The human brain effortlessly solves problems that still pose a challenge for modern computers, such as recognizing patterns in natural images. Many of these problems can be formulated in terms of Bayesian inference, including planning motor movements, combining cues from different modalities, and making predictions. Recent work in psychology and neuroscience suggests that human behavior is often consistent with Bayesian inference. However, most research using probabilistic models has focused on formulating the abstract problems behind cognitive tasks and their optimal solutions, rather than considering mechanisms that could implement these solutions. Therefore, it is critical to understand the psychological models and neural implementations that carry out these notoriously challenging computations.

Exemplar models are a successful class of psychological process models that use an inventory of stored examples to solve problems such as identification, categorization, and function learning. We show that exemplar models can be used to perform a sophisticated form of Monte Carlo approximation known as importance sampling, and thus provide a way to perform approximate Bayesian inference. Simulations of Bayesian inference in speech perception, generalization along a single dimension, making predictions about everyday events, concept learning, and reconstruction from memory show that exemplar models can often account for human performance with only a few exemplars, for both simple and relatively complex prior distributions. These results suggest that exemplar models provide a possible mechanism for implementing at least some forms of Bayesian inference.

The goal of perception is to infer the hidden states in the hierarchical process by which sensory data are generated, a problem that can be solved optimally using Bayesian inference. Here we propose a simple mechanism for Bayesian inference which involves averaging over a few feature detection neurons which fire at a rate determined by their similarity to a sensory stimulus. This mechanism is again based on importance sampling. Moreover, many cognitive and perceptual tasks involve multiple levels of abstraction, which results in ``hierarchical'' models. We show that a simple extension to recursive importance sampling can be used to perform hierarchical Bayesian inference. We identify a scheme for implementing importance sampling with spiking neurons, and show that this scheme can account for human behavior in sensorimotor integration, cue combination, and orientation perception.

Another important function of nervous system is to process temporal information in the dynamical environment, such as motion coordination where the system's state is estimated sequentially based on the constant perceptual feedback. Our study suggests that a neural network structure similar to recursive importance sampling can solve the sequential estimation problem by approximating the posterior updates. This algorithm performs as well as the state-of-the-art sequential Monte Carlo methods know as particle filtering and fulfills many constraints of the biological system. Studying the detailed neural implementation of this algorithm finds an interesting resemblance to neural circuits in cerebellum.

In this study, two separate experiments were conducted with an F10 Brassica napus recombinant inbred (RI) population containing 124 lines derived from a cross between P-efficient cv. 97081 and P-inefficient cv. 97009 by a single seed descent method. One was two-year field trials under the conditions of high P and low P with three replicates, which was used to investigate seed yield and analyze minerals (P, Ca, Mg, Fe, Zn, Mn, and Cu) concentration in seeds with ICP-AES. Another was two paper culture experiments with high P and low P treatments and three replicates, which were used to investigate root morphology, including total root length, root surface area, root volume and root average diameter with WinRhizo analysis system. Based on the construction of genetic linkage map, WinQTLCart software was employed to identify the quantitative trait loci (QTL) for seed minerals concentration and root morphology by whole genome QTL analysis. Totally, 49 QTL for mineral nutrients in seeds and 61 QTL for root morphology were detected, which explained the phenotypic variance from 8.59% to 36.48%. Most of these QTL corresponded specifically to one of the two P conditions, and intervals of some QTL for different traits overlap each other. These results revealed that genetic factors control seed mineral concentration in plants and multigenes involving ion transport are required to regulate mineral balance in plants under conditions of diverse nutrient stress.

Experience-dependent plasticity in adult visual cortex is believed to have important roles in visual coding and perceptual learning. Here we show that repeated stimulation with movies of natural scenes induces a rapid improvement in response reliability in cat visual cortex, whereas stimulation with white noise or flashed bar stimuli does not. The improved reliability can be accounted for by a selective increase in spiking evoked by preferred stimuli, and the magnitude of improvement depends on the sparseness of the response. The increase in reliability persists for at least several minutes in the absence of further movie stimulation. During this period, spontaneous spiking activity shows detectable reverberation of the movie-evoked responses. Thus, repeated exposure to natural stimuli not only induces a rapid improvement in cortical response reliability, but also leaves a 'memory trace' in subsequent spontaneous activity.