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More about the deterministic part of Wold decomposition

This is a follow-up on this question of mine. Wold's representation theorem states that every covariance-stationary time series $\{Y_t\}$ can be written as the sum of two time series, one ...
Richard Hardy's user avatar
5 votes
1 answer
175 views

Role of `trend` argument compared to integral order in ARIMA model

I am currently studying ARIMA models. When I checked for a Python library to train one, I stumbled upon statsmodels which features ARIMA (and SARIMAX from which ...
Marco Bresson's user avatar
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1 answer
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How come the deterministic part of Wold decomposition does not violate stationarity?

Wold's representation theorem states that every covariance-stationary time series $\{Y_t\}$ can be written as the sum of two time series, one deterministic and one stochastic: $$ Y_t=\sum_{j=0}^\infty ...
Richard Hardy's user avatar
1 vote
1 answer
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Can two states have different actions in a deterministic policy? How to specify states which have probability linked with them in the policy?

The agent has two actions, a0 and a1, whose effects in each state σ0; . . . ; σ3 are described in Figure 1. The edges from actions are labeled with the probability that this transition occurs. For ...
Trileo Stark's user avatar
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Modeling the causal impact of insurance benefits on customer satisfaction

Consider the following scenario: A health insurance company offers a few dozen different health insurance plans. Within each plan there are many benefits which can take on different values, such as ...
AJV's user avatar
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3 votes
3 answers
141 views

Deterministic formula for average number of unique items picked

I am curious how to formulate a deterministic answer to a problem I have in mind. I have computed it stochastically, but am unsure of how to frame and compute the problem deterministically. My prob &...
Jason Morrison's user avatar
1 vote
1 answer
38 views

Expected value of the max of scaled powers of the same random variable

I've been looking at order statistics and the behavior of expectations when max is involved, but that literature always discussed iid random variables whereas I have a strange situation where I have ...
Ahmed Fasih's user avatar
1 vote
1 answer
75 views

Deterministic part of ARMA's Wold decomposition

According to Wold's Theorem, any covariance-stationary process can be decomposed as the sum of a deterministic part and a purely non-deterministic part, where the latter one has some MA infinity ...
HNUSTAT's user avatar
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12 votes
4 answers
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Is anything inherently random?

Is anything inherently random? Or is all randomness observed in data either "errors in measurement" or "lack of understanding"? Assume we could measure everything with infinite ...
ColorStatistics's user avatar
3 votes
1 answer
261 views

Derive conditional density when there is a deterministic function describing the relationship between $X$ and $Y$

Suppose there are two random variables $X$ and $Y$. I know the marginal density of $X$ and $Y$ and also that $X$ and $Y$ satisfy $f(X,Y)=0$. I wonder how I could get the conditional density $X|Y$, ...
user1292919's user avatar
1 vote
1 answer
128 views

Optimality in Clustering algorithms and an Optimality guaranteed clustering algorithm

So there are lots of clustering algorithms with different characteristics. What I am interested in now is a clustering algorithm which guarantees to find the optimal clustering result (if exists). And ...
Erik's user avatar
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1 answer
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Length of a probability vector?

I'm doing some work on probability vectors, and came across the idea of probability vector length as a measure of how deterministic a probability vector is, as calculated using this equation: The ...
NEW2R's user avatar
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1 vote
2 answers
3k views

Frequentist vs Bayesian and deterministic vs stochastic [closed]

So this is sort of a general/basic, likely dumb question. I'm hoping to get a general idea, to better guide what I search/read. How do these terms relate to each other. I know with Bayesian theory, ...
user228897's user avatar
1 vote
0 answers
323 views

Is hierarchical clustering (with average-linkage and euclidean distance) deterministic?

If I have a dataset called "A" and run n times a hierarchical clustering with average-linkage and euclidean distance on dataset A, will I get n equal clustering solutions (one for each run)?
Peter's user avatar
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2 votes
0 answers
340 views

Is the copula function invariant only under deterministic monotonic transformation?

I read about the following theorem (see Proposition 3 in the picture below) on the invariance of copula under monotonic transformation, my questions is: 1. Are the $T_i$ mentioned in the following ...
ExcitedSnail's user avatar
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1 vote
0 answers
64 views

Is Determinism important for Hyperparameter Tuning?

When training the Model on GPU, different results are retrieved for the same hyperparameters. This effect can be shut down by using CPU or Tensorflow 2.1. with deterministic settings. The Post on ...
Alexander Vocaet's user avatar
1 vote
0 answers
28 views

How to find the factor which is more contributing to an event

I have two datasets. Dataset#1 consists of information of patients having one of the three diseases and the hospital they are treated. Each patient will have only one disease. ...
arshad's user avatar
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1 vote
1 answer
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Differences between realization of the random variable and deterministic variable?

The first question is that can we classify variable into random variable and deterministic variable? The second question is that The possible values taken by a random variable"X"(Uppercase) are termed ...
Bryan Zhang's user avatar
2 votes
1 answer
571 views

Generate value of variables for given correlation coefficient

I would like to generate test data for script used for correlation analysis between quite long variables. Is it possible for a given length of vectors, to generate in relatively simple way ...
MLearner's user avatar
0 votes
0 answers
132 views

Deterministic Assignment to Treatment

When estimating causal effects, you want to compare individuals as similar as possible. It is from this need that stems the exchangeability (/ignorability) or conditional exchangeability (/ ...
Fabio I.'s user avatar
2 votes
2 answers
187 views

How can we best explain causality for the uninitiated?

