The interest for large underground particle detector is increasing. Phenomena as proton decay and long base line neutrino oscillation are subject for many research projects over the world. Large detectors present also some problems regarding the large number of signals from independent photo multiplier tubes (PMTs). A realistic statistical model for numerical simulation of signal processing and sampling has been developed for the case of a large number of independent particle detectors (LNIPDs). Based on this analytical model of Poisson type, the structure of an automatic decision system based on the decision criterion of maximum a posteriori probability (MAP) or the maximum likelihood (ML) criterion is proposed. The purpose of the system is to analyze the exit from the measurement process and to decode the message transmitted, taking into account the presence of the noise which generates errors in the decoder. The system can be used later for detailed simulation of different types of huge underground particle detectors (like LAGUNA-LBNO experiment), where the large number of signals could become a real problem.

We know that the abstract models are often used for the resolution of various problems. Starting from a detector response function that presents the relationship between the input factors and the output ones, we investigate a relaistic statistical model for numerical simulation of signal processing and sampling for the case of a large number of independent particle detectors (LNIPDs) and Poisson statistics of the detection process [

This paper proposes to use the mathematical model of Poisson detection based on the response function that correlates the random variables in a studied case of a large number of independent particle detectors (LNIPDs) providing a known type function of these complex processes. We define a response function and show that the measurement to detect

In the paper, in order to process the data obtained from the study of the detection process in the LNIPD case, we proposed to use known decision criteria from the theory of information transmission. The method of automatic implementation of this decision process, which was described in this paper, based on the real-time information collected from LNIPD, is a major step forward in the implementation of the strategy proposed for the large underground particle detector implementation.

There are interconnections for which the optimal data analyses can be made automatically, in real time and in different conditions and situations. In the situations characterized by two random variables as in the case of LNIPD, the suitable statistical distribution is of the Poisson conditional type.

For an optimal and efficient settlement of the measurement equipments with minimum costs, automatic machines need to be built, which secure a real-time analysis and assure us of suitable correct decisions, being followed by adequate automatic data after detection processing [

Study of detection statistics represents an essential operation in the realization of an automatic decision system for large number of independent particle detectors (LNIPDs).

Each electron makes a contribution to the output current which is converted into voltage by passing through the load resistance. Conversion process is a stochastic process in nature. From mathematical point of view, the output current is a superposition of the effects produced by each electron emitted. A single electron produces a current response function

A measurement done at the moment

random localizations of the measuring moments,

random values of the measured quantity,

Because

Therefore, we aim to find under what form the properties of the detected field are contained in the response signal and to highlight them.

The model is represented by the probability that the detection process leads to

According to

This problem consists of calculating the probability that all the LNIPD detectors emit

We must calculate composed probability in order to obtain

It results [

Therefore, (

According to (

The quantity

The integral of

Alternately,

It results that variable

The probability (

It results that

For the two types of emission, processes studied of Poisson type and Poisson conditioned type output level of the signal statistics are closely related as has been shown with intensity statistics.

Thus, formula (

Also, the formulas (

In order to process the data obtained from the LNIPD, the proposal of the paper is to use the known decision criteria from the theory of information. The method of automatic implementation of the decision process, which will be described later, based on the real-time information collected from the LNIPD, is a major step forward in the implementation of the automatic decision system in the case of a large number of independent particle detectors.

The decisions are based on the detection statistics of photoelectrons, In the binary systems, we define the messages associated to binary symbols “one” or “zero” as bytes. Byte 1 is associated to the presence of the particle and byte 0 to the noise, in the absence of it.

According to this criterion,

detectors measure the the incident field on the interval of a byte;

on the basis of detection statistics, we calculate the probability

it decides on the byte

According to this criterion,

we define the plausibility function

which means the probability of detecting vector

we calculate the functions

we decide on byte

In the considered case of binary decisions [

The role of MAP decoder (or ML) is to analyze the information resulted from LNIPD and to offer us correct data on the measuring process. The presence of different noise types determines errors in the decoder’s decision.

We consider the distribution

Equation (

From (

The expression of logarithmic plausibility function is [

The expression (

Consequently, we must evaluate only the quantity [

The block scheme of the processing and decision system is presented in Figure

The block scheme of the processing and decision system.

The signals

In the structure, it has a pair of weighted summations circuits of detected signals according to expression (

Summations are discrete correlations of

The discrete version of the decoder is very appropriate for the operational analysis of this type of decoder. In the integrated version of decoder [

Integrated version of Poisson decoder.

The detector response function is used for obtaining the probability as that in the measuring process to determine

We have analysed the structure of an automatic decision system for the Poisson detection, based on the decision criteria (MAP or PM), known from information theory, in the discrete and integrated versions. For the modules of the block scheme, the electronic computation blocks were defined to be compatible with the blocks currently used in the data coding and decoding circuits; therefore, the practical implementation of such systems does not raise any problems. The methods of statistical physics we have discussed are inseparably part in the strategy for observations and measurements on the nuclear particles, as neutrinos. These observations provide us very important data about other low-mass particles which determine large-scale experiments in which these new types of particle detectors will be implemented. Concomitantly, we observe that a lot of work remains to be done to assure the accuracy of the experiments to be developed and built.