Laplace's Method

Kass, R. E.

doi:10.1002/0471667196.ess0315.pub2

Cited by 4 publications

(3 citation statements)

References 56 publications

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“…tions, effectively employing Laplace's method (e.g., Kass 1997), which in many situations furnishes highly accurate approximations with a substantially smaller computational cost than simulation-based methods such as the particle filter. Our own preliminary work suggests that in the context of motor cortical signal decoding, with substantial numbers of neurons and smoothly varying movements, Gaussian approximations can be nearly as accurate as particle filtering.…”

Section: Discussionmentioning

confidence: 99%

Recursive Bayesian Decoding of Motor Cortical Signals by Particle Filtering

Brockwell

Rojas

Kass

2004

Journal of Neurophysiology

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The population vector (PV) algorithm and optimal linear estimation (OLE) have been used to reconstruct movement by combining signals from multiple neurons in the motor cortex. While these linear methods are effective, recursive Bayesian decoding schemes, which are nonlinear, can be more powerful when probability model assumptions are satisfied. We have implemented a recursive Bayesian algorithm for reconstructing hand movement from neurons in the motor cortex. The algorithm uses a recently developed numerical method known as "particle filtering" and follows the same general strategy as that used by Brown et al. to reconstruct the path of a foraging rat from hippocampal place cells. We investigated the method in a numerical simulation study in which neural firing rate was assumed to be positive, but otherwise a linear function of movement velocity, and preferred directions were not uniformly distributed. In terms of mean-squared error, the approach was approximately 10 times more efficient than the PV algorithm and 5 times more efficient than OLE. Thus use of recursive Bayesian decoding can achieve the accuracy of the PV algorithm (or OLE) with approximately 10 times (or 5 times) fewer neurons. The method was also used to reconstruct hand movement in an ellipse-drawing task from 258 cells in the ventral premotor cortex. Recursive Bayesian decoding was again more efficient than the PV and OLE methods, by factors of roughly seven and three, respectively.

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Section: Discussionmentioning

confidence: 99%

Recursive Bayesian Decoding of Motor Cortical Signals by Particle Filtering

Brockwell

Rojas

Kass

2004

Journal of Neurophysiology

Self Cite

232

173

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“…Now c 0 in can be approximated very well under some conditions by Laplace approximation (see, e.g. Kass, 1997). Substituting x =e y , we rewrite c 0 as …”

Section: Probability Functions and Approximationsmentioning

confidence: 99%

Pareto Sampling versus Sampford and Conditional Poisson Sampling

Bondesson

Traat

Lundqvist

2006

Scandinavian J Statistics

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Pareto sampling was introduced by Rosén in the late 1990s. It is a simple method to get a fixed size "π" ps sample though with inclusion probabilities only approximately as desired. Sampford sampling, introduced by Sampford in 1967, gives the desired inclusion probabilities but it may take time to generate a sample. Using probability functions and Laplace approximations, we show that from a probabilistic point of view these two designs are very close to each other and asymptotically identical. A Sampford sample can rapidly be generated in all situations by letting a Pareto sample pass an acceptance-rejection filter. A new very efficient method to generate conditional Poisson ( CP ) samples appears as a byproduct. Further, it is shown how the inclusion probabilities of all orders for the Pareto design can be calculated from those of the CP design. A new explicit very accurate approximation of the second-order inclusion probabilities, valid for several designs, is presented and applied to get single sum type variance estimates of the Horvitz-Thompson estimator. Copyright 2006 Board of the Foundation of the Scandinavian Journal of Statistics..

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“…Esta esperan¡_;a da distribui¡_;ao a posteriori da fun¡_;ao k -1 (v) em (4 .15) pode ser avaliada usando, por exemplo, o método Laplace (veja Kass, 1997). Contudo, para muitas distribui¡_;oes na classe das misturas de escala normal é possível obter expressoes em forma fechada para (4.15).…”

Section: Esperan<;as Condicionais Para O Algoritmo Emunclassified

Modelos mistos com erros nas variáveis

Alamos¹

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Gostaria de agradecer, em primeiro lugar, a Deus, por me dar saúde e for¡_;as durante toda a trajétoria de meus estudos de doutorado e o desenvolvimento desta tese.A minha esposa Carolina, pelo carinho, estímulo, paciencia, e compreensao e a meu filho Carlos (a mziio da minha vida) pelos momentos de alegría e for<_;a. Ao professor Dr. Heleno Bolfarine pela oportuniclade de ser seu orientando. Agrade¡_;o, a confi-an<_;a, o incentivo, o apoio e a amizade durante todo o meu doutorado, em especial, na elabora¡_;ao cleste trabalho. Na verdacle, me sinto honrado de ter sido orientado pelo professor Heleno. Agrade¡_;o também, pelo espírito esportivo refl.etidos em nossas longas partidas de tenis. Ao meu coorientador professor Dr. Manuel Galea pela confian¡_;a, pelas idéias e sugestoes que tanto contribuíram para o clesenvolvimento deste trabalho. Agrade¡_;o , também , por todo apoio e amizade.A professora Dra. Betsabé Blas, pelo aporte e apoio computacional na obten¡_;ao dos resultados dos Capítulos 4 e 5.A minha família no Chile que sempre me incentivou, em especial, a minha mae Rebeca, tía Nena e irmaos: Juan, Rebeca e Eduardo. Também gostaria de expressar minha profunda gratidiio para a família Sagredo-Martínez (Martín, Patricia, María Carolina e Martín Jr.) pela paciencia, compreensiio, apoio e estímulo destinados nos momentos mais difíceis.A Víctor Leiva, pela verdadeira amizade ao longo dos anos. Sou grato de ter sempre seu apoio e estímulo no profissional e humano.Aos meus queridos amigos Chilenos que moram no Brasil: Enzo García e Carlos Matus, por terem sido mais que amigos, por terem sido parte de minha família em Sao Paulo.A meu querido amigo Gustavo Pereira e sua familia , por sua grande amizacle e companheirismo.A todos os amigos e colegas (antigos e novos) , do IME-USP, em especial, Germán Ibacache e família

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Laplace's Method

Cited by 4 publications

References 56 publications

Recursive Bayesian Decoding of Motor Cortical Signals by Particle Filtering

Recursive Bayesian Decoding of Motor Cortical Signals by Particle Filtering

Pareto Sampling versus Sampford and Conditional Poisson Sampling

Modelos mistos com erros nas variáveis

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