Bayesian analysis of a correlated binomial model

Diniz, Carlos Alberto Ribeiro; Tutia, Marcelo Hiroshi; Leite, José Galvâo

doi:10.1214/08-bjps014

Cited by 28 publications

(26 citation statements)

References 16 publications

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“…Although for some very restricted synaptic wiring models it would be possible to find a closed-form expression for the distribution P ( N syn ) (e.g. Diniz et al, 2010), we chose to solve for it numerically because doing so allows for arbitrary arrangements of pairwise dendritic correlations between all of the presynaptic neurons. After evaluating P ( N syn ), we calculated the distribution for the fraction of synapses f ( i ) that have a given number i synapses on their dendrite from

f (i) = \frac{P (i) \times i \times d}{N_{italicpre}}

which is the product of the probability of getting i synapses on a dendrite, and that number of synapses i , and the number of dendrites d , all divided by the total number of synapses N pre .…”

Section: Methodsmentioning

confidence: 99%

Selective Memory Generalization by Spatial Patterning of Protein Synthesis

O’Donnell

Sejnowski

2014

Neuron

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Summary Protein synthesis is crucial for both persistent synaptic plasticity and long-term memory. De novo protein expression can be restricted to specific neurons within a population, and to specific dendrites within a single neuron. Despite its ubiquity, the functional benefits of spatial protein regulation for learning are unknown. We used computational modeling to study this problem. We found that spatially patterned protein synthesis can enable selective consolidation of some memories but forgetting of others, even for simultaneous events that are represented by the same neural population. Key factors regulating selectivity include the functional clustering of synapses on dendrites, and the sparsity and overlap of neural activity patterns at the circuit level. Based on these findings we proposed a novel two-step model for selective memory generalization during REM and slow-wave sleep. The pattern-matching framework we propose may be broadly applicable to spatial protein signaling throughout cortex and hippocampus.

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f (i) = \frac{P (i) \times i \times d}{N_{italicpre}}

which is the product of the probability of getting i synapses on a dendrite, and that number of synapses i , and the number of dendrites d , all divided by the total number of synapses N pre .…”

Section: Methodsmentioning

confidence: 99%

Selective Memory Generalization by Spatial Patterning of Protein Synthesis

O’Donnell

Sejnowski

2014

Neuron

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“…In the CBM the neurons are assumed directly correlated. It was studied in [18,19], and 288 is denoted by CBin(n, p, ρ), where n is the number of correlated Bernoulli trials 289 (simultaneously recorded neurons in our model setting), 0 < p < 1 is the probability 290 P (X i t = 1), and ρ is the correlation coefficient. In this model the number of neurons z 291 attending stimulus 1 follows a mixture of two distributions.…”

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confidence: 99%

Distinguishing between parallel and serial processing in visual attention from neurobiological data

Kadohisa

Kusunoki

et al. 2018

Preprint

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Serial and parallel processing in visual search have been long debated in psychology but the processing mechanism remains an open issue. Serial processing allows only one object at a time to be processed, whereas parallel processing assumes that various objects are processed simultaneously. Here we present novel neural models for the two types of processing mechanisms based on analysis of simultaneously recorded spike trains using electrophysiological data from prefrontal cortex of rhesus monkeys while processing task-relevant visual displays. We combine mathematical models describing neuronal attention and point process models for spike trains. The same model can explain both serial and parallel processing by adopting different parameter regimes. We present statistical methods to distinguish between serial and parallel processing based on both maximum likelihood estimates and decoding the momentary focus of attention when two stimuli are presented simultaneously. Results show that both processing mechanisms are in play for the simultaneously recorded neurons, but neurons tend to follow parallel processing in the beginning after the onset of the stimulus pair, whereas they tend to serial processing later on. This could be explained by parallel processing being related to sensory bottom-up signals or feedforward processing, which typically occur in the beginning after stimulus onset, whereas top-down signals related to cognitive modulatory influences guiding attentional effects in recurrent feedback connections occur after a small delay, and is related to serial processing, where all processing capacities are being directed towards the attended object.1 Introduction 1 A fundamental question in theories of visual search is whether the process is serial or 2 parallel for given types of stimulus material (for comprehensive reviews, see [1][2][3]). In 3 serial search, only one stimulus is attended at a time, whereas in parallel search, several 4 stimuli are attended at the same time. The question of serial versus parallel search has 5 been extensively investigated by behavioral methods in cognitive psychology, but it is 6 still highly controversial. In this article, we briefly review extant empirical methods and 7 their results and then present and exemplify a new method for distinguishing between 8 42 on error rates. The linear relations between mean response time and N predicted by 43 simple serial models are difficult to explain by parallel models with independent 44 channels. However, the linear relations can be explained by parallel models with limited 45 processing capacity [12,13]. 46A multi-feature whole-report paradigm for investigating serial versus parallel 47 July 20, 2018 2/31 be cases in which just one feature from each of the two stimuli completes processing 51 before the interruption. This event, in which the observer has only partially encoded 52 each of the two stimuli, should never happen when processing is serial. Thus, states 53 with partial information from more than one stimulus are strong indic...

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“…However, when data have a cluster structure, the distribution of the sign statistic cannot be represented by a binomial distribution due to dependence among within-cluster observations. In this case, probability distribution of a sum of Bernoulli random variables can be constructed through correlated binomial distribution (Tallis 1962;Luceno 1995;Luceno and Ceballos 1995;Diniz et al 2010;Carlos et al 2010). Under the assumptions of exchangeability and equicorrelation among within-cluster observations, we derived the exact null distribution of the test statistic using correlated binomial distribution.…”

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confidence: 99%

Quantile inference based on clustered data

Öztürk

Türkmen

2016

Metrika

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One-sample sign test is one of the common procedures to develop distribution-free inference for a quantile of a population. A basic requirement of this test is that the observations in a sample must be independent. This assumption is violated in certain settings, such as clustered data, grouped data and longitudinal studies. Failure to account for dependence structure leads to erroneous statistical inferences. In this study, we have developed statistical inference for a population quantile of order p in either balanced or unbalanced designs by incorporating dependence structure when the distribution of within-cluster observations is exchangeable. We provide a point estimate, develop a testing procedure and construct confidence intervals for a population quantile of order p. Simulation studies are performed to demonstrate that the confidence intervals achieve their nominal coverage probabilities. We finally apply the proposed procedure to Academic Performance Index data.

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Bayesian analysis of a correlated binomial model

Cited by 28 publications

References 16 publications

Selective Memory Generalization by Spatial Patterning of Protein Synthesis

Selective Memory Generalization by Spatial Patterning of Protein Synthesis

Distinguishing between parallel and serial processing in visual attention from neurobiological data

Quantile inference based on clustered data

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