definition of a scalar parameter? ...
0
votes
0answers
14 views

Reparameterize b(K,pi) in terms of theta

Question: $X_1, ... , X_n$ follows a binomial distribution with parameters K and 0 < $\pi\ <1.$ Use properties of Regular Exponential Class of distributions to show that the sample total $T = \...
0
votes
0answers
13 views

Delimit the area in that parameter space that contains 95.4% confidence

Given the equation $y = fc + fe\times \sin(2\pi(x-t_0)/12)$ Considering the two parameters of amplitude fc and fe simultaneously, delimit (using the χ2 variation method) the area in that parameter ...
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 ...
0
votes
0answers
35 views

Robustness of a model to learnt parameters

There is a recent push to study how sensitive a model is to small changes in its input. This has also been studied from an adversarial point of view: e.g what is the smallest input perturbation that ...
0
votes
2answers
85 views

Why can't algorithms avoid overfitting themselves?

So, I understand overfitting (bonus question: precise statistical definition of overfitting?). You don't want to match the noise in your sample. What I don't understand is why this requires a ...
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: ...
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 ...
0
votes
0answers
29 views

Estimate distribution of aleatoric variable using Bayesian inference

Given a model as follows: $$y = cx + e$$ where y is the model output, x is the model input, c is an unknown variable and e is a Gaussian model error with zero mean: $$e \sim N(0,\sigma)$$ Data is ...
0
votes
0answers
41 views

Is this parametrization identifiable?

So I have this problem which I'm unsure of my answer. Any tip on how to treat it differently is more than welcome. X and Y are independent $\mathcal{N}(\mathcal{\mu_1},\sigma^2)$ and $\mathcal{N}(...
0
votes
0answers
27 views

Why are decision trees (especially ID3) non-parametric?

I was going through the definition of parametric and non-parametric models. So the parametric are the ones which have a fixed number of parameters that you are trying to learn and this number is ...
0
votes
0answers
25 views

State whether the model in question is parametric or non-parametric

The number of eggs laid by an insect follows a Poisson distribution with an unknown mean $\lambda$. Once laid, each egg has an unknown chance, $p$, of hatching and the hatching of one egg is ...
3
votes
1answer
67 views

The meaning of a parameterization of the logarithmic distribution

In calculus one learns that $$ p + \frac{p^2} 2 + \frac{p^3} 3 + \frac{p^4} 4 + \cdots = -\log(1-p). \tag 1 $$ Thus a discrete probability distribution on the set $\{1,2,3,\ldots\}$ is given by $$ \Pr(...
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 ...
0
votes
1answer
31 views

Flexible models and parameters

I just started reading Introduction to Statistical Learning with R and I am currently trying to work through the exercises. One of the questions is "What are the advantages and disadvantages of a ...
6
votes
2answers
2k views

gamma parameter in xgboost

I came across one comment in an xgboost tutorial. It says "Remember that gamma brings improvement when you want to use shallow (low max_depth) trees". My understanding is that higher gamma higher ...
0
votes
0answers
11 views

Speed of transition parameter constraints

Given a logistic smooth transition regression \begin{equation} y_{t}=x_{t}^{\prime }\beta _{1}(1-{g}(z_{t};\gamma ,\delta ))+x_{t}^{\prime }\beta _{2}{g}(z_{t};\gamma ,\delta )+\varepsilon _{t}% \text{...
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 ...
0
votes
0answers
46 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
49 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
72 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
votes
1answer
136 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
18 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
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 ...
0
votes
0answers
23 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
votes
0answers
28 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
25 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
95 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 $\ln(X)$ ...
3
votes
1answer
298 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
114 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 ...
2
votes
1answer
172 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
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
2answers
121 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
votes
0answers
128 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
51 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
407 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 ...
1
vote
1answer
113 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
30 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
91 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
49 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
62 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
59 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
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, ...

1 2 3 4 5