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Questions tagged [sequential-monte-carlo]

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0answers
40 views

Posterior as prior for correlated parameters [closed]

I want to use the posterior distribution of the model parameters $\theta$ given data in the time frame $[0,t]$ days, $P(\theta|y_{0:t})$; as a prior for the parameters in the time frame $[t+1, t+n]$ ...
2
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1answer
106 views

sequential Monte Carlo sampler, why the extended space and backward kernel?

Hello cross validated, I am currently studying sequential Monte Carlo samplers. My current understanding is as follows: We are interested in the marginal distribution of some sequence of joint ...
2
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1answer
49 views

Kernel for MCMC moves in sequential monte carlo

I'm trying to understand how to employ MCMC moves in a sequential Monte Carlo procedure for estimating static parameters as in the setting described by Chopin. He proposes, for example, the usage of a ...
2
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1answer
55 views

Why is it necessary to perform resampling step in particle filtering (or sequential monte carlo)?

I read the Wikipedia page on particle filter, it says that during 'prediction-updating', the samples from the distribution are weighted by a likelihood that represents the probability of that particle ...
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0answers
54 views

Sequential monte carlo : A simple example

I am attempting to understand how to implement the sequential monte carlo algorithm using this article. Here are the steps that the author proposes: Example problem: Say I have a self moving robot ...
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1answer
66 views

Particle filter - expectations

I've recently been implementing some particle filter algorithms and I've realized there is a small detail I might have been doing incorrectly. Unfortunately the descriptions of the algorithms in ...
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0answers
62 views

Sequential monte carlo, resampling

In particle filters when one is doing sequential importance sampling, the quantity of interest that is being approximated is usually a weighted sum: $$\hat x_t = \sum_{i=1}^M \Bigl [f(v^{(i)}_{t}) \...
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1answer
106 views

Are the Sequential Monte Carlo algorithm invariant to the step at which we resample?

In a usual textual description (according to SMC in Practice book ) of a SMC algorithm for State-Space models, we usually expand the particles according to the distribution from the transition ...
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2answers
42 views

Variance of a mixture of Normals with same $\sigma^2_i$

Let $Y\sim \sum^N_{i=1}\omega_iN(m_i,h^2 V)$. The text I'm reading states that $Var(Y)=(1+h^2)V$, when $m_i=\theta_i$, where $\theta_i$ are draws taken from $P(\theta|D)$, and $V=Var(\theta|D)$ I ...
2
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2answers
58 views

A doubt on the formula for updating the weights in Sequential Importance Sampling in a State-Space model

Let $x_{0:t}^{(i)}$ be the states from time $0$ to $t$ from sample $i$. Similarly for the observations $y_{1:t}$. The normalized weights are updated according to Where does the term $p(y_t|x_t^{(i)})...
2
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1answer
58 views

SIR explanation in Robert and Casella Intro to Monte Carlo Methods - How to do this derivation?

Why is it an exact simulation from $f$, and not only an approximation? I get $\begin{split} P(X^*\in A) & = \sum_i^n P(X^*\in A , X^* = X_i)=\sum_i^n P(X^*\in A | X^* = X_i)P(X^* = X_i) \\ & ...
3
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1answer
140 views

Importance weight of conditioned particle in conditional SMC

In a generic particle filter, I understand the importance weights for each particle are calculated as $w_t^s \propto w_{t-1}^s \frac{p(y_t \mid z_t^s) p(z_t^s \mid z_{t-1}^s)}{q(z_t^s \mid z_{t-1}^s, ...
3
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2answers
527 views

Understanding Sequential Importance Sampling and Particle Filtering

I am struggling with SIS for particle filtering in the following aspect: In particle filtering (as per this book), the objective is to estimate the full posterior $p( x_{0:k} \mid y_{1:k} )$ rather ...
3
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0answers
51 views

Soft Question: What background do I need to understand Feynmann Kac Formulae by Pierre Del Moral?

I am attempting to understand Sequential Monte Carlo(SMC) deeply, but with little theoretical background on probability theory and stochastic processes. Usually, the 'statistics' perspective of markov ...
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2answers
351 views

How do I calculate the weights in ABC-SMC

I have been reading through the Tutorial on ABC rejection and ABC SMC for parameter estimation and model selection by Tina Toni and Michael P. H. Stumpf. I can't work out how to calculate the weights ...