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# Questions tagged [sequential-monte-carlo]

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### Why do we want to minimise the variance of our importance weights in SIS with respect to the proposal distribution

Is there a clear and precise explanation of why minimising the variance of the weights in SIS with respect to a proposal ensures that the samples generated from the empirical distribution induced by ...
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### Do Sequential Monte Carlo simulations degenerate when you chain them together?

Context: Suppose that I run a Sequential Monte Carlo simulation with likelihood tempering to perform parameter inference on a filtering problem. This takes me from my (unspecified) prior distribution ...
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### Bayesian evidence with Sequential Monte Carlo and an unnormalized likelihood function: a contradiction?

There is a contradiction in my understanding of Sequential Monte Carlo for estimating Bayesian evidence for model comparison: Marginal likelihood (aka normalizing constant, aka Bayesian evidence) ...
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### Example for Resampling in Sequential Monte Carlo

I am currently looking into SMC methods and especially resampling in this context. I know and understand the weight-degeneracy problem when leaving out the resampling step. However, I am wondering if ...
1 vote
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### Difference in Normalizing constants for Annealed Importance Sampling and Sequential Monte Carlo

I have been looking into Annealed Importance Sampling (AIS, Neal, 2001) and Sequential Monte Carlo (SMC, Del Moral et al., 2006) methods lately. I was wondering where the difference in estimating the ...
1 vote
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### Help understanding the proof that Monte Carlo methods that the expectation of $R$ samples is the expectation of the function

The above proof I got from UofT's CS412 lecture slides. So I have a few questions regarding this notation that I don't understand is $x \sim p(\{x^{(r)}\}^R_{r=1})$ supposed to represent $R$ number ...
59 views

### Monte Carlo probability approximation vs Histogram

I am trying to learn the sequential Monte Carlo method (particle filter) in data assimilation. In this method, the aim is to approximate the CDF of the target variable having a random sample of the ...
1 vote
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### Calculating the weights in ABC SMC (2 parameters and more)

Im trying to implement ABC SMC for ODE model which has 2 parameters to estimate. I stopped in the step when calculating the weights as it appear in this answer. My question is should I calculate the ...
54 views

### Particle Filter for structural credit risk model

Kwon (2012)* proposes a structural credit risk model where the asset value process and the noise are estimated based on the observed equity prices: $S$ - equity prices $V$ - value of the assets $Z$ - ...
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### 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 ...
69 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 ...