How can we best explain causality in layman's terms? There seem to be two main types of causality. One is probabilistic causation, the other is called determinism in philosophic circles or just ...
Carl's user avatar
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1 answer
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Are Gaussian Mixture Models stochastic or deterministic?

Each time we generate a gmm model, we obtain slightly different clusters. Can we hence say gmm is stochastic? We obtain the same clusters if a random seed is set; does this mean given a random seed, ...
psangam's user avatar
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5 votes
2 answers
1k views

What is the difference between Markov chain approximation and variational approximation?

I know they are two different approximation approaches to explicit models(which require approximation, that is transforming a non-optimization problem to an optimization problem to avoid the ...
Lerner Zhang's user avatar
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0 votes
1 answer
2k views

What are some examples of application of reinforcement learning to systems without stochastic dynamics?

We typically see examples of reinforcement learning problems modeled as a Markov Decision Processes wherein the state transition probabilities are specified. If the system of interest does not have ...
GSH's user avatar
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1 vote
0 answers
14 views

Evaluate the probability of my experiment being deteministic AKA what tis the chance of something which has never happened happening? [duplicate]

Short version Imagine I run the exact same experiment $n$ independent times and get $n$ times the same result. Can you put a lower bound on the probability of getting the same result the $n+1$ time I ...
Amxx's user avatar
  • 111
2 votes
0 answers
968 views

Stochastic or Deterministic Trend: Supported by the Augmented Dickey-Fuller Test

Below are the sequential steps/question regarding my problem: I am attempting to specify a VAR model in order to analyze impulse response functions. In plotting my first variable (Figure 1) I ...
Amaziah's user avatar
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1 vote
1 answer
181 views

Monte carlo simulation to forecast growth of a loan portfolio

I have to forecast the future gold loan portfolio growth of a financial firm. I have past 36 month growth data. I am planning to use Monte Carlo simulation to forecast, but growth is a deterministic ...
Peter's user avatar
  • 13
3 votes
3 answers
465 views

Deterministic classifier and input features

I call the function estimation based classifiers as deterministic, the ones which estimates the $f(x) = a'x+b$ directly, rather than estimating the conditional or joint probabilities directly. For ...
Shew's user avatar
  • 297
2 votes
0 answers
265 views

How to describe deterministic optimisation algorithms using statistics?

I am solving a large set of nonlinear optimisation problems using different algorithms. I have compared their performance using performance profiles (see Dolan and Moré, 2002). These profiles are ...
H. Vabri's user avatar
  • 143
14 votes
3 answers
21k views

What is the difference between deterministic and stochastic model?

Simple Linear Model: $x=\alpha t + \epsilon_t$ where $\epsilon_t$ ~iid $N(0,\sigma^2)$ with $E(x) = \alpha t$ and $Var(x)=\sigma^2$ AR(1): $X_t =\alpha X_{t-1} + \epsilon_t$ where $\epsilon_t$ ~...
Ken T's user avatar
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4 votes
0 answers
1k views

Specifying deterministic terms in VECM in case of logarithmic varriables

I have constructed a VEC model to study real housing price dynamics in relation to demographic demand, real GDP and costs of mortgages. However, I am stuck with the choice of deterministic terms. ...
MGL's user avatar
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9 votes
1 answer
55k views

Explain what is meant by a deterministic and stochastic trend in relation to the following time series process? [closed]

Explain what is meant by a deterministic and stochastic trend in relation to the following time series process? $y_t = c + y_{t-1} + \varepsilon_t$ where $\varepsilon_t\sim iid(0, \sigma^2)$ this ...
张倩莹's user avatar
8 votes
2 answers
5k views

Can a random variable be a deterministic function of other random variables yet be independent of them?

I was confused by what it means when a Random variable is a deterministic function of another Random variable yet is independent of it? How is this possible? Here's the question: Consider three ...
Christopher's user avatar
1 vote
1 answer
261 views

Simulator - a deterministic function of random variables

In this paper, the first discussion (Universal latent variable representation by C. Andrieu, A. Doucet and A. Lee) authors state that Sampling exactly $Y \sim f(y|\theta)$ on a computer most often ...
Paula's user avatar
  • 288
7 votes
2 answers
9k views

Are linear classifiers (SVM, Logistic Regression) deterministic?

I am just starting to learn about classification and have been playing around with some linear classifiers. I was wondering if linear classifiers are deterministic--given the same model parameters and ...
user3922963's user avatar
0 votes
0 answers
33 views

Existence of data when mean vector and covariance matrix (p.s.d.) is fixed? [duplicate]

I would like to prove that for any positive semidefinite matrix $\Sigma_{n\times n}$ and any vector $\mu_{n\times1}$, are there always data points (no matter how many, as long as finite) whose ...
user112758's user avatar
7 votes
1 answer
2k views

Deterministic sampling from discrete distribution

I'm working on a generalization of the Min-Hash algorithm to allow the meaningful comparison of ordered values such as integers. The core trick is to use deterministic randomness as a replacement for ...
Harald Thomson's user avatar
7 votes
2 answers
7k views

Variance and covariance in the context of deterministic variables

Questions: Can we talk about: variance of a deterministic variable?; covariance between a deterministic variable and a stochastic variable?; covariance between two deterministic variables? Are these ...
Richard Hardy's user avatar
5 votes
0 answers
4k views

What is the difference between a stochastic and a deterministic trend?

Models with stochastic trends i.e., structural time series models are useful in some instances. Firstly, it may be hard to identify multiple structural breaks in the deterministic trend when the ...
Le Max's user avatar
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